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A learned router chooses how many passes each token receives.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Amirkeivan Mohtashami","Matteo Pagliardini","Martin Jaggi"],"record_url":"https://latent-implicit-thinking.github.io/papers/2310.10845/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2310-10845","citation_date":"2023-10-16","json_url":"https://latent-implicit-thinking.github.io/papers/2310.10845/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2310.10845/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2310.10845/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2310.10845/citation.csl.json"},{"id":"2310.14491","title":"Towards a Mechanistic Interpretation of Multi-Step Reasoning Capabilities of Language Models","authors":"Yifan Hou, Jiaoda Li, Yu Fei, Alessandro Stolfo, Wangchunshu Zhou, Guangtao Zeng, Antoine Bosselut, Mrinmaya Sachan","first_public":"2023-10-23","venue":"arXiv","arxiv":"2310.14491","paper_url":"https://arxiv.org/abs/2310.14491","lens":["analysis"],"representation":["hidden-state"],"computation":["depth-wise"],"training":["analysis-only"],"questions":["interpretability","evaluation"],"evidence":["empirical","mechanistic","probing"],"modality":["language"],"summary":"Uses mechanistic analysis to identify internal components involved in multi-step reasoning and test their causal roles.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Yifan Hou","Jiaoda Li","Yu Fei","Alessandro Stolfo","Wangchunshu Zhou","Guangtao Zeng","Antoine Bosselut","Mrinmaya Sachan"],"record_url":"https://latent-implicit-thinking.github.io/papers/2310.14491/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2310-14491","citation_date":"2023-10-23","json_url":"https://latent-implicit-thinking.github.io/papers/2310.14491/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2310.14491/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2310.14491/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2310.14491/citation.csl.json"},{"id":"2311.01460","title":"Implicit Chain of Thought Reasoning via Knowledge Distillation","related_terms":["implicit CoT","latent reasoning","latent chain-of-thought","latent CoT"],"authors":"Yuntian Deng, Kiran Prasad, Roland Fernandez, Paul Smolensky, Vishrav Chaudhary, Stuart Shieber","first_public":"2023-11-02","venue":"arXiv","arxiv":"2311.01460","paper_url":"https://arxiv.org/abs/2311.01460","code_url":"https://github.com/da03/implicit_chain_of_thought/","lens":["internalized"],"representation":["hidden-state"],"computation":["depth-wise"],"training":["distillation"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"First proposes implicit chain-of-thought reasoning: language models carry out intermediate reasoning in continuous hidden states rather than generate it as text. Defines this setting separately from its implementation, which distills an explicit-CoT teacher's hidden states into an emulator and a student that produces the answer.","provenance":"Awesome-Latent-CoT","author_names":["Yuntian Deng","Kiran Prasad","Roland Fernandez","Paul Smolensky","Vishrav Chaudhary","Stuart Shieber"],"record_url":"https://latent-implicit-thinking.github.io/papers/2311.01460/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2311-01460","citation_date":"2023-11-02","json_url":"https://latent-implicit-thinking.github.io/papers/2311.01460/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2311.01460/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2311.01460/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2311.01460/citation.csl.json","demos":[{"id":"multiplication","title":"Multiplication without written steps","label":"Multiplication","description":"Compare GPT-2 models using implicit CoT, explicit CoT, or no CoT on two numbers of up to 20 digits each.","limitations":"The models can make mistakes, including on valid inputs. The implicit model writes answer digits, not intermediate steps.","model":"GPT-2","url":"https://huggingface.co/spaces/yuntian-deng/gpt2-multiplication","model_url":"https://huggingface.co/yuntian-deng/gpt2-implicit-cot-multiplication-20-digits","topic_ids":["internalized"],"paper_relationships":[{"paper_id":"2405.14838","relationship":"implementation"},{"paper_id":"2311.01460","relationship":"related_method"}],"relationship":"related_method"},{"id":"math-word-problems","title":"Math word problems without written steps","label":"Math word problems","description":"Try a Mistral-7B model trained with stepwise internalization on grade-school math word problems.","limitations":"Answers can be wrong. This model is trained for grade-school math word problems, not general conversation. 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Their reported experiments focus on multiplication and grade-school math, not a guarantee of general reasoning ability.","source_ids":["2311.01460","2405.14838"],"source_urls":["https://arxiv.org/html/2311.01460v1#S2.SS3","https://arxiv.org/html/2311.01460v1#S3","https://arxiv.org/html/2405.14838v1#S3"],"source_labels":["Implicit CoT proposal, §2.3","Distillation implementation, §3","Stepwise internalization, §3"],"topic_id":"internalized","topic_label":"Internalized reasoning","topic_url":"https://latent-implicit-thinking.github.io/topics/internalized-reasoning/"},{"title":"Hidden-state distillation: the 2023 method and CODI","text":"The 2023 implicit CoT paper proposes reasoning through hidden states and implements it with a teacher, a thought emulator and an answer-generating student. CODI also transfers explicit reasoning through hidden-state supervision, but uses one model for both teacher and student tasks. It aligns their states just before the answer, while the student takes successive continuous reasoning steps.","source_ids":["2311.01460","2502.21074"],"source_urls":["https://arxiv.org/html/2311.01460v1#S2.SS3","https://arxiv.org/html/2311.01460v1#S3","https://arxiv.org/html/2502.21074v3#S3"],"source_labels":["Deng et al. (2023), §2.3","Deng et al. (2023), §3","CODI, §3"],"topic_id":"internalized","topic_label":"Internalized reasoning","topic_url":"https://latent-implicit-thinking.github.io/topics/internalized-reasoning/"},{"title":"Implicit CoT: proposal and implementation","text":"Deng et al. (2023) proposed implicit chain-of-thought reasoning: language models carry out intermediate reasoning in continuous hidden states rather than generate it as text. Section 2.3 defines this setting; section 3 develops a distillation method to implement it. That method transfers a teacher's reasoning into hidden states across layers. Reasoning through continuous hidden states is the broader proposal; it does not require the particular distillation procedure used in this paper. Its across-layer computation differs from the repeated hidden-state feedback used by later methods such as Coconut.","source_ids":["2311.01460","2412.06769"],"source_urls":["https://arxiv.org/html/2311.01460v1#S2.SS3","https://arxiv.org/html/2311.01460v1#S3","https://arxiv.org/html/2412.06769v3#S3"],"source_labels":["Implicit CoT proposal, §2.3","Distillation implementation, §3","Coconut, §3"],"topic_id":"continuous","topic_label":"Continuous-state reasoning","topic_url":"https://latent-implicit-thinking.github.io/topics/continuous-states/"}]},{"id":"2402.07754","title":"Diffusion of Thoughts: Chain-of-Thought Reasoning in Diffusion Language Models","authors":"Jiacheng Ye, Shansan Gong, Liheng Chen, Lin Zheng, Jiahui Gao, Han Shi, Chuan Wu, Xin Jiang, Zhenguo Li, Wei Bi, Lingpeng Kong","first_public":"2024-02-12","venue":"NeurIPS 2024","arxiv":"2402.07754","paper_url":"https://arxiv.org/abs/2402.07754","lens":["beyond-sequential"],"representation":["text-latent-hybrid"],"computation":["diffusion","parallel"],"training":["supervised"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["language"],"summary":"Refines intermediate reasoning representations over several rounds of denoising. 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The multi-hop study by Yang and colleagues separates recall of a bridge entity from its contribution to the final answer, including interventions on internal representations. Evidence was stronger for the first hop than for the complete two-hop computation and varied by relation type. That distinction matters when interpreting claims that a model reasons internally.","source_ids":["2402.16837"],"source_urls":["https://aclanthology.org/2024.acl-long.550/"],"source_labels":["Yang et al. (2024)"],"topic_id":"analysis","topic_label":"Analysis and evaluation","topic_url":"https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/"}]},{"id":"2403.09629","title":"Quiet-STaR: Language Models Can Teach Themselves to Think Before Speaking","authors":"Eric Zelikman, Georges Harik, Yijia Shao, Varuna Jayasiri, Nick Haber, Noah D. 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Bowman"],"record_url":"https://latent-implicit-thinking.github.io/papers/2404.15758/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2404-15758","citation_date":"2024-04-24","json_url":"https://latent-implicit-thinking.github.io/papers/2404.15758/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2404.15758/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2404.15758/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2404.15758/citation.csl.json"},{"id":"2405.14838","title":"From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step","related_terms":["implicit CoT","latent reasoning","latent chain-of-thought","latent CoT"],"authors":"Yuntian Deng, Yejin Choi, Stuart Shieber","first_public":"2024-05-23","venue":"arXiv","arxiv":"2405.14838","paper_url":"https://arxiv.org/abs/2405.14838","code_url":"https://github.com/da03/Internalize_CoT_Step_by_Step","lens":["internalized"],"representation":["hidden-state"],"computation":["depth-wise"],"training":["curriculum","supervised"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Uses a curriculum that progressively removes intermediate reasoning steps during fine-tuning, teaching a model to internalize an explicit chain of thought.","provenance":"Awesome-Latent-CoT","author_names":["Yuntian Deng","Yejin Choi","Stuart Shieber"],"record_url":"https://latent-implicit-thinking.github.io/papers/2405.14838/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2405-14838","citation_date":"2024-05-23","json_url":"https://latent-implicit-thinking.github.io/papers/2405.14838/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2405.14838/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2405.14838/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2405.14838/citation.csl.json","demos":[{"id":"multiplication","title":"Multiplication without written steps","label":"Multiplication","description":"Compare GPT-2 models using implicit CoT, explicit CoT, or no CoT on two numbers of up to 20 digits each.","limitations":"The models can make mistakes, including on valid inputs. The implicit model writes answer digits, not intermediate steps.","model":"GPT-2","url":"https://huggingface.co/spaces/yuntian-deng/gpt2-multiplication","model_url":"https://huggingface.co/yuntian-deng/gpt2-implicit-cot-multiplication-20-digits","topic_ids":["internalized"],"paper_relationships":[{"paper_id":"2405.14838","relationship":"implementation"},{"paper_id":"2311.01460","relationship":"related_method"}],"relationship":"implementation"},{"id":"math-word-problems","title":"Math word problems without written steps","label":"Math word problems","description":"Try a Mistral-7B model trained with stepwise internalization on grade-school math word problems.","limitations":"Answers can be wrong. This model is trained for grade-school math word problems, not general conversation. It still generates the answer token by token.","model":"Mistral-7B","url":"https://huggingface.co/spaces/yuntian-deng/implicit-cot-math","model_url":"https://huggingface.co/yuntian-deng/implicit-cot-math-mistral7b","topic_ids":["internalized"],"paper_relationships":[{"paper_id":"2405.14838","relationship":"implementation"},{"paper_id":"2311.01460","relationship":"related_method"}],"relationship":"implementation"}],"method_comparisons":[{"title":"Distillation and stepwise internalization","text":"Deng et al. (2023) introduced implicit CoT as reasoning through hidden states rather than written steps; distillation is the paper's implementation of that proposal. It learns to predict a teacher's intermediate hidden states, which help a student produce the answer. Stepwise Internalization instead repeatedly shortens the written solution and fine-tunes the same model on what remains. Both use worked solutions during training; neither requires writing the removed steps at inference. Their reported experiments focus on multiplication and grade-school math, not a guarantee of general reasoning ability.","source_ids":["2311.01460","2405.14838"],"source_urls":["https://arxiv.org/html/2311.01460v1#S2.SS3","https://arxiv.org/html/2311.01460v1#S3","https://arxiv.org/html/2405.14838v1#S3"],"source_labels":["Implicit CoT proposal, §2.3","Distillation implementation, §3","Stepwise internalization, §3"],"topic_id":"internalized","topic_label":"Internalized reasoning","topic_url":"https://latent-implicit-thinking.github.io/topics/internalized-reasoning/"},{"title":"From stepwise internalization to Coconut","text":"Coconut explicitly credits Deng et al. (2024) as the inspiration for its multistage training curriculum. Stepwise internalization gradually removes written CoT tokens until the model answers directly. Coconut instead replaces removed steps with continuous hidden-state inputs, retaining a sequence of internal reasoning steps before the answer. It also follows the earlier work in resetting the optimizer between training stages.","source_ids":["2405.14838","2412.06769"],"source_urls":["https://arxiv.org/html/2405.14838v1#S3","https://arxiv.org/html/2412.06769v3#S3"],"source_labels":["Deng et al. (2024), §3","Coconut, §3"],"topic_id":"continuous","topic_label":"Continuous-state reasoning","topic_url":"https://latent-implicit-thinking.github.io/topics/continuous-states/"},{"title":"Changing generation order or removing written steps","text":"Diffusion of Thought changes how a chain of thought is generated: it refines the solution through denoising rather than committing to words strictly from left to right. This changes the generation schedule, not necessarily the visibility of the reasoning. The resulting chain can still be text, unlike methods that only emit the final answer.","source_ids":["2402.07754","2405.14838"],"source_urls":["https://proceedings.neurips.cc/paper_files/paper/2024/hash/be30024e7fa2c29cac7a6dafcbb8571f-Abstract-Conference.html","https://arxiv.org/html/2405.14838v1#S3"],"source_labels":["Diffusion of Thought","Deng et al. (2024), §3"],"topic_id":"beyond-sequential","topic_label":"Alternative generation methods","topic_url":"https://latent-implicit-thinking.github.io/topics/alternative-reasoning-schedules/"}]},{"id":"2405.15071","title":"Grokked Transformers are Implicit Reasoners: A Mechanistic Journey to the Edge of Generalization","authors":"Boshi Wang, Xiang Yue, Yu Su, Huan Sun","first_public":"2024-05-23","venue":"arXiv","arxiv":"2405.15071","paper_url":"https://arxiv.org/abs/2405.15071","lens":["analysis"],"representation":["hidden-state"],"computation":["depth-wise"],"training":["analysis-only"],"questions":["interpretability","generalization"],"evidence":["empirical","mechanistic"],"modality":["symbolic"],"summary":"Mechanistically studies transformers that learn implicit reasoning after grokking, focusing on how internal algorithms support out-of-distribution generalization.","provenance":"Awesome-Latent-CoT","author_names":["Boshi Wang","Xiang Yue","Yu Su","Huan 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Goldstein","first_public":"2024-06-19","venue":"arXiv","arxiv":"2406.13858","paper_url":"https://arxiv.org/abs/2406.13858","lens":["analysis"],"representation":["hidden-state"],"computation":["parallel","depth-wise"],"training":["analysis-only"],"questions":["interpretability","evaluation"],"evidence":["empirical","probing"],"modality":["language"],"summary":"Finds evidence for parallel internal processes during multi-hop reasoning rather than a single serial written-style chain.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Yuval Shalev","Amir Feder","Ariel 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Kulikov","first_public":"2024-07-08","venue":"arXiv","arxiv":"2407.06023","paper_url":"https://arxiv.org/abs/2407.06023","lens":["internalized"],"representation":["hidden-state"],"computation":["depth-wise"],"training":["distillation"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["language"],"summary":"Uses outputs from a slower deliberative process as training data for a faster model, studying when System-2-like behavior can be compressed into direct prediction.","provenance":"Awesome-Latent-CoT","author_names":["Ping Yu","Jing Xu","Jason Weston","Ilia 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Allen-Zhu","first_public":"2024-07-29","venue":"arXiv","arxiv":"2407.20311","paper_url":"https://arxiv.org/abs/2407.20311","lens":["analysis"],"representation":["hidden-state"],"computation":["depth-wise"],"training":["analysis-only"],"questions":["capability","interpretability","generalization"],"evidence":["empirical","boundary"],"modality":["language","symbolic"],"summary":"Studies the internal computation behind grade-school mathematics, including when models learn robust procedures or rely on data shortcuts.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Tian Ye","Zicheng Xu","Yuanzhi Li","Zeyuan Allen-Zhu"],"record_url":"https://latent-implicit-thinking.github.io/papers/2407.20311/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2407-20311","citation_date":"2024-07-29","json_url":"https://latent-implicit-thinking.github.io/papers/2407.20311/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2407.20311/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2407.20311/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2407.20311/citation.csl.json"},{"id":"2409.08561","title":"Expediting and Elevating Large Language Model Reasoning via Hidden Chain-of-Thought Decoding","authors":"Tianqiao Liu, Zui Chen, Zitao Liu, Mi Tian, Weiqi Luo","first_public":"2024-09-13","venue":"arXiv","arxiv":"2409.08561","paper_url":"https://arxiv.org/abs/2409.08561","lens":["continuous"],"representation":["continuous-state"],"computation":["token-wise"],"training":["supervised"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["language"],"summary":"Trains one model to compress written reasoning into special-token representations, then trains another to answer using those representations.","provenance":"Awesome-Latent-CoT","author_names":["Tianqiao Liu","Zui Chen","Zitao Liu","Mi Tian","Weiqi 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Viteri","first_public":"2024-09-21","venue":"arXiv","arxiv":"2409.14026","paper_url":"https://arxiv.org/abs/2409.14026","lens":["analysis"],"representation":["hidden-state"],"computation":["depth-wise"],"training":["analysis-only"],"questions":["interpretability","evaluation"],"evidence":["empirical","probing"],"modality":["language"],"summary":"Searches hidden activations for directions that encode intermediate reasoning progress and tests how those directions affect behavior.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Jason Zhang","Scott Viteri"],"record_url":"https://latent-implicit-thinking.github.io/papers/2409.14026/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2409-14026","citation_date":"2024-09-21","json_url":"https://latent-implicit-thinking.github.io/papers/2409.14026/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2409.14026/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2409.14026/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2409.14026/citation.csl.json"},{"id":"2410.09918","title":"Dualformer: Controllable Fast and Slow Thinking by Learning with Randomized Reasoning Traces","authors":"DiJia Su, Sainbayar Sukhbaatar, Michael Rabbat, Yuandong Tian, Qinqing Zheng","first_public":"2024-10-13","venue":"arXiv","arxiv":"2410.09918","paper_url":"https://arxiv.org/abs/2410.09918","lens":["internalized"],"representation":["text-latent-hybrid"],"computation":["token-wise"],"training":["supervised"],"questions":["capability","efficiency","controllability"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Randomizes which reasoning steps remain visible during training so one model can interpolate between direct and explicit reasoning.","provenance":"Primary-source literature search, 2026-09-04","author_names":["DiJia Su","Sainbayar Sukhbaatar","Michael Rabbat","Yuandong Tian","Qinqing Zheng"],"record_url":"https://latent-implicit-thinking.github.io/papers/2410.09918/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2410-09918","citation_date":"2024-10-13","json_url":"https://latent-implicit-thinking.github.io/papers/2410.09918/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2410.09918/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2410.09918/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2410.09918/citation.csl.json"},{"id":"2410.13640","title":"Latent Space Chain-of-Embedding Enables Output-free LLM Self-Evaluation","authors":"Yiming Wang, Pei Zhang, Baosong Yang, Derek F. Wong, Rui Wang","first_public":"2024-10-17","venue":"arXiv","arxiv":"2410.13640","paper_url":"https://arxiv.org/abs/2410.13640","lens":["continuous","analysis"],"representation":["continuous-state"],"computation":["token-wise"],"training":["inference-only"],"questions":["evaluation","efficiency"],"evidence":["empirical"],"modality":["language"],"summary":"Uses the sequence of hidden states produced during inference to estimate whether an answer is correct, without extra training or labeled correctness examples.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Yiming Wang","Pei Zhang","Baosong Yang","Derek F. Wong","Rui Wang"],"record_url":"https://latent-implicit-thinking.github.io/papers/2410.13640/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2410-13640","citation_date":"2024-10-17","json_url":"https://latent-implicit-thinking.github.io/papers/2410.13640/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2410.13640/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2410.13640/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2410.13640/citation.csl.json"},{"id":"2411.15862","title":"Do LLMs Really Think Step-by-step In Implicit Reasoning?","authors":"Yijiong Yu","first_public":"2024-11-24","venue":"arXiv","arxiv":"2411.15862","paper_url":"https://arxiv.org/abs/2411.15862","lens":["analysis"],"representation":["hidden-state"],"computation":["depth-wise"],"training":["analysis-only"],"questions":["evaluation","limitations","interpretability"],"evidence":["empirical","boundary"],"modality":["symbolic"],"summary":"Tests whether successful implicit reasoning reflects an internal step-by-step procedure and documents where that interpretation fails.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Yijiong Yu"],"record_url":"https://latent-implicit-thinking.github.io/papers/2411.15862/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2411-15862","citation_date":"2024-11-24","json_url":"https://latent-implicit-thinking.github.io/papers/2411.15862/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2411.15862/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2411.15862/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2411.15862/citation.csl.json"},{"id":"2412.06769","title":"Training Large Language Models to Reason in a Continuous Latent Space","authors":"Shibo Hao, Sainbayar Sukhbaatar, DiJia Su, Xian Li, Zhiting Hu, Jason Weston, Yuandong Tian","first_public":"2024-12-09","venue":"COLM 2025","arxiv":"2412.06769","paper_url":"https://arxiv.org/abs/2412.06769","code_url":"https://github.com/facebookresearch/coconut","lens":["continuous"],"representation":["continuous-state"],"computation":["recurrent","token-wise"],"training":["curriculum"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Feeds a model's last hidden state back as its next input, enabling recurrent reasoning in continuous space before returning to language.","provenance":"Awesome-Latent-CoT","author_names":["Shibo Hao","Sainbayar Sukhbaatar","DiJia Su","Xian Li","Zhiting Hu","Jason Weston","Yuandong Tian"],"record_url":"https://latent-implicit-thinking.github.io/papers/2412.06769/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2412-06769","citation_date":"2024-12-09","json_url":"https://latent-implicit-thinking.github.io/papers/2412.06769/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2412.06769/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2412.06769/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2412.06769/citation.csl.json","publication":{"title":"Training Large Language Models to Reason in a Continuous Latent Space","author_names":["Shibo Hao","Sainbayar Sukhbaatar","DiJia Su","Xian Li","Zhiting Hu","Jason E Weston","Yuandong Tian"],"year":2025,"type":"paper-conference","container_title":"Conference on Language Modeling (COLM 2025)","url":"https://openreview.net/forum?id=Itxz7S4Ip3","source_url":"https://colmweb.org/2025/AcceptedPapers.html","verified_at":"2026-10-18"},"publication_bibtex_url":"https://latent-implicit-thinking.github.io/papers/2412.06769/publication.bib","publication_csl_url":"https://latent-implicit-thinking.github.io/papers/2412.06769/publication.csl.json","method_comparisons":[{"title":"Implicit CoT: proposal and implementation","text":"Deng et al. (2023) proposed implicit chain-of-thought reasoning: language models carry out intermediate reasoning in continuous hidden states rather than generate it as text. Section 2.3 defines this setting; section 3 develops a distillation method to implement it. That method transfers a teacher's reasoning into hidden states across layers. Reasoning through continuous hidden states is the broader proposal; it does not require the particular distillation procedure used in this paper. Its across-layer computation differs from the repeated hidden-state feedback used by later methods such as Coconut.","source_ids":["2311.01460","2412.06769"],"source_urls":["https://arxiv.org/html/2311.01460v1#S2.SS3","https://arxiv.org/html/2311.01460v1#S3","https://arxiv.org/html/2412.06769v3#S3"],"source_labels":["Implicit CoT proposal, §2.3","Distillation implementation, §3","Coconut, §3"],"topic_id":"continuous","topic_label":"Continuous-state reasoning","topic_url":"https://latent-implicit-thinking.github.io/topics/continuous-states/"},{"title":"From stepwise internalization to Coconut","text":"Coconut explicitly credits Deng et al. (2024) as the inspiration for its multistage training curriculum. Stepwise internalization gradually removes written CoT tokens until the model answers directly. Coconut instead replaces removed steps with continuous hidden-state inputs, retaining a sequence of internal reasoning steps before the answer. It also follows the earlier work in resetting the optimizer between training stages.","source_ids":["2405.14838","2412.06769"],"source_urls":["https://arxiv.org/html/2405.14838v1#S3","https://arxiv.org/html/2412.06769v3#S3"],"source_labels":["Deng et al. (2024), §3","Coconut, §3"],"topic_id":"continuous","topic_label":"Continuous-state reasoning","topic_url":"https://latent-implicit-thinking.github.io/topics/continuous-states/"},{"title":"Coconut and CODI: similar computation, different training","text":"Coconut and CODI both pass continuous states between reasoning steps, but supervise them differently. Coconut gradually replaces written steps with hidden-state inputs and trains on the remaining text. CODI jointly trains explicit and implicit reasoning tasks, matching their hidden states at a selected position before the answer. These models avoid decoding a word at every intermediate step; they still perform successive model passes, so fewer written tokens does not mean no reasoning-time computation.","source_ids":["2412.06769","2502.21074"],"source_urls":["https://arxiv.org/html/2412.06769v3#S3","https://arxiv.org/html/2502.21074v3#S3"],"source_labels":["Coconut, §3","CODI, §3"],"topic_id":"continuous","topic_label":"Continuous-state reasoning","topic_url":"https://latent-implicit-thinking.github.io/topics/continuous-states/"}]},{"id":"2412.08635","title":"Multimodal Latent Language Modeling with Next-Token Diffusion","authors":"Yutao Sun, Hangbo Bao, Wenhui Wang, Zhiliang Peng, Li Dong, Shaohan Huang, Jianyong Wang, Furu Wei","first_public":"2024-12-11","venue":"arXiv","arxiv":"2412.08635","paper_url":"https://arxiv.org/abs/2412.08635","lens":["beyond-sequential"],"representation":["multimodal-latent"],"computation":["diffusion"],"training":["pretraining"],"questions":["capability"],"evidence":["empirical"],"modality":["multimodal"],"summary":"Encodes continuous data such as images as vectors, then generates those vectors with diffusion inside a causal transformer. This is related work on multimodal generation, rather than a method trained directly on reasoning steps.","provenance":"Awesome-Latent-CoT","author_names":["Yutao Sun","Hangbo Bao","Wenhui Wang","Zhiliang Peng","Li Dong","Shaohan Huang","Jianyong Wang","Furu Wei"],"record_url":"https://latent-implicit-thinking.github.io/papers/2412.08635/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2412-08635","citation_date":"2024-12-11","json_url":"https://latent-implicit-thinking.github.io/papers/2412.08635/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2412.08635/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2412.08635/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2412.08635/citation.csl.json"},{"id":"2412.13171","title":"Compressed Chain of Thought: Efficient Reasoning Through Dense Representations","authors":"Jeffrey Cheng, Benjamin Van Durme","first_public":"2024-12-17","venue":"arXiv","arxiv":"2412.13171","paper_url":"https://arxiv.org/abs/2412.13171","lens":["continuous"],"representation":["continuous-state"],"computation":["token-wise"],"training":["distillation"],"questions":["efficiency","capability"],"evidence":["empirical"],"modality":["language"],"summary":"Compresses verbose reasoning traces into shorter dense representations and evaluates the trade-off between reasoning quality and generated length.","provenance":"Awesome-Latent-CoT","author_names":["Jeffrey Cheng","Benjamin Van Durme"],"record_url":"https://latent-implicit-thinking.github.io/papers/2412.13171/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2412-13171","citation_date":"2024-12-17","json_url":"https://latent-implicit-thinking.github.io/papers/2412.13171/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2412.13171/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2412.13171/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2412.13171/citation.csl.json"},{"id":"2501.19201","title":"Efficient Reasoning with Hidden Thinking","authors":"Xuan Shen, Yizhou Wang, Yufa Zhou, Xiangxi Shi, Pu Zhao, Yanzhi Wang, Jiuxiang Gu","first_public":"2025-01-31","venue":"arXiv","arxiv":"2501.19201","paper_url":"https://arxiv.org/abs/2501.19201","lens":["internalized","continuous"],"representation":["continuous-state"],"computation":["token-wise"],"training":["distillation"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["language"],"summary":"Compresses visible reasoning into hidden thinking states to reduce generated reasoning length while preserving task performance.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Xuan Shen","Yizhou Wang","Yufa Zhou","Xiangxi Shi","Pu Zhao","Yanzhi Wang","Jiuxiang Gu"],"record_url":"https://latent-implicit-thinking.github.io/papers/2501.19201/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2501-19201","citation_date":"2025-01-31","json_url":"https://latent-implicit-thinking.github.io/papers/2501.19201/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2501.19201/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2501.19201/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2501.19201/citation.csl.json"},{"id":"2502.03275","title":"Token Assorted: Mixing Latent and Text Tokens for Improved Language Model Reasoning","authors":"DiJia Su, Hanlin Zhu, Yingchen Xu, Jiantao Jiao, Yuandong Tian, Qinqing Zheng","first_public":"2025-02-05","venue":"arXiv","arxiv":"2502.03275","paper_url":"https://arxiv.org/abs/2502.03275","lens":["learned-tokens","continuous"],"representation":["discrete-token","text-latent-hybrid"],"computation":["token-wise"],"training":["supervised"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Interleaves latent and textual tokens so a model can combine compressed internal computation with readable reasoning steps.","provenance":"Primary-source literature search, 2026-09-04","author_names":["DiJia Su","Hanlin Zhu","Yingchen Xu","Jiantao Jiao","Yuandong Tian","Qinqing 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Bartoldson, Bhavya Kailkhura, Abhinav Bhatele, Tom Goldstein","first_public":"2025-02-07","venue":"arXiv","arxiv":"2502.05171","paper_url":"https://arxiv.org/abs/2502.05171","code_url":"https://github.com/seal-rg/recurrent-pretraining","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent"],"training":["pretraining"],"questions":["capability","scaling"],"evidence":["empirical","scaling"],"modality":["language"],"summary":"Pretrains a depth-recurrent language model whose computation can be extended at inference time, separating test-time compute from generated token length.","provenance":"Awesome-Latent-CoT","author_names":["Jonas Geiping","Sean McLeish","Neel Jain","John Kirchenbauer","Siddharth Singh","Brian R. Bartoldson","Bhavya Kailkhura","Abhinav Bhatele","Tom Goldstein"],"record_url":"https://latent-implicit-thinking.github.io/papers/2502.05171/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2502-05171","citation_date":"2025-02-07","json_url":"https://latent-implicit-thinking.github.io/papers/2502.05171/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2502.05171/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2502.05171/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2502.05171/citation.csl.json","publication":{"title":"Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach","author_names":["Jonas Geiping","Sean McLeish","Neel Jain","John Kirchenbauer","Siddharth Singh","Brian Bartoldson","Bhavya Kailkhura","Abhinav Bhatele","Tom Goldstein"],"year":2025,"type":"paper-conference","container_title":"Advances in Neural Information Processing Systems","publisher":"Curran Associates, Inc.","doi":"10.52202/085713-1380","pages":"41340-41391","volume":"38","url":"https://proceedings.neurips.cc/paper_files/paper/2025/hash/3b01972cf31e6fa0fe29e4b8b5c2a0a1-Abstract-Conference.html","source_url":"https://proceedings.neurips.cc/paper_files/paper/2025/hash/3b01972cf31e6fa0fe29e4b8b5c2a0a1-Abstract-Conference.html","verified_at":"2026-10-18"},"publication_bibtex_url":"https://latent-implicit-thinking.github.io/papers/2502.05171/publication.bib","publication_csl_url":"https://latent-implicit-thinking.github.io/papers/2502.05171/publication.csl.json","method_comparisons":[{"title":"Recurrent depth and fixed points","text":"Recurrent depth and fixed-point models repeat computation in different ways. Geiping and colleagues reuse a transformer block, allowing the number of passes to change at inference. The implicit state-space models studied by Schöne and colleagues instead iterate toward a fixed point, with experiments testing when approximate convergence is sufficient. Both add computation without adding a written reasoning trace, but their stopping rules and training costs differ.","source_ids":["2502.05171","2502.07827"],"source_urls":["https://proceedings.neurips.cc/paper_files/paper/2025/hash/3b01972cf31e6fa0fe29e4b8b5c2a0a1-Abstract-Conference.html","https://proceedings.mlr.press/v267/schone25a.html"],"source_labels":["Recurrent-depth paper","Implicit state-space paper"],"topic_id":"recurrent","topic_label":"Recurrent reasoning","topic_url":"https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/"}]},{"id":"2502.07827","title":"Implicit Language Models are RNNs: Balancing Parallelization and Expressivity","authors":"Mark Schöne, Babak Rahmani, Heiner Kremer, Fabian Falck, Hitesh Ballani, Jannes Gladrow","first_public":"2025-02-10","venue":"ICML 2025","arxiv":"2502.07827","paper_url":"https://arxiv.org/abs/2502.07827","lens":["recurrent","analysis"],"representation":["continuous-state"],"computation":["recurrent","parallel"],"training":["pretraining"],"questions":["theory","architecture","efficiency"],"evidence":["formal","empirical"],"modality":["language"],"summary":"Connects implicit language models to recurrent computation and analyzes the trade-off between parallel training and expressive sequential depth.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Mark Schöne","Babak Rahmani","Heiner Kremer","Fabian Falck","Hitesh Ballani","Jannes Gladrow"],"record_url":"https://latent-implicit-thinking.github.io/papers/2502.07827/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2502-07827","citation_date":"2025-02-10","json_url":"https://latent-implicit-thinking.github.io/papers/2502.07827/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2502.07827/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2502.07827/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2502.07827/citation.csl.json","publication":{"title":"Implicit Language Models are RNNs: Balancing Parallelization and Expressivity","author_names":["Mark Schöne","Babak Rahmani","Heiner Kremer","Fabian Falck","Hitesh Ballani","Jannes Gladrow"],"year":2025,"type":"paper-conference","container_title":"Proceedings of the 42nd International Conference on Machine Learning","publisher":"PMLR","pages":"53439-53466","volume":"267","url":"https://proceedings.mlr.press/v267/schone25a.html","source_url":"https://proceedings.mlr.press/v267/schone25a.html","verified_at":"2026-10-18"},"publication_bibtex_url":"https://latent-implicit-thinking.github.io/papers/2502.07827/publication.bib","publication_csl_url":"https://latent-implicit-thinking.github.io/papers/2502.07827/publication.csl.json","method_comparisons":[{"title":"Recurrent depth and fixed points","text":"Recurrent depth and fixed-point models repeat computation in different ways. Geiping and colleagues reuse a transformer block, allowing the number of passes to change at inference. The implicit state-space models studied by Schöne and colleagues instead iterate toward a fixed point, with experiments testing when approximate convergence is sufficient. Both add computation without adding a written reasoning trace, but their stopping rules and training costs differ.","source_ids":["2502.05171","2502.07827"],"source_urls":["https://proceedings.neurips.cc/paper_files/paper/2025/hash/3b01972cf31e6fa0fe29e4b8b5c2a0a1-Abstract-Conference.html","https://proceedings.mlr.press/v267/schone25a.html"],"source_labels":["Recurrent-depth paper","Implicit state-space paper"],"topic_id":"recurrent","topic_label":"Recurrent reasoning","topic_url":"https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/"}]},{"id":"2502.08524","title":"LLM Pretraining with Continuous Concepts","authors":"Jihoon Tack, Jack Lanchantin, Jane Yu, Andrew Cohen, Ilia Kulikov, Janice Lan, Shibo Hao, Yuandong Tian, Jason Weston, Xian Li","first_public":"2025-02-12","venue":"arXiv","arxiv":"2502.08524","paper_url":"https://arxiv.org/abs/2502.08524","code_url":"https://github.com/facebookresearch/RAM/tree/main/projects/cocomix","lens":["continuous"],"representation":["continuous-state"],"computation":["token-wise"],"training":["pretraining"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["language"],"summary":"Interleaves continuous concept representations with text during pretraining so language models learn to compute over concepts as well as tokens.","provenance":"Awesome-Latent-CoT","author_names":["Jihoon Tack","Jack Lanchantin","Jane Yu","Andrew Cohen","Ilia Kulikov","Janice Lan","Shibo Hao","Yuandong Tian","Jason Weston","Xian Li"],"record_url":"https://latent-implicit-thinking.github.io/papers/2502.08524/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2502-08524","citation_date":"2025-02-12","json_url":"https://latent-implicit-thinking.github.io/papers/2502.08524/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2502.08524/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2502.08524/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2502.08524/citation.csl.json"},{"id":"2502.13842","title":"Inner Thinking Transformer: Leveraging Dynamic Depth Scaling to Foster Adaptive Internal Thinking","authors":"Yilong Chen, Junyuan Shang, Zhenyu Zhang, Yanxi Xie, Jiawei Sheng, Tingwen Liu, Shuohuan Wang, Yu Sun, Hua Wu, Haifeng Wang","first_public":"2025-02-19","venue":"arXiv","arxiv":"2502.13842","paper_url":"https://arxiv.org/abs/2502.13842","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["supervised"],"questions":["capability","efficiency","controllability"],"evidence":["empirical"],"modality":["language"],"summary":"Routes selected tokens through extra computation while reusing model parameters. Marks successive thinking steps so the model can distinguish one pass from the next.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Yilong Chen","Junyuan Shang","Zhenyu Zhang","Yanxi Xie","Jiawei Sheng","Tingwen Liu","Shuohuan Wang","Yu Sun","Hua Wu","Haifeng Wang"],"record_url":"https://latent-implicit-thinking.github.io/papers/2502.13842/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2502-13842","citation_date":"2025-02-19","json_url":"https://latent-implicit-thinking.github.io/papers/2502.13842/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2502.13842/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2502.13842/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2502.13842/citation.csl.json"},{"id":"2502.15589","title":"LightThinker: Thinking Step-by-Step Compression","authors":"Jintian Zhang, Yuqi Zhu, Mengshu Sun, Yujie Luo, Shuofei Qiao, Lun Du, Da Zheng, Huajun Chen, Ningyu Zhang","first_public":"2025-02-21","venue":"arXiv","arxiv":"2502.15589","paper_url":"https://arxiv.org/abs/2502.15589","lens":["internalized","continuous"],"representation":["continuous-state"],"computation":["token-wise"],"training":["distillation"],"questions":["efficiency","capability"],"evidence":["empirical"],"modality":["language"],"summary":"Compresses segments of a generated reasoning chain into dense states while retaining a stepwise inference process.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Jintian Zhang","Yuqi Zhu","Mengshu Sun","Yujie Luo","Shuofei Qiao","Lun Du","Da Zheng","Huajun Chen","Ningyu Zhang"],"record_url":"https://latent-implicit-thinking.github.io/papers/2502.15589/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2502-15589","citation_date":"2025-02-21","json_url":"https://latent-implicit-thinking.github.io/papers/2502.15589/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2502.15589/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2502.15589/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2502.15589/citation.csl.json"},{"id":"2502.17416","title":"Reasoning with Latent Thoughts: On the Power of Looped Transformers","authors":"Nikunj Saunshi, Nishanth Dikkala, Zhiyuan Li, Sanjiv Kumar, Sashank J. Reddi","first_public":"2025-02-24","venue":"ICLR 2025","arxiv":"2502.17416","paper_url":"https://arxiv.org/abs/2502.17416","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent"],"training":["supervised"],"questions":["theory","capability"],"evidence":["empirical","formal"],"modality":["symbolic"],"summary":"Analyzes the expressive power of transformers that repeatedly apply shared layers, treating recurrent depth as a form of internal reasoning.","provenance":"Awesome-Latent-CoT","author_names":["Nikunj Saunshi","Nishanth Dikkala","Zhiyuan Li","Sanjiv Kumar","Sashank J. Reddi"],"record_url":"https://latent-implicit-thinking.github.io/papers/2502.17416/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2502-17416","citation_date":"2025-02-24","json_url":"https://latent-implicit-thinking.github.io/papers/2502.17416/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2502.17416/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2502.17416/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2502.17416/citation.csl.json"},{"id":"2502.21074","title":"CODI: Compressing Chain-of-Thought into Continuous Space via Self-Distillation","authors":"Zhenyi Shen, Hanqi Yan, Linhai Zhang, Zhanghao Hu, Yali Du, Yulan He","first_public":"2025-02-28","venue":"EMNLP 2025","arxiv":"2502.21074","paper_url":"https://arxiv.org/abs/2502.21074","lens":["continuous","internalized"],"representation":["continuous-state"],"computation":["token-wise"],"training":["self-distillation"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Uses self-distillation to align continuous internal reasoning states with explicit chain-of-thought behavior while reducing visible reasoning tokens.","provenance":"Awesome-Latent-CoT","author_names":["Zhenyi Shen","Hanqi Yan","Linhai Zhang","Zhanghao Hu","Yali Du","Yulan He"],"record_url":"https://latent-implicit-thinking.github.io/papers/2502.21074/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2502-21074","citation_date":"2025-02-28","json_url":"https://latent-implicit-thinking.github.io/papers/2502.21074/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2502.21074/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2502.21074/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2502.21074/citation.csl.json","publication":{"title":"CODI: Compressing Chain-of-Thought into Continuous Space via Self-Distillation","author_names":["Zhenyi Shen","Hanqi Yan","Linhai Zhang","Zhanghao Hu","Yali Du","Yulan He"],"year":2025,"type":"paper-conference","container_title":"Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing","publisher":"Association for Computational Linguistics","doi":"10.18653/v1/2025.emnlp-main.36","pages":"677-693","url":"https://aclanthology.org/2025.emnlp-main.36/","source_url":"https://aclanthology.org/2025.emnlp-main.36/","verified_at":"2026-10-18"},"publication_bibtex_url":"https://latent-implicit-thinking.github.io/papers/2502.21074/publication.bib","publication_csl_url":"https://latent-implicit-thinking.github.io/papers/2502.21074/publication.csl.json","method_comparisons":[{"title":"Hidden-state distillation: the 2023 method and CODI","text":"The 2023 implicit CoT paper proposes reasoning through hidden states and implements it with a teacher, a thought emulator and an answer-generating student. CODI also transfers explicit reasoning through hidden-state supervision, but uses one model for both teacher and student tasks. It aligns their states just before the answer, while the student takes successive continuous reasoning steps.","source_ids":["2311.01460","2502.21074"],"source_urls":["https://arxiv.org/html/2311.01460v1#S2.SS3","https://arxiv.org/html/2311.01460v1#S3","https://arxiv.org/html/2502.21074v3#S3"],"source_labels":["Deng et al. (2023), §2.3","Deng et al. (2023), §3","CODI, §3"],"topic_id":"internalized","topic_label":"Internalized reasoning","topic_url":"https://latent-implicit-thinking.github.io/topics/internalized-reasoning/"},{"title":"Coconut and CODI: similar computation, different training","text":"Coconut and CODI both pass continuous states between reasoning steps, but supervise them differently. Coconut gradually replaces written steps with hidden-state inputs and trains on the remaining text. CODI jointly trains explicit and implicit reasoning tasks, matching their hidden states at a selected position before the answer. These models avoid decoding a word at every intermediate step; they still perform successive model passes, so fewer written tokens does not mean no reasoning-time computation.","source_ids":["2412.06769","2502.21074"],"source_urls":["https://arxiv.org/html/2412.06769v3#S3","https://arxiv.org/html/2502.21074v3#S3"],"source_labels":["Coconut, §3","CODI, §3"],"topic_id":"continuous","topic_label":"Continuous-state reasoning","topic_url":"https://latent-implicit-thinking.github.io/topics/continuous-states/"}]},{"id":"2503.07604","title":"Implicit Reasoning in Transformers is Reasoning through Shortcuts","authors":"Tianhe Lin, Jian Xie, Siyu Yuan, Deqing Yang","first_public":"2025-03-10","venue":"arXiv","arxiv":"2503.07604","paper_url":"https://arxiv.org/abs/2503.07604","lens":["analysis"],"representation":["hidden-state"],"computation":["depth-wise"],"training":["analysis-only"],"questions":["interpretability","limitations"],"evidence":["empirical","boundary"],"modality":["symbolic"],"summary":"Tests whether apparent implicit multi-step reasoning reflects compositional algorithms or learned shortcuts, emphasizing failure modes under distribution shift.","provenance":"Awesome-Latent-CoT","author_names":["Tianhe Lin","Jian Xie","Siyu Yuan","Deqing Yang"],"record_url":"https://latent-implicit-thinking.github.io/papers/2503.07604/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2503-07604","citation_date":"2025-03-10","json_url":"https://latent-implicit-thinking.github.io/papers/2503.07604/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2503.07604/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2503.07604/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2503.07604/citation.csl.json"},{"id":"2504.10615","title":"Beyond Chains of Thought: Benchmarking Latent-Space Reasoning Abilities in Large Language Models","authors":"Thilo Hagendorff, Sarah Fabi","first_public":"2025-04-14","venue":"arXiv","arxiv":"2504.10615","paper_url":"https://arxiv.org/abs/2504.10615","lens":["analysis"],"representation":["hidden-state"],"computation":["depth-wise"],"training":["analysis-only"],"questions":["evaluation","capability","limitations"],"evidence":["empirical","boundary"],"modality":["language"],"summary":"Encodes the answer in the language of the model's first response token, forcing a choice before any written explanation. Also tests whether successful answers could come from simple heuristics.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Thilo Hagendorff","Sarah Fabi"],"record_url":"https://latent-implicit-thinking.github.io/papers/2504.10615/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2504-10615","citation_date":"2025-04-14","json_url":"https://latent-implicit-thinking.github.io/papers/2504.10615/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2504.10615/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2504.10615/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2504.10615/citation.csl.json"},{"id":"2504.14992","title":"Efficient Pretraining Length Scaling","authors":"Bohong Wu, Shen Yan, Sijun Zhang, Jianqiao Lu, Yutao Zeng, Ya Wang, Xun Zhou","first_public":"2025-04-21","venue":"arXiv","arxiv":"2504.14992","paper_url":"https://arxiv.org/abs/2504.14992","lens":["learned-tokens","recurrent"],"representation":["hidden-state","cache-memory"],"computation":["token-wise","stateful"],"training":["pretraining"],"questions":["efficiency","scaling","architecture"],"evidence":["empirical","scaling"],"modality":["language"],"summary":"Adds hidden decoding tokens during pretraining, then discards their key/value cache entries after use. Keeps the original tokens' entries to preserve longer-range context.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Bohong Wu","Shen Yan","Sijun Zhang","Jianqiao Lu","Yutao Zeng","Ya Wang","Xun Zhou"],"record_url":"https://latent-implicit-thinking.github.io/papers/2504.14992/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2504-14992","citation_date":"2025-04-21","json_url":"https://latent-implicit-thinking.github.io/papers/2504.14992/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2504.14992/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2504.14992/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2504.14992/citation.csl.json"},{"id":"2505.12629","title":"Enhancing Latent Computation in Transformers with Latent Tokens","authors":"Yuchang Sun, Yanxi Chen, Yaliang Li, Bolin Ding","first_public":"2025-05-19","venue":"arXiv","arxiv":"2505.12629","paper_url":"https://arxiv.org/abs/2505.12629","lens":["learned-tokens"],"representation":["discrete-token"],"computation":["token-wise"],"training":["supervised"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Adds trainable dummy tokens to a pretrained transformer so attention can use them for extra computation during decoding. The tokens can be inserted in different positions at inference time.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Yuchang Sun","Yanxi Chen","Yaliang Li","Bolin Ding"],"record_url":"https://latent-implicit-thinking.github.io/papers/2505.12629/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2505-12629","citation_date":"2025-05-19","json_url":"https://latent-implicit-thinking.github.io/papers/2505.12629/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2505.12629/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2505.12629/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2505.12629/citation.csl.json"},{"id":"2505.13308","title":"Seek in the Dark: Reasoning via Test-Time Instance-Level Policy Gradient in Latent Space","authors":"Hengli Li, Chenxi Li, Tong Wu, Xuekai Zhu, Yuxuan Wang, Zhaoxin Yu, Eric Hanchen Jiang, Song-Chun Zhu, Zixia Jia, Ying Nian Wu, Zilong Zheng","first_public":"2025-05-19","venue":"arXiv","arxiv":"2505.13308","paper_url":"https://arxiv.org/abs/2505.13308","lens":["continuous"],"representation":["continuous-state"],"computation":["search"],"training":["test-time-optimization"],"questions":["capability","controllability"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Optimizes latent states for individual problems at test time using policy gradients rather than searching over written reasoning traces.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Hengli Li","Chenxi Li","Tong Wu","Xuekai Zhu","Yuxuan Wang","Zhaoxin Yu","Eric Hanchen Jiang","Song-Chun Zhu","Zixia Jia","Ying Nian Wu","Zilong Zheng"],"record_url":"https://latent-implicit-thinking.github.io/papers/2505.13308/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2505-13308","citation_date":"2025-05-19","json_url":"https://latent-implicit-thinking.github.io/papers/2505.13308/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2505.13308/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2505.13308/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2505.13308/citation.csl.json"},{"id":"2505.13898","title":"Do Language Models Use Their Depth Efficiently?","authors":"Róbert Csordás, Christopher D. Manning, Christopher Potts","first_public":"2025-05-20","venue":"arXiv","arxiv":"2505.13898","paper_url":"https://arxiv.org/abs/2505.13898","lens":["analysis","recurrent"],"representation":["hidden-state"],"computation":["depth-wise","recurrent"],"training":["analysis-only"],"questions":["efficiency","architecture","limitations"],"evidence":["empirical","boundary"],"modality":["language","symbolic"],"summary":"Skips layers and compares shallow and deep models to examine what extra layers compute. In the models studied, later layers mostly make smaller refinements rather than adding new reasoning steps.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Róbert Csordás","Christopher D. Manning","Christopher Potts"],"record_url":"https://latent-implicit-thinking.github.io/papers/2505.13898/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2505-13898","citation_date":"2025-05-20","json_url":"https://latent-implicit-thinking.github.io/papers/2505.13898/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2505.13898/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2505.13898/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2505.13898/citation.csl.json"},{"id":"2505.14530","title":"Internal Chain-of-Thought: Empirical Evidence for Layer-wise Subtask Scheduling in LLMs","authors":"Zhipeng Yang, Junzhuo Li, Siyu Xia, Xuming Hu","first_public":"2025-05-20","venue":"arXiv","arxiv":"2505.14530","paper_url":"https://arxiv.org/abs/2505.14530","code_url":"https://github.com/yzp11/Internal-Chain-of-Thought","lens":["analysis"],"representation":["hidden-state"],"computation":["depth-wise"],"training":["analysis-only"],"questions":["interpretability"],"evidence":["empirical","probing"],"modality":["language"],"summary":"Presents evidence that transformer layers schedule intermediate subtasks internally, offering a layer-wise view of implicit reasoning.","provenance":"Awesome-Latent-CoT","author_names":["Zhipeng Yang","Junzhuo Li","Siyu Xia","Xuming Hu"],"record_url":"https://latent-implicit-thinking.github.io/papers/2505.14530/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2505-14530","citation_date":"2025-05-20","json_url":"https://latent-implicit-thinking.github.io/papers/2505.14530/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2505.14530/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2505.14530/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2505.14530/citation.csl.json"},{"id":"2505.14827","title":"Text Generation Beyond Discrete Token Sampling","authors":"Yufan Zhuang, Liyuan Liu, Chandan Singh, Jingbo Shang, Jianfeng Gao","first_public":"2025-05-20","venue":"arXiv","arxiv":"2505.14827","paper_url":"https://arxiv.org/abs/2505.14827","lens":["continuous","beyond-sequential"],"representation":["continuous-state"],"computation":["token-wise"],"training":["inference-only"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["language"],"summary":"Feeds posterior expectations back into a language model so intermediate generation can remain continuous instead of sampling discrete tokens.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Yufan Zhuang","Liyuan Liu","Chandan Singh","Jingbo Shang","Jianfeng Gao"],"record_url":"https://latent-implicit-thinking.github.io/papers/2505.14827/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2505-14827","citation_date":"2025-05-20","json_url":"https://latent-implicit-thinking.github.io/papers/2505.14827/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2505.14827/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2505.14827/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2505.14827/citation.csl.json"},{"id":"2505.16552","title":"Think Silently, Think Fast: Dynamic Latent Compression of LLM Reasoning Chains","authors":"Wenhui Tan, Jiaze Li, Jianzhong Ju, Zhenbo Luo, Ruihua Song, Jian Luan","first_public":"2025-05-22","venue":"arXiv","arxiv":"2505.16552","paper_url":"https://arxiv.org/abs/2505.16552","lens":["internalized","continuous"],"representation":["continuous-state"],"computation":["token-wise"],"training":["distillation","supervised"],"questions":["efficiency","capability","controllability"],"evidence":["empirical"],"modality":["language"],"summary":"Dynamically compresses portions of a reasoning chain into latent states according to the problem and intermediate context.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Wenhui Tan","Jiaze Li","Jianzhong Ju","Zhenbo Luo","Ruihua Song","Jian Luan"],"record_url":"https://latent-implicit-thinking.github.io/papers/2505.16552/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2505-16552","citation_date":"2025-05-22","json_url":"https://latent-implicit-thinking.github.io/papers/2505.16552/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2505.16552/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2505.16552/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2505.16552/citation.csl.json"},{"id":"2505.16782","title":"Reasoning Beyond Language: A Comprehensive Survey on Latent Chain-of-Thought Reasoning","authors":"Xinghao Chen, Anhao Zhao, Heming Xia, Xuan Lu, Hanlin Wang, Yanjun Chen, Wei Zhang, Jian Wang, Wenjie Li, Xiaoyu Shen","first_public":"2025-05-22","venue":"arXiv survey","arxiv":"2505.16782","paper_url":"https://arxiv.org/abs/2505.16782","code_url":"https://github.com/EIT-NLP/Awesome-Latent-CoT","lens":["analysis"],"representation":["survey"],"computation":["survey"],"training":["analysis-only"],"questions":["survey","taxonomy"],"evidence":["survey"],"modality":["language","multimodal"],"summary":"Surveys latent chain-of-thought methods and organizes a broad, continuously updated bibliography spanning token-wise, structural, representational, and analytical work.","provenance":"Awesome-Latent-CoT","author_names":["Xinghao Chen","Anhao Zhao","Heming Xia","Xuan Lu","Hanlin Wang","Yanjun Chen","Wei Zhang","Jian Wang","Wenjie Li","Xiaoyu Shen"],"record_url":"https://latent-implicit-thinking.github.io/papers/2505.16782/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2505-16782","citation_date":"2025-05-22","json_url":"https://latent-implicit-thinking.github.io/papers/2505.16782/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2505.16782/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2505.16782/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2505.16782/citation.csl.json"},{"id":"2505.17923","title":"Language Models Can Learn Implicit Multi-Hop Reasoning, but Only If They Have Lots of Training Data","authors":"Yuekun Yao, Yupei Du, Dawei Zhu, Michael Hahn, Alexander Koller","first_public":"2025-05-23","venue":"arXiv","arxiv":"2505.17923","paper_url":"https://arxiv.org/abs/2505.17923","lens":["analysis"],"representation":["hidden-state"],"computation":["depth-wise"],"training":["analysis-only"],"questions":["capability","scaling","limitations"],"evidence":["empirical","scaling","boundary"],"modality":["language","symbolic"],"summary":"Studies the data requirements for learning implicit multi-hop reasoning and identifies sharp limitations in low-data regimes.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Yuekun Yao","Yupei Du","Dawei Zhu","Michael Hahn","Alexander Koller"],"record_url":"https://latent-implicit-thinking.github.io/papers/2505.17923/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2505-17923","citation_date":"2025-05-23","json_url":"https://latent-implicit-thinking.github.io/papers/2505.17923/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2505.17923/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2505.17923/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2505.17923/citation.csl.json"},{"id":"2505.18454","title":"Hybrid Latent Reasoning via Reinforcement Learning","authors":"Zhenrui Yue, Bowen Jin, Huimin Zeng, Honglei Zhuang, Zhen Qin, Jinsung Yoon, Lanyu Shang, Jiawei Han, Dong Wang","first_public":"2025-05-24","venue":"arXiv","arxiv":"2505.18454","paper_url":"https://arxiv.org/abs/2505.18454","lens":["continuous","internalized"],"representation":["text-latent-hybrid","continuous-state"],"computation":["token-wise"],"training":["reinforcement-learning"],"questions":["capability","efficiency","controllability"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Uses reinforcement learning to choose and train a mixture of latent and written reasoning steps.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Zhenrui Yue","Bowen Jin","Huimin Zeng","Honglei Zhuang","Zhen Qin","Jinsung Yoon","Lanyu Shang","Jiawei Han","Dong Wang"],"record_url":"https://latent-implicit-thinking.github.io/papers/2505.18454/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2505-18454","citation_date":"2025-05-24","json_url":"https://latent-implicit-thinking.github.io/papers/2505.18454/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2505.18454/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2505.18454/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2505.18454/citation.csl.json"},{"id":"2505.18962","title":"System-1.5 Reasoning: Traversal in Language and Latent Spaces with Dynamic Shortcuts","authors":"Xiaoqiang Wang, Suyuchen Wang, Yun Zhu, Bang Liu","first_public":"2025-05-25","venue":"arXiv","arxiv":"2505.18962","paper_url":"https://arxiv.org/abs/2505.18962","lens":["continuous","internalized"],"representation":["text-latent-hybrid","continuous-state"],"computation":["token-wise"],"training":["supervised"],"questions":["capability","efficiency","controllability"],"evidence":["empirical"],"modality":["language"],"summary":"Learns dynamic shortcuts between language and latent states to skip portions of an otherwise explicit reasoning trajectory.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Xiaoqiang Wang","Suyuchen Wang","Yun Zhu","Bang Liu"],"record_url":"https://latent-implicit-thinking.github.io/papers/2505.18962/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2505-18962","citation_date":"2025-05-25","json_url":"https://latent-implicit-thinking.github.io/papers/2505.18962/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2505.18962/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2505.18962/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2505.18962/citation.csl.json"},{"id":"2505.19245","title":"To CoT or To Loop? A Formal Comparison Between Chain-of-Thought and Looped Transformers","authors":"Kevin Xu, Issei Sato","first_public":"2025-05-25","venue":"arXiv","arxiv":"2505.19245","paper_url":"https://arxiv.org/abs/2505.19245","lens":["analysis","recurrent"],"representation":["hidden-state"],"computation":["recurrent"],"training":["analysis-only"],"questions":["theory"],"evidence":["formal"],"modality":["symbolic"],"summary":"Formally compares explicit chain-of-thought computation with repeated internal transformations in looped transformer architectures.","provenance":"Awesome-Latent-CoT","author_names":["Kevin Xu","Issei Sato"],"record_url":"https://latent-implicit-thinking.github.io/papers/2505.19245/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2505-19245","citation_date":"2025-05-25","json_url":"https://latent-implicit-thinking.github.io/papers/2505.19245/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2505.19245/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2505.19245/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2505.19245/citation.csl.json"},{"id":"2505.20674","title":"PonderLM: Pretraining Language Models to Ponder in Continuous Space","authors":"Boyi Zeng, Shixiang Song, Siyuan Huang, Yixuan Wang, He Li, Ziwei He, Xinbing Wang, Zhiyu Li, Zhouhan Lin","first_public":"2025-05-27","venue":"arXiv","arxiv":"2505.20674","paper_url":"https://arxiv.org/abs/2505.20674","lens":["continuous","recurrent"],"representation":["continuous-state"],"computation":["recurrent","token-wise"],"training":["pretraining"],"questions":["capability","efficiency","scaling"],"evidence":["empirical","scaling"],"modality":["language"],"summary":"Pretrains language models with repeated continuous-space pondering steps before token prediction.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Boyi Zeng","Shixiang Song","Siyuan Huang","Yixuan Wang","He Li","Ziwei He","Xinbing Wang","Zhiyu Li","Zhouhan Lin"],"record_url":"https://latent-implicit-thinking.github.io/papers/2505.20674/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2505-20674","citation_date":"2025-05-27","json_url":"https://latent-implicit-thinking.github.io/papers/2505.20674/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2505.20674/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2505.20674/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2505.20674/citation.csl.json"},{"id":"2505.23648","title":"Continuous Chain of Thought Enables Parallel Exploration and Reasoning","authors":"Halil Alperen Gozeten, M. Emrullah Ildiz, Xuechen Zhang, Hrayr Harutyunyan, Ankit Singh Rawat, Samet Oymak","first_public":"2025-05-29","venue":"arXiv","arxiv":"2505.23648","paper_url":"https://arxiv.org/abs/2505.23648","lens":["continuous","analysis"],"representation":["continuous-state"],"computation":["parallel"],"training":["analysis-only"],"questions":["theory","capability"],"evidence":["formal","empirical"],"modality":["symbolic"],"summary":"Analyzes and demonstrates how continuous intermediate states can explore several candidate reasoning paths in parallel.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Halil Alperen Gozeten","M. Emrullah Ildiz","Xuechen Zhang","Hrayr Harutyunyan","Ankit Singh Rawat","Samet Oymak"],"record_url":"https://latent-implicit-thinking.github.io/papers/2505.23648/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2505-23648","citation_date":"2025-05-29","json_url":"https://latent-implicit-thinking.github.io/papers/2505.23648/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2505.23648/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2505.23648/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2505.23648/citation.csl.json"},{"id":"2506.11752","title":"DART: Distilling Autoregressive Reasoning to Silent Thought","authors":"Nan Jiang, Ziming Wu, De-Chuan Zhan, Fuming Lai, Shaobing Lian","first_public":"2025-06-13","venue":"arXiv","arxiv":"2506.11752","paper_url":"https://arxiv.org/abs/2506.11752","lens":["internalized","continuous"],"representation":["continuous-state"],"computation":["token-wise"],"training":["distillation"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Distills an autoregressive textual reasoner into a model that carries the intermediate process through silent internal states.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Nan Jiang","Ziming Wu","De-Chuan Zhan","Fuming Lai","Shaobing Lian"],"record_url":"https://latent-implicit-thinking.github.io/papers/2506.11752/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2506-11752","citation_date":"2025-06-13","json_url":"https://latent-implicit-thinking.github.io/papers/2506.11752/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2506.11752/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2506.11752/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2506.11752/citation.csl.json"},{"id":"2506.17218","title":"Machine Mental Imagery: Empower Multimodal Reasoning with Latent Visual Tokens","authors":"Zeyuan Yang, Xueyang Yu, Delin Chen, Maohao Shen, Chuang Gan","first_public":"2025-06-20","venue":"arXiv","arxiv":"2506.17218","paper_url":"https://arxiv.org/abs/2506.17218","lens":["learned-tokens","continuous"],"representation":["multimodal-latent"],"computation":["token-wise"],"training":["supervised"],"questions":["capability","interpretability"],"evidence":["empirical"],"modality":["multimodal","vision"],"summary":"Uses latent visual tokens as an internal imagery channel for multimodal reasoning without rendering every intermediate state.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Zeyuan Yang","Xueyang Yu","Delin Chen","Maohao Shen","Chuang Gan"],"record_url":"https://latent-implicit-thinking.github.io/papers/2506.17218/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2506-17218","citation_date":"2025-06-20","json_url":"https://latent-implicit-thinking.github.io/papers/2506.17218/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2506.17218/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2506.17218/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2506.17218/citation.csl.json"},{"id":"2506.18582","title":"Parallel Continuous Chain-of-Thought with Jacobi Iteration","authors":"Haoyi Wu, Zhihao Teng, Kewei Tu","first_public":"2025-06-23","venue":"arXiv","arxiv":"2506.18582","paper_url":"https://arxiv.org/abs/2506.18582","lens":["continuous","beyond-sequential"],"representation":["continuous-state"],"computation":["parallel"],"training":["supervised"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Applies Jacobi-style iteration to update continuous reasoning states in parallel rather than strictly one step at a time.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Haoyi Wu","Zhihao Teng","Kewei Tu"],"record_url":"https://latent-implicit-thinking.github.io/papers/2506.18582/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2506-18582","citation_date":"2025-06-23","json_url":"https://latent-implicit-thinking.github.io/papers/2506.18582/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2506.18582/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2506.18582/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2506.18582/citation.csl.json"},{"id":"2506.21734","title":"Hierarchical Reasoning Model","authors":"Guan Wang, Jin Li, Yuhao Sun, Xing Chen, Changling Liu, Yue Wu, Meng Lu, Sen Song, Yasin Abbasi Yadkori","first_public":"2025-06-26","venue":"arXiv","arxiv":"2506.21734","paper_url":"https://arxiv.org/abs/2506.21734","code_url":"https://github.com/sapientinc/HRM","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent","hierarchical"],"training":["supervised"],"questions":["capability","architecture"],"evidence":["empirical"],"modality":["symbolic","vision"],"summary":"Uses coupled recurrent modules operating at different timescales to perform iterative internal computation on difficult reasoning tasks.","provenance":"Awesome-Latent-CoT","author_names":["Guan Wang","Jin Li","Yuhao Sun","Xing Chen","Changling Liu","Yue Wu","Meng Lu","Sen Song","Yasin Abbasi Yadkori"],"record_url":"https://latent-implicit-thinking.github.io/papers/2506.21734/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2506-21734","citation_date":"2025-06-26","json_url":"https://latent-implicit-thinking.github.io/papers/2506.21734/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2506.21734/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2506.21734/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2506.21734/citation.csl.json"},{"id":"2507.02199","title":"Latent Chain-of-Thought? Decoding the Depth-Recurrent Transformer","authors":"Wenquan Lu, Yuechuan Yang, Kyle Lee, Yanshu Li, Enqi Liu","first_public":"2025-07-02","venue":"arXiv","arxiv":"2507.02199","paper_url":"https://arxiv.org/abs/2507.02199","code_url":"https://github.com/wenquanlu/huginn-latent-cot","lens":["analysis","recurrent"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["analysis-only"],"questions":["interpretability","evaluation","limitations"],"evidence":["empirical","probing"],"modality":["language"],"summary":"Probes a depth-recurrent transformer to test what its repeated hidden-state computation represents and whether it behaves like a latent chain of thought.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Wenquan Lu","Yuechuan Yang","Kyle Lee","Yanshu Li","Enqi Liu"],"record_url":"https://latent-implicit-thinking.github.io/papers/2507.02199/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2507-02199","citation_date":"2025-07-02","json_url":"https://latent-implicit-thinking.github.io/papers/2507.02199/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2507.02199/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2507.02199/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2507.02199/citation.csl.json"},{"id":"2507.06203","title":"A Survey on Latent Reasoning","authors":"Rui-Jie Zhu, Tianhao Peng, Tianhao Cheng, Xingwei Qu, Jinfa Huang, Dawei Zhu, Hao Wang, Kaiwen Xue, Xuanliang Zhang, Yong Shan, Tianle Cai, Taylor Kergan, Assel Kembay, Andrew Smith, Chenghua Lin, Binh Nguyen, Yuqi Pan, Yuhong Chou, Zefan Cai, Zhenhe Wu, Yongchi Zhao, Tianyu Liu, Jian Yang, Wangchunshu Zhou, Chujie Zheng, Chongxuan Li, Yuyin Zhou, Zhoujun Li, Zhaoxiang Zhang, Jiaheng Liu, Ge Zhang, Wenhao Huang, Jason Eshraghian","first_public":"2025-07-08","venue":"arXiv survey","arxiv":"2507.06203","paper_url":"https://arxiv.org/abs/2507.06203","code_url":"https://github.com/multimodal-art-projection/LatentCoT-Horizon","lens":["analysis"],"representation":["survey"],"computation":["survey"],"training":["analysis-only"],"questions":["survey","taxonomy"],"evidence":["survey"],"modality":["language","multimodal"],"summary":"Surveys latent-reasoning methods, evaluation, and applications and accompanies a maintained research bibliography.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Rui-Jie Zhu","Tianhao Peng","Tianhao Cheng","Xingwei Qu","Jinfa Huang","Dawei Zhu","Hao Wang","Kaiwen Xue","Xuanliang Zhang","Yong Shan","Tianle Cai","Taylor Kergan","Assel Kembay","Andrew Smith","Chenghua Lin","Binh Nguyen","Yuqi Pan","Yuhong Chou","Zefan Cai","Zhenhe Wu","Yongchi Zhao","Tianyu Liu","Jian Yang","Wangchunshu Zhou","Chujie Zheng","Chongxuan Li","Yuyin Zhou","Zhoujun Li","Zhaoxiang Zhang","Jiaheng Liu","Ge Zhang","Wenhao Huang","Jason Eshraghian"],"record_url":"https://latent-implicit-thinking.github.io/papers/2507.06203/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2507-06203","citation_date":"2025-07-08","json_url":"https://latent-implicit-thinking.github.io/papers/2507.06203/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2507.06203/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2507.06203/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2507.06203/citation.csl.json"},{"id":"2507.07996","title":"Skip a Layer or Loop it? Test-Time Depth Adaptation of Pretrained LLMs","authors":"Ziyue Li, Yang Li, Tianyi Zhou","first_public":"2025-07-10","venue":"arXiv","arxiv":"2507.07996","paper_url":"https://arxiv.org/abs/2507.07996","lens":["recurrent"],"representation":["hidden-state"],"computation":["depth-wise","recurrent"],"training":["inference-only"],"questions":["capability","efficiency","architecture"],"evidence":["empirical"],"modality":["language"],"summary":"Adapts the depth of pretrained language models at test time by selectively skipping or repeating layers.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Ziyue Li","Yang Li","Tianyi Zhou"],"record_url":"https://latent-implicit-thinking.github.io/papers/2507.07996/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2507-07996","citation_date":"2025-07-10","json_url":"https://latent-implicit-thinking.github.io/papers/2507.07996/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2507.07996/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2507.07996/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2507.07996/citation.csl.json"},{"id":"2507.10524","title":"Mixture-of-Recursions: Learning Dynamic Recursive Depths for Adaptive Token-Level Computation","authors":"Sangmin Bae, Yujin Kim, Reza Bayat, Sungnyun Kim, Jiyoun Ha, Tal Schuster, Adam Fisch, Hrayr Harutyunyan, Ziwei Ji, Aaron Courville, Se-Young Yun","first_public":"2025-07-14","venue":"arXiv","arxiv":"2507.10524","paper_url":"https://arxiv.org/abs/2507.10524","code_url":"https://github.com/raymin0223/mixture_of_recursions","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["pretraining"],"questions":["efficiency","architecture","scaling"],"evidence":["empirical","scaling"],"modality":["language"],"summary":"Learns token-level routing across recursive depths so different positions can receive different amounts of internal computation.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Sangmin Bae","Yujin Kim","Reza Bayat","Sungnyun Kim","Jiyoun Ha","Tal Schuster","Adam Fisch","Hrayr Harutyunyan","Ziwei Ji","Aaron Courville","Se-Young Yun"],"record_url":"https://latent-implicit-thinking.github.io/papers/2507.10524/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2507-10524","citation_date":"2025-07-14","json_url":"https://latent-implicit-thinking.github.io/papers/2507.10524/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2507.10524/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2507.10524/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2507.10524/citation.csl.json"},{"id":"2508.00574","title":"SynAdapt: Learning Adaptive Reasoning in Large Language Models via Synthetic Continuous Chain-of-Thought","authors":"Jianwei Wang, Ziming Wu, Fuming Lai, Shaobing Lian, Ziqian Zeng","first_public":"2025-08-01","venue":"arXiv","arxiv":"2508.00574","paper_url":"https://arxiv.org/abs/2508.00574","lens":["continuous"],"representation":["continuous-state"],"computation":["token-wise"],"training":["supervised"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["language"],"summary":"Uses synthetic continuous reasoning trajectories to train language models to allocate internal reasoning adaptively.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Jianwei Wang","Ziming Wu","Fuming Lai","Shaobing Lian","Ziqian Zeng"],"record_url":"https://latent-implicit-thinking.github.io/papers/2508.00574/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2508-00574","citation_date":"2025-08-01","json_url":"https://latent-implicit-thinking.github.io/papers/2508.00574/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2508.00574/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2508.00574/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2508.00574/citation.csl.json"},{"id":"2508.03440","title":"LLMs are Single-threaded Reasoners: Demystifying the Working Mechanism of Soft Thinking","authors":"Junhong Wu, Jinliang Lu, Zixuan Ren, Gangqiang Hu, Zhi Wu, Dai Dai, Hua Wu","first_public":"2025-08-05","added_at":"2026-10-18","venue":"arXiv","arxiv":"2508.03440","paper_url":"https://arxiv.org/abs/2508.03440","lens":["analysis","continuous"],"representation":["continuous-state"],"computation":["token-wise"],"training":["analysis-only","inference-only"],"questions":["interpretability","limitations","capability"],"evidence":["probing","empirical","boundary"],"modality":["language","symbolic"],"summary":"Probes soft-token reasoning and finds that tested models often follow the highest-probability component rather than exploring several paths at once. Introduces stochastic soft thinking, including Gumbel-Softmax sampling, to reduce this greedy behavior.","provenance":"Awesome-Latent-CoT; primary sources checked 2026-10-18","author_names":["Junhong Wu","Jinliang Lu","Zixuan Ren","Gangqiang Hu","Zhi Wu","Dai Dai","Hua Wu"],"record_url":"https://latent-implicit-thinking.github.io/papers/2508.03440/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2508-03440","citation_date":"2025-08-05","json_url":"https://latent-implicit-thinking.github.io/papers/2508.03440/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2508.03440/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2508.03440/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2508.03440/citation.csl.json"},{"id":"2509.02350","title":"Implicit Reasoning in Large Language Models: A Comprehensive Survey","authors":"Jindong Li, Yali Fu, Li Fan, Jiahong Liu, Yao Shu, Chengwei Qin, Menglin Yang, Irwin King, Rex Ying","first_public":"2025-09-02","venue":"arXiv survey","arxiv":"2509.02350","paper_url":"https://arxiv.org/abs/2509.02350","code_url":"https://github.com/digailab/awesome-llm-implicit-reasoning","lens":["analysis"],"representation":["survey"],"computation":["survey"],"training":["analysis-only"],"questions":["survey","taxonomy"],"evidence":["survey"],"modality":["language"],"summary":"Organizes implicit-reasoning research across model mechanisms, training methods, evaluation, and applications.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Jindong Li","Yali Fu","Li Fan","Jiahong Liu","Yao Shu","Chengwei Qin","Menglin Yang","Irwin King","Rex Ying"],"record_url":"https://latent-implicit-thinking.github.io/papers/2509.02350/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2509-02350","citation_date":"2025-09-02","json_url":"https://latent-implicit-thinking.github.io/papers/2509.02350/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2509.02350/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2509.02350/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2509.02350/citation.csl.json"},{"id":"2509.20317","title":"SIM-CoT: Supervised Implicit Chain-of-Thought","authors":"Xilin Wei, Xiaoran Liu, Yuhang Zang, Xiaoyi Dong, Yuhang Cao, Jiaqi Wang, Xipeng Qiu, Dahua Lin","first_public":"2025-09-24","venue":"arXiv","arxiv":"2509.20317","paper_url":"https://arxiv.org/abs/2509.20317","code_url":"https://github.com/InternLM/SIM-CoT","lens":["continuous","internalized"],"representation":["continuous-state"],"computation":["token-wise"],"training":["supervised","distillation"],"questions":["capability","efficiency","interpretability"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Trains continuous intermediate states with explicit supervision so reasoning can proceed without emitting a full textual trace.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Xilin Wei","Xiaoran Liu","Yuhang Zang","Xiaoyi Dong","Yuhang Cao","Jiaqi Wang","Xipeng Qiu","Dahua Lin"],"record_url":"https://latent-implicit-thinking.github.io/papers/2509.20317/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2509-20317","citation_date":"2025-09-24","json_url":"https://latent-implicit-thinking.github.io/papers/2509.20317/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2509.20317/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2509.20317/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2509.20317/citation.csl.json"},{"id":"2510.04573","title":"LaDiR: Latent Diffusion Enhances LLMs for Text Reasoning","authors":"Haoqiang Kang, Yizhe Zhang, Nikki Lijing Kuang, Nicklas Majamaki, Navdeep Jaitly, Yi-An Ma, Lianhui Qin","first_public":"2025-10-06","added_at":"2026-10-18","venue":"arXiv","arxiv":"2510.04573","paper_url":"https://arxiv.org/abs/2510.04573","lens":["continuous","beyond-sequential"],"representation":["continuous-state"],"computation":["diffusion"],"training":["supervised"],"questions":["architecture","capability","scaling"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Uses a variational autoencoder to compress textual reasoning steps into blocks of continuous states. A diffusion model repeatedly revises each block before generating the next, then produces a textual answer; diversity guidance encourages alternative reasoning trajectories.","provenance":"Awesome-Latent-CoT; primary sources checked 2026-10-18","author_names":["Haoqiang Kang","Yizhe Zhang","Nikki Lijing Kuang","Nicklas Majamaki","Navdeep Jaitly","Yi-An Ma","Lianhui Qin"],"record_url":"https://latent-implicit-thinking.github.io/papers/2510.04573/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2510-04573","citation_date":"2025-10-06","json_url":"https://latent-implicit-thinking.github.io/papers/2510.04573/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2510.04573/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2510.04573/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2510.04573/citation.csl.json"},{"id":"2510.15522","title":"LLM Latent Reasoning as Chain of Superposition","authors":"Jingcheng Deng, Liang Pang, Zihao Wei, Shicheng Xu, Zenghao Duan, Kun Xu, Yang Song, Huawei Shen, Xueqi Cheng","first_public":"2025-10-17","venue":"arXiv","arxiv":"2510.15522","paper_url":"https://arxiv.org/abs/2510.15522","code_url":"https://github.com/DJC-GO-SOLO/Latent-SFT","lens":["continuous"],"representation":["text-latent-hybrid","continuous-state"],"computation":["token-wise","parallel"],"training":["supervised"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["language"],"summary":"Models latent reasoning as a sequence of superposed token distributions and trains the process with supervised fine-tuning.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Jingcheng Deng","Liang Pang","Zihao Wei","Shicheng Xu","Zenghao Duan","Kun Xu","Yang Song","Huawei Shen","Xueqi Cheng"],"record_url":"https://latent-implicit-thinking.github.io/papers/2510.15522/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2510-15522","citation_date":"2025-10-17","json_url":"https://latent-implicit-thinking.github.io/papers/2510.15522/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2510.15522/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2510.15522/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2510.15522/citation.csl.json"},{"id":"2510.24940","title":"SemCoT: Accelerating Chain-of-Thought Reasoning through Semantically-Aligned Implicit Tokens","authors":"Yinhan He, Wendy Zheng, Yaochen Zhu, Zaiyi Zheng, Lin Su, Sriram Vasudevan, Qi Guo, Liangjie Hong, Jundong Li","first_public":"2025-10-28","venue":"arXiv","arxiv":"2510.24940","paper_url":"https://arxiv.org/abs/2510.24940","code_url":"https://github.com/YinhanHe123/SemCoT","lens":["internalized","continuous"],"representation":["continuous-state"],"computation":["token-wise"],"training":["distillation","supervised"],"questions":["efficiency","capability","interpretability"],"evidence":["empirical"],"modality":["language"],"summary":"Compresses textual reasoning into semantically aligned implicit tokens intended to preserve useful intermediate computation with fewer generated steps.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Yinhan He","Wendy Zheng","Yaochen Zhu","Zaiyi Zheng","Lin Su","Sriram Vasudevan","Qi Guo","Liangjie Hong","Jundong Li"],"record_url":"https://latent-implicit-thinking.github.io/papers/2510.24940/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2510-24940","citation_date":"2025-10-28","json_url":"https://latent-implicit-thinking.github.io/papers/2510.24940/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2510.24940/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2510.24940/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2510.24940/citation.csl.json"},{"id":"2510.25741","title":"Scaling Latent Reasoning via Looped Language Models","authors":"Rui-Jie Zhu, Zixuan Wang, Kai Hua, Tianyu Zhang, Ziniu Li, Haoran Que, Boyi Wei, Zixin Wen, Fan Yin, He Xing, Lu Li, Jiajun Shi, Kaijing Ma, Shanda Li, Taylor Kergan, Andrew Smith, Xingwei Qu, Mude Hui, Bohong Wu, Qiyang Min, Hongzhi Huang, Xun Zhou, Wei Ye, Jiaheng Liu, Jian Yang, Yunfeng Shi, Chenghua Lin, Enduo Zhao, Tianle Cai, Ge Zhang, Wenhao Huang, Yoshua Bengio, Jason Eshraghian","first_public":"2025-10-29","venue":"arXiv","arxiv":"2510.25741","paper_url":"https://arxiv.org/abs/2510.25741","code_url":"https://ouro-llm.github.io/","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["pretraining"],"questions":["capability","scaling","efficiency"],"evidence":["empirical","scaling"],"modality":["language"],"summary":"Scales looped language models that reuse layers across recurrent depth and studies how performance changes with additional internal computation.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Rui-Jie Zhu","Zixuan Wang","Kai Hua","Tianyu Zhang","Ziniu Li","Haoran Que","Boyi Wei","Zixin Wen","Fan Yin","He Xing","Lu Li","Jiajun Shi","Kaijing Ma","Shanda Li","Taylor Kergan","Andrew Smith","Xingwei Qu","Mude Hui","Bohong Wu","Qiyang Min","Hongzhi Huang","Xun Zhou","Wei Ye","Jiaheng Liu","Jian Yang","Yunfeng Shi","Chenghua Lin","Enduo Zhao","Tianle Cai","Ge Zhang","Wenhao Huang","Yoshua Bengio","Jason Eshraghian"],"record_url":"https://latent-implicit-thinking.github.io/papers/2510.25741/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2510-25741","citation_date":"2025-10-29","json_url":"https://latent-implicit-thinking.github.io/papers/2510.25741/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2510.25741/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2510.25741/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2510.25741/citation.csl.json"},{"id":"2511.07384","title":"Teaching Pretrained Language Models to Think Deeper with Retrofitted Recurrence","authors":"Sean McLeish, Ang Li, John Kirchenbauer, Dayal Singh Kalra, Brian R. Bartoldson, Bhavya Kailkhura, Avi Schwarzschild, Jonas Geiping, Tom Goldstein, Micah Goldblum","first_public":"2025-11-10","venue":"arXiv","arxiv":"2511.07384","paper_url":"https://arxiv.org/abs/2511.07384","code_url":"https://github.com/mcleish7/retrofitting-recurrence","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["curriculum"],"questions":["capability","efficiency","architecture"],"evidence":["empirical"],"modality":["language"],"summary":"Adds recurrent depth to pretrained language models and trains them to use repeated internal computation without pretraining from scratch.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Sean McLeish","Ang Li","John Kirchenbauer","Dayal Singh Kalra","Brian R. Bartoldson","Bhavya Kailkhura","Avi Schwarzschild","Jonas Geiping","Tom Goldstein","Micah Goldblum"],"record_url":"https://latent-implicit-thinking.github.io/papers/2511.07384/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2511-07384","citation_date":"2025-11-10","json_url":"https://latent-implicit-thinking.github.io/papers/2511.07384/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2511.07384/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2511.07384/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2511.07384/citation.csl.json"},{"id":"2511.08577","title":"Think-at-Hard: Dynamic Looped Transformers for Improved Reasoning","authors":"Tianyu Fu, Yichen You, Zekai Chen, Guohao Dai, Huazhong Yang, Yu Wang","first_public":"2025-11-11","venue":"arXiv","arxiv":"2511.08577","paper_url":"https://arxiv.org/abs/2511.08577","code_url":"https://github.com/thu-nics/TaH","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["supervised"],"questions":["capability","efficiency","controllability"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Uses dynamic looping to vary internal depth with problem difficulty and studies the resulting reasoning and efficiency trade-offs.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Tianyu Fu","Yichen You","Zekai Chen","Guohao Dai","Huazhong Yang","Yu Wang"],"record_url":"https://latent-implicit-thinking.github.io/papers/2511.08577/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2511-08577","citation_date":"2025-11-11","json_url":"https://latent-implicit-thinking.github.io/papers/2511.08577/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2511.08577/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2511.08577/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2511.08577/citation.csl.json"},{"id":"2511.21581","title":"Learning When to Stop: Adaptive Latent Reasoning via Reinforcement Learning","authors":"Alex Ning, Yen-Ling Kuo, Gabe Gomes","first_public":"2025-11-26","venue":"arXiv","arxiv":"2511.21581","paper_url":"https://arxiv.org/abs/2511.21581","code_url":"https://github.com/apning/adaptive-latent-reasoning","lens":["continuous"],"representation":["continuous-state"],"computation":["recurrent","token-wise"],"training":["reinforcement-learning"],"questions":["efficiency","controllability","capability"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Learns a stopping policy for continuous latent reasoning so the model can allocate a variable number of internal steps.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Alex Ning","Yen-Ling Kuo","Gabe Gomes"],"record_url":"https://latent-implicit-thinking.github.io/papers/2511.21581/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2511-21581","citation_date":"2025-11-26","json_url":"https://latent-implicit-thinking.github.io/papers/2511.21581/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2511.21581/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2511.21581/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2511.21581/citation.csl.json"},{"id":"2512.21711","title":"Do Latent Tokens Think? A Causal and Adversarial Analysis of Chain-of-Continuous-Thought","authors":"Yuyi Zhang, Boyu Tang, Tianjie Ju, Sufeng Duan, Gongshen Liu","first_public":"2025-12-25","added_at":"2026-10-18","venue":"arXiv","arxiv":"2512.21711","paper_url":"https://arxiv.org/abs/2512.21711","lens":["analysis","continuous"],"representation":["continuous-state"],"computation":["token-wise"],"training":["analysis-only"],"questions":["interpretability","evaluation","limitations"],"evidence":["empirical","mechanistic","boundary"],"modality":["language"],"summary":"Tests COCONUT with latent-state interventions and deliberately biased examples on MMLU and HotpotQA. Finds weak sensitivity to steering and dependence on dataset shortcuts in the evaluated models, challenging whether their intermediate states faithfully carry the reasoning.","provenance":"Awesome-Latent-CoT; primary sources checked 2026-10-18","author_names":["Yuyi Zhang","Boyu Tang","Tianjie Ju","Sufeng Duan","Gongshen Liu"],"record_url":"https://latent-implicit-thinking.github.io/papers/2512.21711/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2512-21711","citation_date":"2025-12-25","json_url":"https://latent-implicit-thinking.github.io/papers/2512.21711/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2512.21711/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2512.21711/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2512.21711/citation.csl.json"},{"id":"2601.21358","title":"Latent Chain-of-Thought as Planning: Decoupling Reasoning from Verbalization","authors":"Jiecong Wang, Hao Peng, Zhanyi Wang, Chunyang Liu, Guanlin Wu","first_public":"2026-01-29","venue":"arXiv","arxiv":"2601.21358","paper_url":"https://arxiv.org/abs/2601.21358","code_url":"https://github.com/yunsaijc/PLaT","lens":["continuous"],"representation":["continuous-state","text-latent-hybrid"],"computation":["recurrent","token-wise"],"training":["supervised"],"questions":["capability","controllability","interpretability"],"evidence":["empirical"],"modality":["language"],"summary":"Separates an internal planning process from verbalization and studies whether the latent plan supports effective downstream reasoning.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Jiecong Wang","Hao Peng","Zhanyi Wang","Chunyang Liu","Guanlin Wu"],"record_url":"https://latent-implicit-thinking.github.io/papers/2601.21358/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2601-21358","citation_date":"2026-01-29","json_url":"https://latent-implicit-thinking.github.io/papers/2601.21358/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2601.21358/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2601.21358/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2601.21358/citation.csl.json"},{"id":"2601.21576","title":"Chain Of Thought Compression: A Theoretical Analysis","authors":"Juncai Li, Ru Li, Yuxiang Zhou, Boxiang Ma, Jeff Z. Pan","first_public":"2026-01-29","added_at":"2026-10-18","venue":"arXiv","arxiv":"2601.21576","paper_url":"https://arxiv.org/abs/2601.21576","lens":["analysis","internalized","learned-tokens"],"representation":["hidden-state"],"computation":["depth-wise"],"training":["supervised","distillation"],"questions":["theory","evaluation","limitations","efficiency"],"evidence":["formal","empirical","boundary"],"modality":["language","symbolic"],"summary":"Analyzes how skipping intermediate steps weakens learning signals in a simplified parity-task model. Introduces NatBool-DAG to test logical dependencies and ALiCoT, which supervises learned token states with intermediate logical labels or explicit-CoT representations.","provenance":"Awesome-Latent-CoT; primary sources checked 2026-10-18","author_names":["Juncai Li","Ru Li","Yuxiang Zhou","Boxiang Ma","Jeff Z. Pan"],"record_url":"https://latent-implicit-thinking.github.io/papers/2601.21576/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2601-21576","citation_date":"2026-01-29","json_url":"https://latent-implicit-thinking.github.io/papers/2601.21576/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2601.21576/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2601.21576/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2601.21576/citation.csl.json"},{"id":"2601.21598","title":"Beyond Imitation: Reinforcement Learning for Active Latent Planning","authors":"Zhi Zheng, Wee Sun Lee","first_public":"2026-01-29","venue":"arXiv","arxiv":"2601.21598","paper_url":"https://arxiv.org/abs/2601.21598","code_url":"https://github.com/zz1358m/ATP-Latent-master","lens":["continuous"],"representation":["continuous-state"],"computation":["recurrent","token-wise"],"training":["reinforcement-learning"],"questions":["capability","controllability"],"evidence":["empirical"],"modality":["language"],"summary":"Uses reinforcement learning to train an active latent-planning process rather than only imitating supervised reasoning traces.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Zhi Zheng","Wee Sun Lee"],"record_url":"https://latent-implicit-thinking.github.io/papers/2601.21598/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2601-21598","citation_date":"2026-01-29","json_url":"https://latent-implicit-thinking.github.io/papers/2601.21598/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2601.21598/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2601.21598/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2601.21598/citation.csl.json"},{"id":"2602.00449","title":"Do Latent-CoT Models Think Step-by-Step? A Mechanistic Study on Sequential Reasoning Tasks","authors":"Jia Liang, Liangming Pan","first_public":"2026-01-31","venue":"arXiv","arxiv":"2602.00449","paper_url":"https://arxiv.org/abs/2602.00449","code_url":"https://github.com/jialiang19/latent-cot-thinking","lens":["analysis","continuous"],"representation":["continuous-state"],"computation":["token-wise"],"training":["analysis-only"],"questions":["interpretability","limitations","evaluation"],"evidence":["empirical","mechanistic","probing"],"modality":["symbolic"],"summary":"Uses mechanistic interventions on sequential tasks to test whether latent chain-of-thought models actually execute stepwise internal procedures.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Jia Liang","Liangming Pan"],"record_url":"https://latent-implicit-thinking.github.io/papers/2602.00449/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2602-00449","citation_date":"2026-01-31","json_url":"https://latent-implicit-thinking.github.io/papers/2602.00449/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2602.00449/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2602.00449/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2602.00449/citation.csl.json"},{"id":"2602.01148","title":"Capabilities and Fundamental Limits of Latent Chain-of-Thought","authors":"Jiaxuan Zou, Yaozhong Xiong, Yong Liu","first_public":"2026-02-01","venue":"arXiv","arxiv":"2602.01148","paper_url":"https://arxiv.org/abs/2602.01148","lens":["analysis","continuous"],"representation":["continuous-state"],"computation":["recurrent","parallel"],"training":["analysis-only"],"questions":["theory","capability","limitations"],"evidence":["formal","empirical","boundary"],"modality":["symbolic"],"summary":"Characterizes tasks that latent chain-of-thought can express and identifies theoretical and empirical limits of the approach.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Jiaxuan Zou","Yaozhong Xiong","Yong Liu"],"record_url":"https://latent-implicit-thinking.github.io/papers/2602.01148/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2602-01148","citation_date":"2026-02-01","json_url":"https://latent-implicit-thinking.github.io/papers/2602.01148/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2602.01148/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2602.01148/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2602.01148/citation.csl.json"},{"id":"2602.08332","title":"Latent Reasoning with Supervised Thinking States","authors":"Ido Amos, Avi Caciularu, Mor Geva, Amir Globerson, Jonathan Herzig, Lior Shani, Idan Szpektor","first_public":"2026-02-09","venue":"arXiv","arxiv":"2602.08332","paper_url":"https://arxiv.org/abs/2602.08332","lens":["learned-tokens","continuous"],"representation":["text-latent-hybrid","continuous-state"],"computation":["token-wise","recurrent"],"training":["supervised"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["language"],"summary":"Supervises intermediate thinking states that bridge textual reasoning traces and latent computation.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Ido Amos","Avi Caciularu","Mor Geva","Amir Globerson","Jonathan Herzig","Lior Shani","Idan Szpektor"],"record_url":"https://latent-implicit-thinking.github.io/papers/2602.08332/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2602-08332","citation_date":"2026-02-09","json_url":"https://latent-implicit-thinking.github.io/papers/2602.08332/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2602.08332/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2602.08332/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2602.08332/citation.csl.json"},{"id":"2602.11683","title":"ThinkRouter: Efficient Reasoning via Routing Thinking between Latent and Discrete Spaces","authors":"Xin Xu, Tong Yu, Xiang Chen, Haoliang Wang, Julian McAuley, Saayan Mitra","first_public":"2026-02-12","venue":"arXiv, work in progress","arxiv":"2602.11683","paper_url":"https://arxiv.org/abs/2602.11683","lens":["continuous","learned-tokens"],"representation":["text-latent-hybrid","continuous-state"],"computation":["token-wise"],"training":["inference-only"],"questions":["capability","efficiency","controllability"],"evidence":["empirical"],"modality":["language"],"summary":"Routes intermediate computation between latent and discrete representations to trade off reasoning quality, readability, and token cost.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Xin Xu","Tong Yu","Xiang Chen","Haoliang Wang","Julian McAuley","Saayan Mitra"],"record_url":"https://latent-implicit-thinking.github.io/papers/2602.11683/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2602-11683","citation_date":"2026-02-12","json_url":"https://latent-implicit-thinking.github.io/papers/2602.11683/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2602.11683/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2602.11683/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2602.11683/citation.csl.json"},{"id":"2603.02023","title":"PonderLM-3: Adaptive Token-Wise Pondering with Differentiable Masking","authors":"He Li, Feichen Song, Boyi Zeng, Shixiang Song, Zhiqin John Xu, Ziwei He, Zhouhan Lin","first_public":"2026-03-02","venue":"arXiv","arxiv":"2603.02023","paper_url":"https://arxiv.org/abs/2603.02023","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent","token-wise"],"training":["pretraining"],"questions":["efficiency","controllability","scaling"],"evidence":["empirical","scaling"],"modality":["language"],"summary":"Uses differentiable masks to allocate a variable number of recurrent pondering steps to different token positions.","provenance":"Primary-source literature search, 2026-09-04","author_names":["He Li","Feichen Song","Boyi Zeng","Shixiang Song","Zhiqin John Xu","Ziwei He","Zhouhan Lin"],"record_url":"https://latent-implicit-thinking.github.io/papers/2603.02023/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2603-02023","citation_date":"2026-03-02","json_url":"https://latent-implicit-thinking.github.io/papers/2603.02023/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2603.02023/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2603.02023/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2603.02023/citation.csl.json"},{"id":"2604.02371","title":"Internalized Reasoning for Long-Context Visual Document Understanding","authors":"Austin Veselka","first_public":"2026-03-31","added_at":"2026-10-18","venue":"arXiv","arxiv":"2604.02371","paper_url":"https://arxiv.org/abs/2604.02371","lens":["internalized"],"representation":["hidden-state"],"computation":["depth-wise"],"training":["supervised"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["multimodal","vision","language"],"summary":"Trains on synthetic traces that rank document pages and extract relevant evidence, then uses low-strength model merging to internalize the trained reasoning behavior. Compares answering with and without written reasoning on long visual documents.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Austin Veselka"],"record_url":"https://latent-implicit-thinking.github.io/papers/2604.02371/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2604-02371","citation_date":"2026-03-31","json_url":"https://latent-implicit-thinking.github.io/papers/2604.02371/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2604.02371/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2604.02371/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2604.02371/citation.csl.json"},{"id":"2604.24881","title":"Latent Agents: A Post-Training Procedure for Internalized Multi-Agent Debate","authors":"John Seon Keun Yi, Aaron Mueller, Dokyun Lee","first_public":"2026-04-27","venue":"arXiv","arxiv":"2604.24881","paper_url":"https://arxiv.org/abs/2604.24881","code_url":"https://github.com/johnsk95/latent_agents","lens":["internalized"],"representation":["hidden-state"],"computation":["depth-wise"],"training":["reinforcement-learning","distillation"],"questions":["capability","efficiency","interpretability","controllability"],"evidence":["empirical","mechanistic"],"modality":["language"],"summary":"Post-trains a single model to internalize the computation of a multi-agent debate rather than emitting the debate as text.","provenance":"Primary-source literature search, 2026-09-04","author_names":["John Seon Keun Yi","Aaron Mueller","Dokyun Lee"],"record_url":"https://latent-implicit-thinking.github.io/papers/2604.24881/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2604-24881","citation_date":"2026-04-27","json_url":"https://latent-implicit-thinking.github.io/papers/2604.24881/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2604.24881/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2604.24881/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2604.24881/citation.csl.json"},{"id":"2605.28600","title":"Transformers Provably Learn to Internalize Chain-of-Thought","authors":"Yixiao Huang, Hanlin Zhu, Zixuan Wang, Jiantao Jiao, Stuart Russell, Somayeh Sojoudi, Song Mei","first_public":"2026-05-27","venue":"arXiv","arxiv":"2605.28600","paper_url":"https://arxiv.org/abs/2605.28600","lens":["internalized","analysis"],"representation":["hidden-state"],"computation":["depth-wise"],"training":["curriculum"],"questions":["theory","capability"],"evidence":["formal","empirical"],"modality":["symbolic"],"summary":"Provides theoretical and empirical results on when transformers trained with a curriculum learn to internalize explicit reasoning steps.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Yixiao Huang","Hanlin Zhu","Zixuan Wang","Jiantao Jiao","Stuart Russell","Somayeh Sojoudi","Song Mei"],"record_url":"https://latent-implicit-thinking.github.io/papers/2605.28600/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2605-28600","citation_date":"2026-05-27","json_url":"https://latent-implicit-thinking.github.io/papers/2605.28600/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2605.28600/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2605.28600/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2605.28600/citation.csl.json"},{"id":"2606.01243","title":"Unlocking the Black Box of Latent Reasoning: An Interpretability-Guided Approach to Intervention","authors":"Shuochen Chang, Tong Bai, Xiaofeng Zhang, Qianli Ma, Qingyang Liu, Zhaohe Liao, Yibo Miao, Li Niu","first_public":"2026-05-31","added_at":"2026-10-18","venue":"ACL 2026","arxiv":"2606.01243","paper_url":"https://arxiv.org/abs/2606.01243","lens":["analysis","continuous"],"representation":["continuous-state"],"computation":["token-wise"],"training":["supervised","test-time-optimization"],"questions":["interpretability","controllability","capability"],"evidence":["probing","mechanistic","empirical"],"modality":["language","symbolic"],"summary":"Uses probes, ablations, and targeted edits to study how continuous reasoning states affect answers. Builds interventions from learned semantic mappings and geometric constraints, improving the evaluated models by editing their latent states without updating base-model weights.","provenance":"Awesome-Latent-CoT; primary sources checked 2026-10-18","author_names":["Shuochen Chang","Tong Bai","Xiaofeng Zhang","Qianli Ma","Qingyang Liu","Zhaohe Liao","Yibo Miao","Li Niu"],"record_url":"https://latent-implicit-thinking.github.io/papers/2606.01243/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2606-01243","citation_date":"2026-05-31","json_url":"https://latent-implicit-thinking.github.io/papers/2606.01243/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2606.01243/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2606.01243/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2606.01243/citation.csl.json"},{"id":"2606.12689","title":"Observable Patterns Are Not Explanations: A Causal-Geometric Analysis of Latent Reasoning Models","authors":"Darpan Aswal, Thomas Palmeira Ferraz, Yongxin Zhou, Maxime Peyrard","first_public":"2026-06-10","added_at":"2026-10-18","venue":"arXiv","arxiv":"2606.12689","paper_url":"https://arxiv.org/abs/2606.12689","lens":["analysis","continuous"],"representation":["continuous-state"],"computation":["token-wise"],"training":["analysis-only"],"questions":["interpretability","evaluation","limitations"],"evidence":["empirical","mechanistic","probing","boundary"],"modality":["language","symbolic"],"summary":"Compares Coconut and CODI with controls lacking their proposed reasoning recurrence or curriculum. Finds that decodable patterns can also appear in controls, while interventions reveal varying causal use of latent states concentrated in low-dimensional directions.","provenance":"Awesome-Latent-CoT; primary sources checked 2026-10-18","author_names":["Darpan Aswal","Thomas Palmeira Ferraz","Yongxin Zhou","Maxime Peyrard"],"record_url":"https://latent-implicit-thinking.github.io/papers/2606.12689/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2606-12689","citation_date":"2026-06-10","json_url":"https://latent-implicit-thinking.github.io/papers/2606.12689/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2606.12689/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2606.12689/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2606.12689/citation.csl.json"},{"id":"2606.13106","title":"Demystifying Hidden-State Recurrence: Switchable Latent Reasoning with On-Policy Reinforcement Learning","authors":"Jiayu Yang, Chao Chen, Shengen Wu, Yinhong Liu, Yuxuan Fan, Lujundong Li, Songning Lai, Chengwei Qin, Zhijiang Guo","first_public":"2026-06-11","venue":"arXiv","arxiv":"2606.13106","paper_url":"https://arxiv.org/abs/2606.13106","lens":["continuous","recurrent","analysis"],"representation":["continuous-state","text-latent-hybrid"],"computation":["recurrent","token-wise"],"training":["reinforcement-learning","curriculum"],"questions":["capability","interpretability","controllability"],"evidence":["empirical","mechanistic"],"modality":["language"],"summary":"Trains switchable hidden-state recurrence with on-policy reinforcement learning and analyzes how the internal loop contributes to reasoning.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Jiayu Yang","Chao Chen","Shengen Wu","Yinhong Liu","Yuxuan Fan","Lujundong Li","Songning Lai","Chengwei Qin","Zhijiang Guo"],"record_url":"https://latent-implicit-thinking.github.io/papers/2606.13106/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2606-13106","citation_date":"2026-06-11","json_url":"https://latent-implicit-thinking.github.io/papers/2606.13106/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2606.13106/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2606.13106/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2606.13106/citation.csl.json"},{"id":"2606.18206","title":"Fixed-Point Reasoners: Stable and Adaptive Deep Looped Transformers","authors":"Sajad Movahedi, Vera Milovanović, Shlomo Libo Feigin, Alexander Theus, Thomas Hofmann, Valentina Boeva, T. Konstantin Rusch, Antonio Orvieto","first_public":"2026-06-16","venue":"arXiv","arxiv":"2606.18206","paper_url":"https://arxiv.org/abs/2606.18206","code_url":"https://github.com/nilskiKonjIzDunava/fprm","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["supervised"],"questions":["capability","efficiency","architecture","controllability"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Stabilizes repeated transformer layers and stops looping when the hidden state converges, allowing the model to spend different amounts of computation on different problems.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Sajad Movahedi","Vera Milovanović","Shlomo Libo Feigin","Alexander Theus","Thomas Hofmann","Valentina Boeva","T. Konstantin Rusch","Antonio Orvieto"],"record_url":"https://latent-implicit-thinking.github.io/papers/2606.18206/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2606-18206","citation_date":"2026-06-16","json_url":"https://latent-implicit-thinking.github.io/papers/2606.18206/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2606.18206/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2606.18206/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2606.18206/citation.csl.json"},{"id":"2606.20075","title":"What Makes Effective Supervision in Latent Chain-of-Thought: An Information-Theoretic Analysis","authors":"Xinghao Chen, Chak Tou Leong, Wenjin Guo, Jian Wang, Wenjie Li, Xiaoyu Shen","first_public":"2026-06-18","venue":"arXiv","arxiv":"2606.20075","paper_url":"https://arxiv.org/abs/2606.20075","code_url":"https://github.com/EIT-NLP/Supervision-in-Latent-CoT","lens":["analysis","continuous"],"representation":["continuous-state"],"computation":["token-wise"],"training":["analysis-only"],"questions":["theory","interpretability","limitations"],"evidence":["formal","empirical"],"modality":["language","symbolic"],"summary":"Uses information-theoretic analysis to study which supervision signals make latent chain-of-thought training effective.","provenance":"Primary-source literature search, 2026-09-04","author_names":["Xinghao Chen","Chak Tou Leong","Wenjin Guo","Jian Wang","Wenjie Li","Xiaoyu Shen"],"record_url":"https://latent-implicit-thinking.github.io/papers/2606.20075/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2606-20075","citation_date":"2026-06-18","json_url":"https://latent-implicit-thinking.github.io/papers/2606.20075/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2606.20075/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2606.20075/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2606.20075/citation.csl.json"},{"id":"2607.00341","title":"DiscoLoop: Looping Discrete Embeddings and Continuous Hidden States for Multi-hop Reasoning","authors":"Hengyu Fu, Tianyu Guo, Zixuan Wang, Hanlin Zhu, Jason D. Lee, Jiantao Jiao, Stuart Russell, Song Mei","first_public":"2026-07-01","venue":"arXiv","arxiv":"2607.00341","paper_url":"https://arxiv.org/abs/2607.00341","lens":["recurrent","continuous"],"representation":["discrete-token","continuous-state"],"computation":["recurrent","depth-wise"],"training":["pretraining","supervised"],"questions":["architecture","capability","generalization"],"evidence":["empirical","mechanistic","probing"],"modality":["language","symbolic"],"summary":"Feeds both token embeddings and hidden states back through repeated transformer layers to connect successive steps of multi-hop reasoning.","provenance":"Primary-source literature search, 2026-09-05","author_names":["Hengyu Fu","Tianyu Guo","Zixuan Wang","Hanlin Zhu","Jason D. Lee","Jiantao Jiao","Stuart Russell","Song Mei"],"record_url":"https://latent-implicit-thinking.github.io/papers/2607.00341/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2607-00341","citation_date":"2026-07-01","json_url":"https://latent-implicit-thinking.github.io/papers/2607.00341/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2607.00341/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2607.00341/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2607.00341/citation.csl.json"},{"id":"2608.13570","title":"Think in Latent, Explain in Language: Self-Explainable Latent Reasoning","authors":"Dayuan Zhao, Shengcao Cao, Yu-Xiong Wang, Liang-Yan Gui","first_public":"2026-07-01","venue":"arXiv","arxiv":"2608.13570","paper_url":"https://arxiv.org/abs/2608.13570","code_url":"https://jasondayuan.github.io/SELR/","lens":["continuous","analysis"],"representation":["continuous-state","text-latent-hybrid"],"computation":["token-wise"],"training":["supervised"],"questions":["capability","efficiency","interpretability"],"evidence":["empirical"],"modality":["language","multimodal","vision"],"summary":"Jointly trains latent states for answer prediction and for decoding back into readable reasoning, using one model rather than a separate post-hoc explanation decoder.","provenance":"Primary-source literature search, 2026-09-05","author_names":["Dayuan Zhao","Shengcao Cao","Yu-Xiong Wang","Liang-Yan Gui"],"record_url":"https://latent-implicit-thinking.github.io/papers/2608.13570/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2608-13570","citation_date":"2026-07-01","json_url":"https://latent-implicit-thinking.github.io/papers/2608.13570/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2608.13570/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2608.13570/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2608.13570/citation.csl.json"},{"id":"2607.06648","title":"Final Checkpoints Are Not Enough: Analyzing Latent Reasoning Faithfulness Along Training Trajectories","authors":"Hengyu Jin, Shu Yang, Di Wang","first_public":"2026-07-07","venue":"arXiv","arxiv":"2607.06648","paper_url":"https://arxiv.org/abs/2607.06648","lens":["analysis","continuous"],"representation":["continuous-state"],"computation":["token-wise"],"training":["analysis-only"],"questions":["interpretability","evaluation","limitations"],"evidence":["empirical","mechanistic","boundary"],"modality":["language","symbolic"],"summary":"Tests how answers respond to changed inputs and altered hidden reasoning states throughout training. These responses can change even while accuracy remains high.","provenance":"Primary-source literature search, 2026-09-05","author_names":["Hengyu Jin","Shu Yang","Di Wang"],"record_url":"https://latent-implicit-thinking.github.io/papers/2607.06648/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2607-06648","citation_date":"2026-07-07","json_url":"https://latent-implicit-thinking.github.io/papers/2607.06648/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2607.06648/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2607.06648/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2607.06648/citation.csl.json"},{"id":"2607.15178","title":"T²MLR: Transformer with Temporal Middle-Layer Recurrence","authors":"Ziyang Cai, Xingyu Zhu, Yihe Dong, Yinghui He, Sanjeev Arora","first_public":"2026-07-16","venue":"arXiv","arxiv":"2607.15178","paper_url":"https://arxiv.org/abs/2607.15178","lens":["recurrent"],"representation":["hidden-state","cache-memory"],"computation":["recurrent","stateful","token-wise"],"training":["pretraining","supervised"],"questions":["architecture","capability","efficiency"],"evidence":["empirical"],"modality":["language"],"summary":"Carries a cached middle-layer state from one token position into an earlier layer at the next position, providing localized temporal recurrence that can also be retrofitted into pretrained transformers.","provenance":"Primary-source literature search, 2026-09-05","author_names":["Ziyang Cai","Xingyu Zhu","Yihe Dong","Yinghui He","Sanjeev Arora"],"record_url":"https://latent-implicit-thinking.github.io/papers/2607.15178/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2607-15178","citation_date":"2026-07-16","json_url":"https://latent-implicit-thinking.github.io/papers/2607.15178/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2607.15178/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2607.15178/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2607.15178/citation.csl.json"},{"id":"2607.16972","title":"Training Continuous Chain of Thought Models: A Tale of Two Regimes","authors":"Varun Yerram, He He, Eunsol Choi","first_public":"2026-07-18","venue":"arXiv","arxiv":"2607.16972","paper_url":"https://arxiv.org/abs/2607.16972","code_url":"https://github.com/Varun221/cmtp_research","lens":["continuous","analysis"],"representation":["continuous-state"],"computation":["token-wise"],"training":["supervised"],"questions":["capability","efficiency","evaluation","limitations"],"evidence":["empirical","boundary"],"modality":["language","symbolic"],"summary":"Introduces direct latent supervision through averaged trace embeddings and finds that both direct and indirect continuous-CoT training degrade sharply on tasks with substantially longer reasoning traces.","provenance":"Primary-source literature search, 2026-09-05","author_names":["Varun Yerram","He He","Eunsol Choi"],"record_url":"https://latent-implicit-thinking.github.io/papers/2607.16972/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2607-16972","citation_date":"2026-07-18","json_url":"https://latent-implicit-thinking.github.io/papers/2607.16972/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2607.16972/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2607.16972/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2607.16972/citation.csl.json"},{"id":"2608.02585","title":"GradCuit: Credit-Assigned Gradient Flow Enables Robust and Interpretable Test-Time Latent Reasoning","authors":"Zhaoxin Yu, Qi Shen, Hengli Li, Zhaowei Zhang, Song-Chun Zhu, Chi Zhang, Zilong Zheng","first_public":"2026-08-03","venue":"arXiv","arxiv":"2608.02585","paper_url":"https://arxiv.org/abs/2608.02585","lens":["continuous"],"representation":["continuous-state"],"computation":["token-wise"],"training":["test-time-optimization"],"questions":["capability","scaling","efficiency","interpretability"],"evidence":["empirical","probing"],"modality":["language","symbolic"],"summary":"At test time, adjusts extra hidden states inside the transformer using feedback on generated answers, while keeping the model’s weights fixed.","provenance":"Primary-source literature search, 2026-09-05","author_names":["Zhaoxin Yu","Qi Shen","Hengli Li","Zhaowei Zhang","Song-Chun Zhu","Chi Zhang","Zilong Zheng"],"record_url":"https://latent-implicit-thinking.github.io/papers/2608.02585/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2608-02585","citation_date":"2026-08-03","json_url":"https://latent-implicit-thinking.github.io/papers/2608.02585/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2608.02585/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2608.02585/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2608.02585/citation.csl.json"},{"id":"2608.03624","title":"LoopMTP: A looped transformer guided by latent multi-token prediction","authors":"Behzad Shomali, Markus Frey, David Berghaus, Joachim Koehler, Mehdi Ali","first_public":"2026-08-04","venue":"arXiv","arxiv":"2608.03624","paper_url":"https://arxiv.org/abs/2608.03624","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["pretraining"],"questions":["architecture","capability","scaling"],"evidence":["empirical"],"modality":["language"],"summary":"Trains each transformer loop to anticipate a different future token, using token embeddings to guide its hidden state.","provenance":"Primary-source literature search, 2026-09-05","author_names":["Behzad Shomali","Markus Frey","David Berghaus","Joachim Koehler","Mehdi Ali"],"record_url":"https://latent-implicit-thinking.github.io/papers/2608.03624/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2608-03624","citation_date":"2026-08-04","json_url":"https://latent-implicit-thinking.github.io/papers/2608.03624/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2608.03624/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2608.03624/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2608.03624/citation.csl.json"},{"id":"2608.04928","title":"Does Out-of-Sight Equal Out-of-Mind in CoT Monitorability?","authors":"Pedro Ferreira, Wilker Aziz, Ivan Titov","first_public":"2026-08-05","venue":"arXiv","arxiv":"2608.04928","paper_url":"https://arxiv.org/abs/2608.04928","lens":["analysis","continuous"],"representation":["continuous-state","text-latent-hybrid"],"computation":["token-wise"],"training":["analysis-only"],"questions":["evaluation","interpretability","limitations"],"evidence":["empirical","probing"],"modality":["language","symbolic"],"summary":"Compares monitoring from explicit traces, latent-state probes, and latent verbalizations, finding that monitorability depends strongly on task structure and level of internal access.","provenance":"Primary-source literature search, 2026-09-05","author_names":["Pedro Ferreira","Wilker Aziz","Ivan Titov"],"record_url":"https://latent-implicit-thinking.github.io/papers/2608.04928/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2608-04928","citation_date":"2026-08-05","json_url":"https://latent-implicit-thinking.github.io/papers/2608.04928/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2608.04928/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2608.04928/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2608.04928/citation.csl.json"},{"id":"2608.18222","title":"Think Shallow, Solve Deep: Controlling Recurrent Dynamics for Reliable Test-Time Depth","authors":"Ivan Viakhirev, Kirill Borodin, Amirah Almutairi, Serguei Barannikov, Maxim Abramov, Grach Mkrtchian","first_public":"2026-08-18","venue":"arXiv","arxiv":"2608.18222","paper_url":"https://arxiv.org/abs/2608.18222","lens":["recurrent","analysis"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["supervised","analysis-only"],"questions":["theory","controllability","generalization","limitations"],"evidence":["formal","empirical","boundary"],"modality":["language","symbolic"],"summary":"Studies when extra transformer loops improve an answer or make it worse. Gives a condition under which further loops cannot change the answer, and trains models toward this stable behavior.","provenance":"Primary-source literature search, 2026-09-05","author_names":["Ivan Viakhirev","Kirill Borodin","Amirah Almutairi","Serguei Barannikov","Maxim Abramov","Grach Mkrtchian"],"record_url":"https://latent-implicit-thinking.github.io/papers/2608.18222/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2608-18222","citation_date":"2026-08-18","json_url":"https://latent-implicit-thinking.github.io/papers/2608.18222/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2608.18222/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2608.18222/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2608.18222/citation.csl.json"},{"id":"2608.18230","title":"Allocating Recurrent Compute in Looped Language Models","authors":"Ruhai Lin, Yiyang Guo, Rui-Jie Zhu, Hao Ye, Jason K. Eshraghian","first_public":"2026-08-18","venue":"arXiv","arxiv":"2608.18230","paper_url":"https://arxiv.org/abs/2608.18230","lens":["recurrent","analysis"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["pretraining"],"questions":["architecture","efficiency","capability"],"evidence":["empirical","mechanistic"],"modality":["language"],"summary":"Studies which transformer components should recur and introduces MixerLoop, which repeats the sequence mixer while applying the dense feed-forward component once.","provenance":"Primary-source literature search, 2026-09-05","author_names":["Ruhai Lin","Yiyang Guo","Rui-Jie Zhu","Hao Ye","Jason K. Eshraghian"],"record_url":"https://latent-implicit-thinking.github.io/papers/2608.18230/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2608-18230","citation_date":"2026-08-18","json_url":"https://latent-implicit-thinking.github.io/papers/2608.18230/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2608.18230/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2608.18230/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2608.18230/citation.csl.json"},{"id":"2608.29956","title":"Detecting Hidden Chain-of-Thought in Large Language Models with Linguistic, Behavioral, and Mechanistic Indicators","authors":"Armaan Singh, Ryan Trinh Le, Jasmine Kaur, Abdullah Sultan, Edward Lue Chee Lip, Kiran Nijjer, Adnan Ahmed, Vasu Sharma","first_public":"2026-08-30","venue":"arXiv","arxiv":"2608.29956","paper_url":"https://arxiv.org/abs/2608.29956","lens":["analysis"],"representation":["hidden-state"],"computation":["depth-wise"],"training":["analysis-only"],"questions":["evaluation","interpretability","limitations"],"evidence":["empirical","probing","boundary"],"modality":["language","symbolic"],"summary":"Compares behavior under neutral, explicit-CoT, and no-CoT prompts using linguistic and internal-state measurements. Its score measures resemblance to CoT behavior, not direct evidence of a hidden reasoning trace; calibration controls expose important confounds.","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Armaan Singh","Ryan Trinh Le","Jasmine Kaur","Abdullah Sultan","Edward Lue Chee Lip","Kiran Nijjer","Adnan Ahmed","Vasu Sharma"],"record_url":"https://latent-implicit-thinking.github.io/papers/2608.29956/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2608-29956","citation_date":"2026-08-30","json_url":"https://latent-implicit-thinking.github.io/papers/2608.29956/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2608.29956/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2608.29956/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2608.29956/citation.csl.json"},{"id":"2609.22197","title":"Dissecting Hierarchical Reasoning Models: A Mechanistic Study","authors":"Leo Raphael Rodrigues, Jian Kang","first_public":"2026-08-30","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.22197","paper_url":"https://arxiv.org/abs/2609.22197","lens":["analysis","recurrent"],"representation":["hidden-state"],"computation":["recurrent","hierarchical"],"training":["analysis-only"],"questions":["interpretability","evaluation","limitations"],"evidence":["empirical","mechanistic","probing"],"modality":["symbolic"],"summary":"Uses state interventions, probes, and feature ablations to study how hierarchical recurrent models solve Sudoku, mazes, and ARC tasks. Compares hierarchical and single-state recurrence, and distinguishes information that can be read from a state from information that causally affects an answer.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Leo Raphael Rodrigues","Jian Kang"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.22197/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-22197","citation_date":"2026-08-30","json_url":"https://latent-implicit-thinking.github.io/papers/2609.22197/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.22197/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.22197/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.22197/citation.csl.json"},{"id":"2609.00874","title":"A Score Is Not a Policy: Measuring the Value of Adaptive Revision","authors":"Ayushi Chadha","first_public":"2026-09-01","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.00874","paper_url":"https://arxiv.org/abs/2609.00874","lens":["analysis","recurrent"],"representation":["hidden-state"],"computation":["recurrent","hierarchical"],"training":["analysis-only"],"questions":["evaluation","controllability","limitations"],"evidence":["empirical","mechanistic"],"modality":["symbolic"],"summary":"Tests when a hierarchical reasoner should revise the internal plan guiding its lower-level computation. Compares learned revision schedules with fixed schedules, separating whether a controller responds to its state from whether that response improves decisions.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Ayushi Chadha"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.00874/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-00874","citation_date":"2026-09-01","json_url":"https://latent-implicit-thinking.github.io/papers/2609.00874/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.00874/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.00874/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.00874/citation.csl.json"},{"id":"2609.01117","title":"Latent Recurrent Thoughts: Recurrent Refinement of Proposed Latents for Reasoning with Frozen LLMs","authors":"Zhaoliang Chen, Jie Fu","first_public":"2026-09-01","venue":"arXiv","arxiv":"2609.01117","paper_url":"https://arxiv.org/abs/2609.01117","lens":["continuous","recurrent"],"representation":["continuous-state"],"computation":["recurrent"],"training":["supervised"],"questions":["architecture","capability","efficiency"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Uses a task-specific proposer and small recurrent auxiliary network to iteratively refine continuous thoughts that a frozen language model then decodes.","provenance":"Primary-source literature search, 2026-09-05","author_names":["Zhaoliang Chen","Jie Fu"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.01117/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-01117","citation_date":"2026-09-01","json_url":"https://latent-implicit-thinking.github.io/papers/2609.01117/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.01117/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.01117/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.01117/citation.csl.json"},{"id":"2609.01343","title":"SMELT: Scaling Laws for Compute-Matched MoE Looped Transformers","authors":"Shaowen Wang, Ge Zhang, Kairong Luo, Yuhao Wu, Shaofan Liu, Jiaheng Liu, Wenhao Huang, Shen Yan, Jian Li","first_public":"2026-09-01","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.01343","paper_url":"https://arxiv.org/abs/2609.01343","lens":["recurrent","analysis"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["pretraining"],"questions":["scaling","architecture","efficiency"],"evidence":["empirical","scaling","mechanistic"],"modality":["language"],"summary":"Loops the middle half of a mixture-of-experts transformer twice while matching an unlooped baseline on computation, parameter count, and KV-cache size. Studies how the comparison changes with model scale and examines the attention patterns produced by revisiting layers.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Shaowen Wang","Ge Zhang","Kairong Luo","Yuhao Wu","Shaofan Liu","Jiaheng Liu","Wenhao Huang","Shen Yan","Jian Li"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.01343/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-01343","citation_date":"2026-09-01","json_url":"https://latent-implicit-thinking.github.io/papers/2609.01343/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.01343/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.01343/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.01343/citation.csl.json"},{"id":"2609.01449","title":"Diffusion as a Training Curriculum for Timestep-Free Iterative Reasoning","authors":"Mariia Drozdova, Aidan Sirbu, Pietro Miotti, Robert Obryk, Mayalen Etcheverry, Eyvind Niklasson, Blake Richards","first_public":"2026-09-01","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.01449","paper_url":"https://arxiv.org/abs/2609.01449","lens":["recurrent","beyond-sequential"],"representation":["hidden-state","continuous-state"],"computation":["recurrent","diffusion"],"training":["supervised","curriculum"],"questions":["architecture","generalization","capability"],"evidence":["empirical"],"modality":["symbolic"],"summary":"Turns a diffusion denoiser into a recurrent puzzle solver by adding a persistent hidden state and removing timestep conditioning. Separates the role of denoising during training from the role of repeated updates and noise at inference.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Mariia Drozdova","Aidan Sirbu","Pietro Miotti","Robert Obryk","Mayalen Etcheverry","Eyvind Niklasson","Blake Richards"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.01449/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-01449","citation_date":"2026-09-01","json_url":"https://latent-implicit-thinking.github.io/papers/2609.01449/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.01449/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.01449/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.01449/citation.csl.json"},{"id":"2609.01924","title":"Looped Transformers under the Jacobian Lens: Does the Global Workspace Survive Recurrence?","authors":"Wenlong Wang, Fergal Reid","first_public":"2026-09-01","venue":"arXiv","arxiv":"2609.01924","paper_url":"https://arxiv.org/abs/2609.01924","lens":["analysis","recurrent"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["analysis-only"],"questions":["interpretability","architecture","limitations"],"evidence":["empirical","mechanistic","probing"],"modality":["language"],"summary":"Tracks information that can be decoded from, and altered within, repeated transformer layers. Finds that Ouro reconstructs this information each loop, while Huginn carries it forward.","provenance":"Primary-source literature search, 2026-09-05","author_names":["Wenlong Wang","Fergal Reid"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.01924/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-01924","citation_date":"2026-09-01","json_url":"https://latent-implicit-thinking.github.io/papers/2609.01924/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.01924/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.01924/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.01924/citation.csl.json"},{"id":"2609.03379","title":"RecurTrace: Adaptive Latent Reasoning with Loop-Time Memory","authors":"Yuxiang Wang, Kunyu Feng, Yingda Shen, Haoning Xu, Junyu Wang, Zhizheng Wu","first_public":"2026-09-03","venue":"arXiv","arxiv":"2609.03379","paper_url":"https://arxiv.org/abs/2609.03379","lens":["recurrent"],"representation":["hidden-state","cache-memory"],"computation":["recurrent","depth-wise","stateful"],"training":["supervised"],"questions":["capability","efficiency","controllability","scaling"],"evidence":["empirical","scaling"],"modality":["language","symbolic"],"summary":"Lets looped layers attend to their own earlier iteration states and learns a halting head that allocates recurrent depth per input.","provenance":"Primary-source literature search, 2026-09-05","author_names":["Yuxiang Wang","Kunyu Feng","Yingda Shen","Haoning Xu","Junyu Wang","Zhizheng Wu"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.03379/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-03379","citation_date":"2026-09-03","json_url":"https://latent-implicit-thinking.github.io/papers/2609.03379/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.03379/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.03379/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.03379/citation.csl.json"},{"id":"2609.03807","title":"Almost Free State Prediction Separation","previous_titles":["Free Pause Tokens"],"authors":"John Langford, Nathan Godey, Giovanni Monea, Yoav Artzi, Harry Dong, Ying Fan, Gustavo de Rosa, Zheng Zhan","first_public":"2026-09-03","venue":"arXiv","arxiv":"2609.03807","paper_url":"https://arxiv.org/abs/2609.03807","lens":["learned-tokens","beyond-sequential"],"representation":["hidden-state"],"computation":["parallel","depth-wise"],"training":["pretraining"],"questions":["architecture","capability","efficiency"],"evidence":["empirical"],"modality":["language"],"summary":"Moves pause-token computation into a parallel, weight-shared prediction stream, providing additional internal compute without increasing generated sequence length or key/value-cache length.","provenance":"Primary-source literature search, 2026-09-05","author_names":["John Langford","Nathan Godey","Giovanni Monea","Yoav Artzi","Harry Dong","Ying Fan","Gustavo de Rosa","Zheng Zhan"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.03807/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-03807","citation_date":"2026-09-03","json_url":"https://latent-implicit-thinking.github.io/papers/2609.03807/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.03807/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.03807/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.03807/citation.csl.json"},{"id":"2609.04489","title":"Towards Understanding Pause Token Fine-Tuning Dynamics: A Mode Retention Perspective","authors":"Jaehyeon Kim, Suhwan Kim, Nakyung Lee, Yeongoon Kim, Jimin Seo, Giho Lee, Jungwoo Lee","first_public":"2026-09-03","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.04489","paper_url":"https://arxiv.org/abs/2609.04489","summary":"Places pause tokens at reasoning-step boundaries and masks their training loss. Studies how this affects learning new tasks while retaining earlier capabilities, including during reinforcement learning.","lens":["learned-tokens","analysis"],"representation":["discrete-token","text-latent-hybrid"],"computation":["token-wise"],"training":["supervised","reinforcement-learning"],"questions":["capability","generalization","interpretability"],"evidence":["empirical","probing"],"modality":["language","symbolic"],"provenance":"Primary-source literature search, 2026-10-18","author_names":["Jaehyeon Kim","Suhwan Kim","Nakyung Lee","Yeongoon Kim","Jimin Seo","Giho Lee","Jungwoo Lee"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.04489/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-04489","citation_date":"2026-09-03","json_url":"https://latent-implicit-thinking.github.io/papers/2609.04489/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.04489/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.04489/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.04489/citation.csl.json"},{"id":"2609.04963","title":"Fractal basins trap latent reasoning","authors":"Jeffrey Lai, Anthony Bao, John Quinn, William Gilpin","first_public":"2026-09-04","venue":"arXiv","arxiv":"2609.04963","paper_url":"https://arxiv.org/abs/2609.04963","lens":["analysis","recurrent"],"representation":["hidden-state"],"computation":["recurrent"],"training":["analysis-only"],"questions":["theory","interpretability","efficiency"],"evidence":["empirical","mechanistic"],"modality":["symbolic","vision"],"summary":"Studies recurrent reasoning trajectories as dynamical systems on puzzles and mathematical logic. Links long solution times in the tested models to transient trapping near unstable states associated with nearly correct solutions.","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Jeffrey Lai","Anthony Bao","John Quinn","William Gilpin"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.04963/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-04963","citation_date":"2026-09-04","json_url":"https://latent-implicit-thinking.github.io/papers/2609.04963/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.04963/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.04963/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.04963/citation.csl.json"},{"id":"2609.05988","title":"DART: Distributional Adversarial Recurrent Training for Algorithm Learning","authors":"Hieu Tran Bao, Phung Thanh Dang, Pham Quang Nhat Minh, Hoang Thanh Tung","first_public":"2026-09-05","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.05988","paper_url":"https://arxiv.org/abs/2609.05988","summary":"Trains recurrent reasoners against a distribution of targets near each correct solution, using an adversarial objective instead of a single point target. Evaluates generalization and stability on maze, chess, and Sudoku tasks.","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent"],"training":["supervised"],"questions":["capability","generalization"],"evidence":["empirical"],"modality":["symbolic"],"provenance":"Primary-source literature search, 2026-10-18","author_names":["Hieu Tran Bao","Phung Thanh Dang","Pham Quang Nhat Minh","Hoang Thanh Tung"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.05988/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-05988","citation_date":"2026-09-05","json_url":"https://latent-implicit-thinking.github.io/papers/2609.05988/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.05988/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.05988/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.05988/citation.csl.json"},{"id":"2609.09928","title":"Structural Process Supervision for Latent Chain-of-Thought Reasoning","authors":"Yiqi Li, Xu Chen, Chen Ju, Jiangchao Yao, Zhaoyang Li, Jinsong Lan, Xiaoyong Zhu, Yu Wang","first_public":"2026-09-09","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.09928","paper_url":"https://arxiv.org/abs/2609.09928","lens":["continuous"],"representation":["continuous-state"],"computation":["token-wise"],"training":["supervised","distillation","curriculum"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Aligns continuous thoughts with written reasoning through shared, learnable prototypes, allowing several text steps to supervise several latent states. A positional alignment constraint is gradually relaxed during training.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Yiqi Li","Xu Chen","Chen Ju","Jiangchao Yao","Zhaoyang Li","Jinsong Lan","Xiaoyong Zhu","Yu Wang"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.09928/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-09928","citation_date":"2026-09-09","json_url":"https://latent-implicit-thinking.github.io/papers/2609.09928/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.09928/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.09928/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.09928/citation.csl.json"},{"id":"2609.13060","title":"CanvasAnneal: Curriculum Reinforcement Learning for Diffusion Language Models","authors":"Blake Olson, Yuhang Song, Emmett McQuinn, Yuan Shangguan","first_public":"2026-09-11","lens":["beyond-sequential"],"representation":["discrete-token"],"training":["reinforcement-learning","curriculum"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Starts diffusion-model reinforcement learning with teacher-written reasoning partially filled into the output, then gradually removes that guidance. Tests whether this curriculum improves exploration on mathematics and tool-use tasks; inference still produces textual reasoning.","computation":["diffusion"],"venue":"arXiv","arxiv":"2609.13060","paper_url":"https://arxiv.org/abs/2609.13060","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Blake Olson","Yuhang Song","Emmett McQuinn","Yuan Shangguan"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.13060/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-13060","citation_date":"2026-09-11","json_url":"https://latent-implicit-thinking.github.io/papers/2609.13060/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.13060/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.13060/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.13060/citation.csl.json"},{"id":"2609.15160","title":"T-LoopFormer: Token-Level Elastic-Depth Looped Transformers with Dynamic Routing","authors":"Mingqian Yu, Wenpeng Zhang, Shaobo Cui, Peilin Zhao","first_public":"2026-09-14","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.15160","paper_url":"https://arxiv.org/abs/2609.15160","summary":"Learns a router that chooses how many recurrent passes each token receives, and keeps separate key/value caches for each pass.","lens":["recurrent"],"representation":["hidden-state","cache-memory"],"computation":["recurrent","depth-wise","token-wise"],"training":["pretraining"],"questions":["architecture","efficiency","capability"],"evidence":["empirical"],"modality":["language"],"provenance":"Primary-source literature search, 2026-10-18","author_names":["Mingqian Yu","Wenpeng Zhang","Shaobo Cui","Peilin Zhao"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.15160/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-15160","citation_date":"2026-09-14","json_url":"https://latent-implicit-thinking.github.io/papers/2609.15160/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.15160/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.15160/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.15160/citation.csl.json"},{"id":"2609.16372","title":"Register Tokens for Bounded-State Reasoning in Diffusion Language Models","authors":"Albert Ge, Chandan Singh, Yufan Zhuang, Xiaodong Liu, Jianfeng Gao, Frederic Sala","first_public":"2026-09-14","venue":"arXiv","arxiv":"2609.16372","paper_url":"https://arxiv.org/abs/2609.16372","lens":["continuous","beyond-sequential"],"representation":["continuous-state","discrete-token"],"computation":["diffusion","stateful"],"training":["supervised","reinforcement-learning"],"questions":["architecture","capability","efficiency"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Trains a diffusion language model to carry a fixed number of continuous register states between generated chunks. The model still writes text within each chunk, but clears earlier text and continues from the prompt and retained registers.","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Albert Ge","Chandan Singh","Yufan Zhuang","Xiaodong Liu","Jianfeng Gao","Frederic Sala"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.16372/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-16372","citation_date":"2026-09-14","json_url":"https://latent-implicit-thinking.github.io/papers/2609.16372/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.16372/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.16372/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.16372/citation.csl.json"},{"id":"2609.16665","title":"Right Direction, Wrong Step: Geometric Analysis of Finite-Step Failure in Looped Transformers","authors":"Zhihao Guo, Zonghan Wu, Haizhou Du, Huan Huo, Yilei Shao, Athanasios V. Vasilakos, Qingsong Wen","first_public":"2026-09-15","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.16665","paper_url":"https://arxiv.org/abs/2609.16665","summary":"Studies updates that initially increase support for a reference answer but overshoot when applied in full. Uses curvature along each update to explain failures and identify smaller useful steps.","lens":["analysis","recurrent"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["analysis-only"],"questions":["theory","limitations","controllability"],"evidence":["formal","empirical","boundary"],"modality":["language","symbolic"],"provenance":"Primary-source literature search, 2026-10-18","author_names":["Zhihao Guo","Zonghan Wu","Haizhou Du","Huan Huo","Yilei Shao","Athanasios V. Vasilakos","Qingsong Wen"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.16665/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-16665","citation_date":"2026-09-15","json_url":"https://latent-implicit-thinking.github.io/papers/2609.16665/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.16665/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.16665/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.16665/citation.csl.json"},{"id":"2609.17184","title":"LoopSpec: Pipelined Self-Speculative Decoding for Looped Transformers","authors":"SangLyul Cho, Langqing Cui, Sehoon Kim, Dongsu Han, Insu Han","first_public":"2026-09-15","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.17184","paper_url":"https://arxiv.org/abs/2609.17184","summary":"Drafts future tokens from early loops while later loops verify current tokens, overlapping the work without training an extra model. Final verification preserves the full model's decoding behavior.","lens":["recurrent","beyond-sequential"],"representation":["hidden-state"],"computation":["recurrent","depth-wise","parallel"],"training":["inference-only"],"questions":["efficiency","architecture"],"evidence":["empirical","formal"],"modality":["language"],"provenance":"Primary-source literature search, 2026-10-18","author_names":["SangLyul Cho","Langqing Cui","Sehoon Kim","Dongsu Han","Insu Han"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.17184/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-17184","citation_date":"2026-09-15","json_url":"https://latent-implicit-thinking.github.io/papers/2609.17184/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.17184/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.17184/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.17184/citation.csl.json"},{"id":"2609.19107","title":"How Model Growth, Recursion, and Boundary Operators Influence Scaling Exponents","authors":"Zixi Chen, Akshay Vegesna, Samip Dahal, Andrew Gordon Wilson","first_public":"2026-09-16","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.19107","paper_url":"https://arxiv.org/abs/2609.19107","lens":["recurrent","analysis"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["pretraining"],"questions":["scaling","architecture","efficiency"],"evidence":["empirical","scaling"],"modality":["language"],"summary":"Studies how growing a model during training, reusing layers, and modifying the connections between repeated blocks affect language-model scaling. Compares shared and unshared weights and operators that normalize or reintroduce earlier representations.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Zixi Chen","Akshay Vegesna","Samip Dahal","Andrew Gordon Wilson"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.19107/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-19107","citation_date":"2026-09-16","json_url":"https://latent-implicit-thinking.github.io/papers/2609.19107/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.19107/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.19107/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.19107/citation.csl.json"},{"id":"2609.19521","title":"Storing Is Not Remembering: LSTM-UT and Bounded Gated Memory for Looped Transformers","authors":"Aras Kavuncu, Muhammad Burhan Hafez","first_public":"2026-09-17","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.19521","paper_url":"https://arxiv.org/abs/2609.19521","lens":["recurrent","analysis"],"representation":["hidden-state","cache-memory"],"computation":["recurrent","depth-wise","stateful"],"training":["pretraining","supervised"],"questions":["architecture","generalization","interpretability"],"evidence":["empirical","mechanistic"],"modality":["symbolic","language"],"summary":"Adds a small gated memory to a looped transformer and compares it with storing the full history of recurrent states. Uses a cellular-automaton task and language modeling to test whether memory remains useful as computation grows.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Aras Kavuncu","Muhammad Burhan Hafez"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.19521/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-19521","citation_date":"2026-09-17","json_url":"https://latent-implicit-thinking.github.io/papers/2609.19521/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.19521/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.19521/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.19521/citation.csl.json"},{"id":"2609.19717","title":"Learn Your Own Thoughts: Abstract Token Curriculum","authors":"Khashayar Gatmiry, Avrajit Ghosh, Parsa Mirtaheri, Jason D. Lee, Nika Haghtalab, Emmanuel Abbe, Peter Bartlett","first_public":"2026-09-17","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.19717","paper_url":"https://arxiv.org/abs/2609.19717","lens":["continuous"],"representation":["continuous-state"],"computation":["token-wise"],"training":["curriculum"],"questions":["capability","theory","generalization"],"evidence":["empirical","formal"],"modality":["symbolic"],"summary":"Trains on progressively harder problems so that a model learns continuous intermediate thoughts without explicit reasoning-step supervision. Analyzes parity learning theoretically and tests graph reachability and arithmetic.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Khashayar Gatmiry","Avrajit Ghosh","Parsa Mirtaheri","Jason D. Lee","Nika Haghtalab","Emmanuel Abbe","Peter Bartlett"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.19717/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-19717","citation_date":"2026-09-17","json_url":"https://latent-implicit-thinking.github.io/papers/2609.19717/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.19717/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.19717/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.19717/citation.csl.json"},{"id":"2609.19878","title":"Uni-LaDiR: Latent Diffusion Unifies Multimodal Reasoning","authors":"Haoqiang Kang, Yizhe Zhang, Nikki Lijing Kuang, Jiatao Gu, Yian Ma, Lianhui Qin","first_public":"2026-09-17","venue":"arXiv","arxiv":"2609.19878","paper_url":"https://arxiv.org/abs/2609.19878","lens":["continuous","beyond-sequential"],"representation":["multimodal-latent","continuous-state"],"computation":["diffusion"],"training":["supervised","distillation"],"questions":["architecture","capability","generalization"],"evidence":["empirical"],"modality":["multimodal","vision","language"],"summary":"Encodes teacher reasoning steps from text, images, point clouds, and robot states into a shared continuous representation. A jointly trained diffusion reasoner generates these states at inference, evaluated on visual question answering and robotic manipulation.","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Haoqiang Kang","Yizhe Zhang","Nikki Lijing Kuang","Jiatao Gu","Yian Ma","Lianhui Qin"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.19878/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-19878","citation_date":"2026-09-17","json_url":"https://latent-implicit-thinking.github.io/papers/2609.19878/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.19878/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.19878/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.19878/citation.csl.json"},{"id":"2609.20398","title":"Schema-Anchored Latent Reasoning for Semantic Parsing-Based Knowledge Base Question Answering","authors":"Guangze Gao, Zixuan Li, Sikui Zhang, Chunfeng Yuan, Wenjuan Li, Bing Li, Xiaolong Jin, Weiming Hu","first_public":"2026-09-17","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.20398","paper_url":"https://arxiv.org/abs/2609.20398","lens":["continuous"],"representation":["continuous-state"],"computation":["token-wise"],"training":["supervised"],"questions":["capability","interpretability"],"evidence":["empirical","probing"],"modality":["language","symbolic"],"summary":"Aligns continuous thoughts with a codebook of knowledge-base relations and classes, using schema traces derived from correct logical forms. Feeds the aligned codes into later reasoning steps before generating an executable query.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Guangze Gao","Zixuan Li","Sikui Zhang","Chunfeng Yuan","Wenjuan Li","Bing Li","Xiaolong Jin","Weiming Hu"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.20398/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-20398","citation_date":"2026-09-17","json_url":"https://latent-implicit-thinking.github.io/papers/2609.20398/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.20398/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.20398/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.20398/citation.csl.json"},{"id":"2609.20981","title":"CaLR: Causal Latent Revision for Robust Diffusion Reasoning","authors":"Wei Cai, Jian Zhao, Yuchen Yuan, Xuelong Li","first_public":"2026-09-17","lens":["continuous","beyond-sequential"],"representation":["continuous-state"],"training":["test-time-optimization"],"questions":["capability","controllability"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Uses an expert-derived causal dependency matrix to guide gradient-based revision of diffusion reasoning states. The aim is to preserve logical dependencies while revising several intermediate positions during parallel generation.","computation":["diffusion","parallel"],"venue":"arXiv","arxiv":"2609.20981","paper_url":"https://arxiv.org/abs/2609.20981","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Wei Cai","Jian Zhao","Yuchen Yuan","Xuelong Li"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.20981/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-20981","citation_date":"2026-09-17","json_url":"https://latent-implicit-thinking.github.io/papers/2609.20981/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.20981/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.20981/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.20981/citation.csl.json"},{"id":"2609.21605","title":"Trading Depth for Time in Recurrent Transformers","authors":"Zeyi Huang, Xuehai He, Yelong Shen, Yong Jae Lee","first_public":"2026-09-18","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.21605","paper_url":"https://arxiv.org/abs/2609.21605","lens":["recurrent","learned-tokens"],"representation":["hidden-state","continuous-state"],"computation":["recurrent","token-wise","stateful"],"training":["pretraining"],"questions":["architecture","efficiency","scaling"],"evidence":["empirical","scaling"],"modality":["language"],"summary":"Inserts a hidden-state refinement step between consecutive text tokens in a recurrent transformer. Compares this extra thinking time with adding physical layers or transformer loops under matched computation budgets.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Zeyi Huang","Xuehai He","Yelong Shen","Yong Jae Lee"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.21605/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-21605","citation_date":"2026-09-18","json_url":"https://latent-implicit-thinking.github.io/papers/2609.21605/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.21605/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.21605/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.21605/citation.csl.json"},{"id":"2609.21662","title":"When Steering Fails in Latent Reasoning: A Latent-to-Language Transition Gap","authors":"Gaoxiang Huang, Lei Qi","first_public":"2026-09-18","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.21662","paper_url":"https://arxiv.org/abs/2609.21662","summary":"Tests whether changing continuous reasoning states changes the model's later text output. Finds weaker steering effects than in explicit chain-of-thought, despite comparable changes to the hidden representations.","lens":["analysis","continuous"],"representation":["continuous-state","text-latent-hybrid"],"computation":["token-wise"],"training":["analysis-only"],"questions":["controllability","interpretability","limitations"],"evidence":["empirical","probing","boundary"],"modality":["language"],"provenance":"Primary-source literature search, 2026-10-18","author_names":["Gaoxiang Huang","Lei Qi"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.21662/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-21662","citation_date":"2026-09-18","json_url":"https://latent-implicit-thinking.github.io/papers/2609.21662/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.21662/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.21662/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.21662/citation.csl.json"},{"id":"2609.23033","title":"WaveFront Decoding: Parallelized Self-Speculative Decoding for Looped Language Models","authors":"Hyeongju Ha, Jae-Joon Kim","first_public":"2026-09-19","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.23033","paper_url":"https://arxiv.org/abs/2609.23033","lens":["recurrent","beyond-sequential"],"representation":["hidden-state"],"computation":["recurrent","depth-wise","parallel"],"training":["inference-only"],"questions":["efficiency","architecture"],"evidence":["empirical"],"modality":["language"],"summary":"Uses intermediate loop depths to propose tokens that later loops verify. Arranges speculation across recurrent depths so that more of the draft and verification work can run together.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Hyeongju Ha","Jae-Joon Kim"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.23033/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-23033","citation_date":"2026-09-19","json_url":"https://latent-implicit-thinking.github.io/papers/2609.23033/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.23033/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.23033/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.23033/citation.csl.json"},{"id":"2609.24196","title":"LoopCD: Loop-wise Contrastive Decoding for Improving Reasoning in Looped Language Models","authors":"Byeongho Yu, Junhyuk So, Eunhyeok Park","first_public":"2026-09-21","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.24196","paper_url":"https://arxiv.org/abs/2609.24196","summary":"Uses differences between early- and late-loop predictions to adjust token sampling at inference time, without retraining the model.","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["inference-only"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["language"],"provenance":"Primary-source literature search, 2026-10-18","author_names":["Byeongho Yu","Junhyuk So","Eunhyeok Park"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.24196/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-24196","citation_date":"2026-09-21","json_url":"https://latent-implicit-thinking.github.io/papers/2609.24196/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.24196/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.24196/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.24196/citation.csl.json"},{"id":"2609.24346","title":"LADDER: Graph-Guided Diffusion Language Models for Efficient Multi-Hop Reasoning","authors":"Senlei Zhang, Linhao Luo, Qian-Wen Zhang, Siyu An, Junnan Dong, Shuhao Zhang, Xing Sun","first_public":"2026-09-21","lens":["beyond-sequential"],"representation":["discrete-token"],"training":["supervised"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["language"],"summary":"Triggers graph retrieval when new entities become identifiable in a partially denoised draft, then uses graph propagation to provide multi-hop evidence for subsequent updates. This combines retrieval with parallel textual reasoning rather than removing the text trace.","computation":["diffusion","parallel"],"venue":"arXiv","arxiv":"2609.24346","paper_url":"https://arxiv.org/abs/2609.24346","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Senlei Zhang","Linhao Luo","Qian-Wen Zhang","Siyu An","Junnan Dong","Shuhao Zhang","Xing Sun"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.24346/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-24346","citation_date":"2026-09-21","json_url":"https://latent-implicit-thinking.github.io/papers/2609.24346/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.24346/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.24346/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.24346/citation.csl.json"},{"id":"2609.27220","title":"LOCKR: A Hidden-State Trajectory-Guided Planner for Detecting and Repairing Stable-but-Wrong Lock-In in Diffusion Language Models","authors":"Guoshenghui Zhao, Tan Yu, Weijie Zhao","first_public":"2026-09-23","lens":["analysis","beyond-sequential"],"representation":["hidden-state","discrete-token"],"training":["supervised","inference-only"],"questions":["evaluation","interpretability","capability"],"evidence":["empirical","probing"],"modality":["language","symbolic"],"summary":"Uses the history of diffusion hidden states to detect answers that become stable but remain wrong. A planner selects targeted repair branches and verifies continuations, testing whether these internal trajectories support better repair decisions than confidence or a single snapshot.","computation":["diffusion","search"],"venue":"arXiv","arxiv":"2609.27220","paper_url":"https://arxiv.org/abs/2609.27220","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Guoshenghui Zhao","Tan Yu","Weijie Zhao"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.27220/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-27220","citation_date":"2026-09-23","json_url":"https://latent-implicit-thinking.github.io/papers/2609.27220/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.27220/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.27220/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.27220/citation.csl.json"},{"id":"2609.27373","title":"Attention Routing Stabilizes Early: Working-Set Inference for Recurrent Language Models","authors":"Ke Wan, Chen Chen","first_public":"2026-09-23","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.27373","paper_url":"https://arxiv.org/abs/2609.27373","lens":["recurrent","analysis"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["inference-only","analysis-only"],"questions":["interpretability","efficiency","architecture"],"evidence":["empirical","mechanistic"],"modality":["language"],"summary":"Studies when a recurrent language model settles on which context tokens to attend to. Reuses that selected working set in later loops while still recomputing attention weights and hidden-state updates.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Ke Wan","Chen Chen"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.27373/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-27373","citation_date":"2026-09-23","json_url":"https://latent-implicit-thinking.github.io/papers/2609.27373/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.27373/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.27373/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.27373/citation.csl.json"},{"id":"2609.28272","title":"Towards Efficient Reasoning: Learning Causal Shortcuts for Diffusion Language Models","authors":"Dian Jin, Kairong Han, Baohong Li, Xinpeng Dong, Zijing Hu, Nuanqiao Shan, Fei Wu, Kun Kuang","first_public":"2026-09-23","venue":"arXiv","arxiv":"2609.28272","paper_url":"https://arxiv.org/abs/2609.28272","lens":["beyond-sequential"],"representation":["discrete-token"],"computation":["diffusion","parallel"],"training":["supervised"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Extracts reasoning-guiding token chains and prioritizes them during diffusion-model training to improve denoising speed and accuracy. This is a related text-generating approach, not reasoning without a written trace.","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Dian Jin","Kairong Han","Baohong Li","Xinpeng Dong","Zijing Hu","Nuanqiao Shan","Fei Wu","Kun Kuang"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.28272/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-28272","citation_date":"2026-09-23","json_url":"https://latent-implicit-thinking.github.io/papers/2609.28272/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.28272/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.28272/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.28272/citation.csl.json"},{"id":"2609.29102","title":"ELF-REG: Scaling Continuous Diffusion Language Models to Reasoning Tasks","authors":"Zeyu Michael Li, William Xingxu Chen, Bingshuo Qian, Jiayin Liu, Xiang Cheng","first_public":"2026-09-24","lens":["continuous","beyond-sequential"],"representation":["continuous-state"],"training":["supervised","distillation"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Adapts continuous diffusion to mathematics and code using intermediate-feature supervision and a global representation from a frozen autoregressive teacher. It denoises continuous response representations and decodes all response tokens only at the end.","computation":["diffusion","parallel"],"venue":"arXiv","arxiv":"2609.29102","paper_url":"https://arxiv.org/abs/2609.29102","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Zeyu Michael Li","William Xingxu Chen","Bingshuo Qian","Jiayin Liu","Xiang Cheng"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.29102/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-29102","citation_date":"2026-09-24","json_url":"https://latent-implicit-thinking.github.io/papers/2609.29102/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.29102/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.29102/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.29102/citation.csl.json"},{"id":"2610.08820","title":"Task-Oriented Key-Layer KV Communication for Efficient Latent Multi-Agent Collaboration","authors":"Dongsen Zhang, Peipei Li, Zekun Li, Wenjun Xu","first_public":"2026-09-24","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.08820","paper_url":"https://arxiv.org/abs/2610.08820","lens":["continuous"],"representation":["cache-memory","hidden-state"],"computation":["token-wise","stateful"],"training":["inference-only"],"questions":["capability","efficiency","architecture"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Lets agents perform hidden-state reasoning and pass working memory through the key-value cache of one selected transformer layer. Reuses that layer as the entry point for subsequent reasoning updates, avoiding earlier layers and decoding only the final agent's response into text.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Dongsen Zhang","Peipei Li","Zekun Li","Wenjun Xu"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.08820/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-08820","citation_date":"2026-09-24","json_url":"https://latent-implicit-thinking.github.io/papers/2610.08820/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.08820/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.08820/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.08820/citation.csl.json"},{"id":"2609.30783","title":"Skip the Talk, Re-Focus on Vision: Latent Reasoning for Reasoning Segmentation in Multimodal Large Language Models","authors":"Tianhang Guo, Yulin He, Wei Chen, Wenjuan Zhou, Yuhang Li, Xinbiao Gan","first_public":"2026-09-25","venue":"arXiv","arxiv":"2609.30783","paper_url":"https://arxiv.org/abs/2609.30783","lens":["learned-tokens"],"representation":["discrete-token","hidden-state","multimodal-latent"],"computation":["token-wise"],"training":["supervised","reinforcement-learning"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["multimodal","vision"],"summary":"LIRSeg generates a fixed sequence of learned special tokens before a target description and bounding box used for segmentation. Spatial alignment grounds the tokens' hidden states in relevant image regions, followed by training with segmentation rewards.","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Tianhang Guo","Yulin He","Wei Chen","Wenjuan Zhou","Yuhang Li","Xinbiao Gan"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.30783/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-30783","citation_date":"2026-09-25","json_url":"https://latent-implicit-thinking.github.io/papers/2609.30783/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.30783/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.30783/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.30783/citation.csl.json"},{"id":"2609.33134","title":"Ceiling of a Task: When Can a Transformer Succeed Without Its Chain of Thought?","authors":"Jiashu He, Jinxuan Fan, Xiao Xiao, Radu Marculescu, Alejandro Ribeiro","first_public":"2026-09-27","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.33134","paper_url":"https://arxiv.org/abs/2609.33134","lens":["analysis","learned-tokens"],"representation":["discrete-token"],"computation":["token-wise"],"training":["analysis-only"],"questions":["theory","limitations","evaluation"],"evidence":["formal","empirical","boundary"],"modality":["language","symbolic"],"summary":"Analyzes tasks for which a fixed-depth transformer needs an informative chain of thought to exceed a task-specific accuracy limit. Combines circuit-based results with experiments that replace, erase, or shuffle reasoning tokens, including comparisons with filler tokens.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Jiashu He","Jinxuan Fan","Xiao Xiao","Radu Marculescu","Alejandro Ribeiro"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.33134/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-33134","citation_date":"2026-09-27","json_url":"https://latent-implicit-thinking.github.io/papers/2609.33134/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.33134/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.33134/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.33134/citation.csl.json"},{"id":"2609.33144","title":"Beyond the Training Horizon: Mechanisms and Limits of Length Generalization in Looped Transformers","authors":"Jia Liang, Xi Jin, Liangming Pan","first_public":"2026-09-27","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.33144","paper_url":"https://arxiv.org/abs/2609.33144","summary":"Compares how two looped-transformer training schemes solve multi-step tasks beyond their training length. Uses hidden-state interventions to identify how intermediate information moves through each model and where that process breaks down.","lens":["analysis","recurrent"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["supervised","analysis-only"],"questions":["interpretability","generalization","limitations"],"evidence":["empirical","mechanistic","boundary"],"modality":["symbolic"],"provenance":"Primary-source literature search, 2026-10-18","author_names":["Jia Liang","Xi Jin","Liangming Pan"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.33144/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-33144","citation_date":"2026-09-27","json_url":"https://latent-implicit-thinking.github.io/papers/2609.33144/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.33144/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.33144/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.33144/citation.csl.json"},{"id":"2609.33270","title":"Structured Sparse Memory for Recurrent Reasoning","authors":"Zixuan Zhao, Samuel Wheeler, Neil Getty, Xiaotian Duan, Rick Stevens, Fangfang Xia","first_public":"2026-09-27","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.33270","paper_url":"https://arxiv.org/abs/2609.33270","summary":"Combines a recurrent reasoner with sparse, compositional task embeddings for ARC puzzles. Studies how task-memory size, recurrent depth, and training horizon affect performance.","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent","stateful"],"training":["supervised"],"questions":["architecture","capability","generalization","efficiency"],"evidence":["empirical"],"modality":["symbolic","vision"],"provenance":"Primary-source literature search, 2026-10-18","author_names":["Zixuan Zhao","Samuel Wheeler","Neil Getty","Xiaotian Duan","Rick Stevens","Fangfang Xia"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.33270/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-33270","citation_date":"2026-09-27","json_url":"https://latent-implicit-thinking.github.io/papers/2609.33270/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.33270/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.33270/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.33270/citation.csl.json"},{"id":"2609.33271","title":"Next Thoughts Are Distributions: Generative Autoregressive Reasoning in the Latent Space","authors":"Yang Li, Yi Wang, Shiyuan Huang, Yang Liu, Hao Wang, Chengzhi Mao","first_public":"2026-09-27","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.33271","paper_url":"https://arxiv.org/abs/2609.33271","lens":["continuous","beyond-sequential"],"representation":["continuous-state"],"computation":["token-wise","diffusion"],"training":["supervised","reinforcement-learning"],"questions":["capability","efficiency","scaling"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Adds a diffusion head that samples the next continuous thought from a distribution rather than predicting one fixed vector. Feeds each sampled thought back into an autoregressive reasoner, supporting variable-length latent traces and multiple reasoning paths.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Yang Li","Yi Wang","Shiyuan Huang","Yang Liu","Hao Wang","Chengzhi Mao"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.33271/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-33271","citation_date":"2026-09-27","json_url":"https://latent-implicit-thinking.github.io/papers/2609.33271/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.33271/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.33271/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.33271/citation.csl.json"},{"id":"2609.33402","title":"VaME: Exploring Variational Latent Reasoning for Multimodal Embeddings","authors":"Peixi Wu, Mingzhou Jiang, Feipeng Ma, Biao Yang, Yunhao Zhou, Wei Yuan, Bosong Chai, Huizu Lin, Jie Chen, Zhangchi Hu, Fan Yang, Wenwu Ou, Hebei Li, Xiaoyan Sun","first_public":"2026-09-27","venue":"arXiv","arxiv":"2609.33402","paper_url":"https://arxiv.org/abs/2609.33402","lens":["continuous"],"representation":["multimodal-latent","continuous-state"],"computation":["token-wise","search"],"training":["supervised","reinforcement-learning"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["multimodal","vision"],"summary":"Learns a distribution over continuous reasoning trajectories before producing a retrieval embedding. A lightweight decoder provides reconstruction supervision and a semantic reward for reinforcement learning, evaluated on image, video, and visual-document retrieval.","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Peixi Wu","Mingzhou Jiang","Feipeng Ma","Biao Yang","Yunhao Zhou","Wei Yuan","Bosong Chai","Huizu Lin","Jie Chen","Zhangchi Hu","Fan Yang","Wenwu Ou","Hebei Li","Xiaoyan Sun"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.33402/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-33402","citation_date":"2026-09-27","json_url":"https://latent-implicit-thinking.github.io/papers/2609.33402/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.33402/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.33402/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.33402/citation.csl.json"},{"id":"2609.34218","title":"Loop Dropout: Regularizing Shared Updates in Looped Language Models","authors":"Zirui Zhu, Hailun Xu, Xuanlei Zhao, Yong Liu, Yingxuan Ren, Kanchan Sarkar, Kun Xu, Yang You","first_public":"2026-09-28","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.34218","paper_url":"https://arxiv.org/abs/2609.34218","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["supervised"],"questions":["architecture","capability"],"evidence":["empirical"],"modality":["language"],"summary":"Regularizes fine-tuning of looped language models by randomly masking adapter updates at selected loops. The shared backbone still runs at every loop; the method targets adapter updates that otherwise become concentrated at particular depths.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Zirui Zhu","Hailun Xu","Xuanlei Zhao","Yong Liu","Yingxuan Ren","Kanchan Sarkar","Kun Xu","Yang You"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.34218/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-34218","citation_date":"2026-09-28","json_url":"https://latent-implicit-thinking.github.io/papers/2609.34218/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.34218/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.34218/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.34218/citation.csl.json"},{"id":"2609.34408","title":"Distilling Visual Reasoning into Text Space","authors":"Wenhan Yang, Nilay Naharas, Ali Payani, Baharan Mirzasoleiman","first_public":"2026-09-28","venue":"arXiv","arxiv":"2609.34408","paper_url":"https://arxiv.org/abs/2609.34408","lens":["internalized"],"representation":["hidden-state","text-latent-hybrid"],"computation":["token-wise"],"training":["distillation","supervised","reinforcement-learning"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["multimodal","vision","language"],"summary":"Distills a teacher's interleaved visual and textual reasoning into a student that no longer generates intermediate visual representations. The student still writes a textual chain of thought; what is internalized is the visual portion of the reasoning.","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Wenhan Yang","Nilay Naharas","Ali Payani","Baharan Mirzasoleiman"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.34408/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-34408","citation_date":"2026-09-28","json_url":"https://latent-implicit-thinking.github.io/papers/2609.34408/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.34408/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.34408/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.34408/citation.csl.json"},{"id":"2609.34488","title":"FlexLoop: Depth-Elastic Looped Policies for Adaptive Test-Time Computation in Deep RL","authors":"Xun Wang, Ruishuo Chen, Yu Chen, Zhuoran Li, Longbo Huang","first_public":"2026-09-28","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.34488","paper_url":"https://arxiv.org/abs/2609.34488","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["reinforcement-learning","distillation"],"questions":["efficiency","controllability","capability"],"evidence":["empirical"],"modality":["symbolic"],"summary":"Post-trains a looped reinforcement-learning policy to make useful decisions at several recurrent depths. Combines its original objective with distillation between neighboring depths, then uses agreement across depths to decide when to stop.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Xun Wang","Ruishuo Chen","Yu Chen","Zhuoran Li","Longbo Huang"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.34488/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-34488","citation_date":"2026-09-28","json_url":"https://latent-implicit-thinking.github.io/papers/2609.34488/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.34488/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.34488/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.34488/citation.csl.json"},{"id":"2609.34538","title":"Shallow Queries, Mature Values: Depth-Asynchronous Self-Speculation for Looped Transformers","authors":"Guanghao Li, Zihan Su, Hao Yu, Jinyang Jiang, Tao Ren, Zehao Li, Feng Lu, Ming Tang, Chun Yuan","first_public":"2026-09-28","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.34538","paper_url":"https://arxiv.org/abs/2609.34538","lens":["recurrent","beyond-sequential"],"representation":["hidden-state","cache-memory"],"computation":["recurrent","depth-wise","parallel"],"training":["inference-only"],"questions":["efficiency","architecture","interpretability"],"evidence":["empirical","mechanistic"],"modality":["language"],"summary":"Uses shallower-loop queries with values from deeper loops to improve draft-token predictions in a looped language model. Studies the different rates at which queries, keys, and values develop, and uses that difference for self-speculative decoding.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Guanghao Li","Zihan Su","Hao Yu","Jinyang Jiang","Tao Ren","Zehao Li","Feng Lu","Ming Tang","Chun Yuan"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.34538/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-34538","citation_date":"2026-09-28","json_url":"https://latent-implicit-thinking.github.io/papers/2609.34538/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.34538/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.34538/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.34538/citation.csl.json"},{"id":"2609.35472","title":"Why Deterministic PRM Guidance Underperforms in Discrete Diffusion Reasoning","authors":"Yan Zhan, Shaobo Liu, Zhijun Gao","first_public":"2026-09-28","venue":"arXiv","arxiv":"2609.35472","paper_url":"https://arxiv.org/abs/2609.35472","lens":["analysis","beyond-sequential"],"representation":["discrete-token"],"computation":["diffusion","search"],"training":["analysis-only","supervised"],"questions":["evaluation","efficiency","limitations"],"evidence":["empirical","boundary"],"modality":["language","symbolic"],"summary":"Compares process-reward guidance with independent sampling and final-answer reranking at matched forward-pass budgets. In the tested diffusion models, early pruning removes promising candidates and intermediate-state scorers can be poor final judges; the generated solutions remain textual.","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Yan Zhan","Shaobo Liu","Zhijun Gao"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.35472/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-35472","citation_date":"2026-09-28","json_url":"https://latent-implicit-thinking.github.io/papers/2609.35472/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.35472/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.35472/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.35472/citation.csl.json"},{"id":"2609.35694","title":"Reasoning with Continuous Latent Diffusion","authors":"Xiang Cheng","first_public":"2026-09-28","lens":["continuous","beyond-sequential"],"representation":["continuous-state"],"training":["supervised","distillation","reinforcement-learning","curriculum"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"CEDR learns compact representations from several teacher layers, denoises them at different rates, and trains a smaller prompt encoder to replace the teacher at inference. It generates complete mathematical and coding solutions through continuous refinement before text decoding.","computation":["diffusion","parallel"],"venue":"arXiv","arxiv":"2609.35694","paper_url":"https://arxiv.org/abs/2609.35694","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Xiang Cheng"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.35694/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-35694","citation_date":"2026-09-28","json_url":"https://latent-implicit-thinking.github.io/papers/2609.35694/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.35694/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.35694/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.35694/citation.csl.json"},{"id":"2609.35748","title":"Improving Test-Time Scaling with Adaptive Looped Transformers","authors":"Yichen You, Tianyu Fu, Aosong Feng, Xingtai Lv, Xuefei Ning, Ning Ding, Yu Wang","first_public":"2026-09-28","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.35748","paper_url":"https://arxiv.org/abs/2609.35748","summary":"Trains an iteration controller to give extra transformer loops only to tokens whose predictions benefit from them. Compares reasoning accuracy as both output length and internal computation increase.","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent","depth-wise","token-wise"],"training":["supervised"],"questions":["controllability","efficiency","scaling","capability"],"evidence":["empirical","scaling"],"modality":["language","symbolic"],"provenance":"Primary-source literature search, 2026-10-18","author_names":["Yichen You","Tianyu Fu","Aosong Feng","Xingtai Lv","Xuefei Ning","Ning Ding","Yu Wang"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.35748/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-35748","citation_date":"2026-09-28","json_url":"https://latent-implicit-thinking.github.io/papers/2609.35748/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.35748/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.35748/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.35748/citation.csl.json"},{"id":"2609.35751","title":"How to Loop MoE: Flatten the Experts, Untie the Attention","authors":"Shouren Wang, Chuang Ma, Mohsen Hariri, Debargha Ganguly, Wang Yang, Xiaoqing Tong, Qianying Liu, Xiaotian Han, Vipin Chaudhary","first_public":"2026-09-28","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.35751","paper_url":"https://arxiv.org/abs/2609.35751","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["pretraining"],"questions":["architecture","efficiency","capability"],"evidence":["empirical"],"modality":["language"],"summary":"Builds a looped mixture-of-experts model by pooling experts across layers and revisiting them. Shares experts and routing across passes while giving each pass its own attention parameters.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Shouren Wang","Chuang Ma","Mohsen Hariri","Debargha Ganguly","Wang Yang","Xiaoqing Tong","Qianying Liu","Xiaotian Han","Vipin Chaudhary"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.35751/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-35751","citation_date":"2026-09-28","json_url":"https://latent-implicit-thinking.github.io/papers/2609.35751/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.35751/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.35751/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.35751/citation.csl.json"},{"id":"2610.08833","title":"CoDR: Training-Free Confidence-Drift Remasking for Diffusion Language Models","authors":"Yue Wu, Qinghe Zhang, Yu Zhang, Jian Huang","first_public":"2026-09-28","lens":["beyond-sequential"],"representation":["discrete-token"],"training":["inference-only"],"questions":["capability","efficiency","evaluation"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Checks whether tokens committed earlier in diffusion decoding become less plausible as context fills in. CoDR remasks and regenerates those positions, testing targeted revision against extra-compute controls on reasoning and code tasks.","computation":["diffusion"],"venue":"arXiv","arxiv":"2610.08833","paper_url":"https://arxiv.org/abs/2610.08833","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Yue Wu","Qinghe Zhang","Yu Zhang","Jian Huang"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.08833/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-08833","citation_date":"2026-09-28","json_url":"https://latent-implicit-thinking.github.io/papers/2610.08833/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.08833/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.08833/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.08833/citation.csl.json"},{"id":"2609.36452","title":"Reliable Parallel Decoding in Masked Diffusion Language Models","authors":"Zhenghao He, Bohan Liu, Guangzhi Xiong, Aidong Zhang","first_public":"2026-09-29","lens":["analysis","beyond-sequential"],"representation":["discrete-token","hidden-state"],"training":["inference-only"],"questions":["efficiency","evaluation","limitations"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Studies when simultaneously committing several predicted tokens breaks their reasoning dependencies. RPD combines stability across final layers with confidence and uncertainty in preceding positions to defer unsupported predictions while retaining parallel text generation.","computation":["diffusion","parallel"],"venue":"arXiv","arxiv":"2609.36452","paper_url":"https://arxiv.org/abs/2609.36452","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Zhenghao He","Bohan Liu","Guangzhi Xiong","Aidong Zhang"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.36452/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-36452","citation_date":"2026-09-29","json_url":"https://latent-implicit-thinking.github.io/papers/2609.36452/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.36452/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.36452/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.36452/citation.csl.json"},{"id":"2609.36636","title":"What Makes Recurrence Effective in Looped Language Models?","authors":"Xinlin Zhuang, Siyuan Wang, Imran Razzak, Weiyang Liu","first_public":"2026-09-29","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.36636","paper_url":"https://arxiv.org/abs/2609.36636","lens":["recurrent","analysis"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["pretraining","analysis-only"],"questions":["architecture","scaling","limitations"],"evidence":["empirical"],"modality":["language"],"summary":"Compares loop layouts and ways of passing information between loops in language models. Examines when recurrence helps reasoning and when it helps less on knowledge-dependent tasks.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Xinlin Zhuang","Siyuan Wang","Imran Razzak","Weiyang Liu"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.36636/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-36636","citation_date":"2026-09-29","json_url":"https://latent-implicit-thinking.github.io/papers/2609.36636/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.36636/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.36636/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.36636/citation.csl.json"},{"id":"2609.36653","title":"Scheduling Recursive Reasoning in Looped Transformers","authors":"Boyuan Wang, Chengyao Yu, Jiaxi Ren, Hongxin Wei, Bingyi Jing, Yuxin Tao","first_public":"2026-09-29","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.36653","paper_url":"https://arxiv.org/abs/2609.36653","summary":"Adjusts the size of each hidden-state update based on whether recent updates make consistent progress or fluctuate. Tests the resulting scheduler with and without additional training.","lens":["recurrent","analysis"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["inference-only","supervised"],"questions":["theory","controllability","efficiency","capability"],"evidence":["formal","empirical"],"modality":["symbolic"],"provenance":"Primary-source literature search, 2026-10-18","author_names":["Boyuan Wang","Chengyao Yu","Jiaxi Ren","Hongxin Wei","Bingyi Jing","Yuxin Tao"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.36653/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-36653","citation_date":"2026-09-29","json_url":"https://latent-implicit-thinking.github.io/papers/2609.36653/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.36653/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.36653/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.36653/citation.csl.json"},{"id":"2609.37351","title":"Port-Hamiltonian Latent Deliberation: Mitigating the Deliberation Drift Cliff in Test-Time Compute Scaling","authors":"Zeyu Jia","first_public":"2026-09-29","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.37351","paper_url":"https://arxiv.org/abs/2609.37351","summary":"Separates hidden-state updates into attracting and rotating components to reduce errors from running a recurrent reasoner for more steps. Tests a tensor-based implementation on logical and multi-hop reasoning tasks.","lens":["recurrent","continuous"],"representation":["continuous-state"],"computation":["recurrent"],"training":["supervised"],"questions":["theory","generalization","limitations","efficiency"],"evidence":["formal","empirical"],"modality":["language","symbolic"],"provenance":"Primary-source literature search, 2026-10-18","author_names":["Zeyu Jia"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.37351/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-37351","citation_date":"2026-09-29","json_url":"https://latent-implicit-thinking.github.io/papers/2609.37351/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.37351/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.37351/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.37351/citation.csl.json"},{"id":"2609.37379","title":"Looped Transformers as Optimizers","authors":"Yulong Huang, Chen Jiang, Zhanpeng Zhou, Hongtao Zhang, Tianyu Li, Tianyu He, Xiangyu Zhang, Bojun Cheng","first_public":"2026-09-29","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.37379","paper_url":"https://arxiv.org/abs/2609.37379","summary":"Treats each recurrent hidden-state update as an optimization step and derives loop designs from this view. Introduces OperLoop, combining adaptive step sizes and weight decay.","lens":["recurrent","analysis"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["pretraining"],"questions":["architecture","theory","capability"],"evidence":["formal","empirical"],"modality":["language"],"provenance":"Primary-source literature search, 2026-10-18","author_names":["Yulong Huang","Chen Jiang","Zhanpeng Zhou","Hongtao Zhang","Tianyu Li","Tianyu He","Xiangyu Zhang","Bojun Cheng"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.37379/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-37379","citation_date":"2026-09-29","json_url":"https://latent-implicit-thinking.github.io/papers/2609.37379/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.37379/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.37379/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.37379/citation.csl.json"},{"id":"2609.37432","title":"Looped Actor: Depth-Recurrent Reasoning Models for Reinforcement Learning","authors":"T. Konstantin Rusch, Tim Seyde, Jared Boyer, Zach J. Patterson, Daniela Rus","first_public":"2026-09-29","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.37432","paper_url":"https://arxiv.org/abs/2609.37432","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["reinforcement-learning"],"questions":["architecture","controllability","efficiency","theory"],"evidence":["formal","empirical"],"modality":["symbolic"],"summary":"Uses a shared transformer block to refine a reinforcement-learning policy's internal state before choosing an action. Learns to vary the number of loops with the current state, and studies adaptive computation in puzzles and robotic-control tasks.","provenance":"Primary-source literature search, 2026-10-18","author_names":["T. Konstantin Rusch","Tim Seyde","Jared Boyer","Zach J. Patterson","Daniela Rus"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.37432/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-37432","citation_date":"2026-09-29","json_url":"https://latent-implicit-thinking.github.io/papers/2609.37432/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.37432/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.37432/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.37432/citation.csl.json"},{"id":"2609.38426","title":"LoopVL: Recurrent Visual Intelligence","authors":"Zhe Qian, Ziyang Gong, Zhongxing Xu, Hehan Li, Zhonghua Wang, Hanmeng Liu, Liwei Qian, Xin Pei, Peizhi Xu, Fei Luo, Mingxuan Wang, Xue Yang, Shiwei Liu, Yanbiao Ma, Junchi Yan, Jungong Han","first_public":"2026-09-29","venue":"arXiv","arxiv":"2609.38426","paper_url":"https://arxiv.org/abs/2609.38426","lens":["recurrent"],"representation":["hidden-state","multimodal-latent"],"computation":["recurrent","depth-wise"],"training":["pretraining","supervised","reinforcement-learning"],"questions":["architecture","capability"],"evidence":["empirical"],"modality":["multimodal","vision","language"],"summary":"Extends shared-module and whole-model looping to vision-language models, repeatedly updating a joint visual-language state. Trains from scratch through language and multimodal stages and evaluates visual understanding and reasoning.","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Zhe Qian","Ziyang Gong","Zhongxing Xu","Hehan Li","Zhonghua Wang","Hanmeng Liu","Liwei Qian","Xin Pei","Peizhi Xu","Fei Luo","Mingxuan Wang","Xue Yang","Shiwei Liu","Yanbiao Ma","Junchi Yan","Jungong Han"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.38426/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-38426","citation_date":"2026-09-29","json_url":"https://latent-implicit-thinking.github.io/papers/2609.38426/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.38426/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.38426/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.38426/citation.csl.json"},{"id":"2609.38806","title":"Blackboard Intelligence Can Surpass Autoregressive on Globally Constrained Problems","authors":"Woosang Jeon, Jaeyeon Kim, Sham Kakade, Yilun Du, Amrit Singh Bedi, Arun Kumar Chithanar, Chul Lee, Taehyeong Kim, Sitan Chen","first_public":"2026-09-30","lens":["beyond-sequential"],"representation":["discrete-token"],"training":["inference-only"],"questions":["capability","evaluation"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Uses a fixed, revisable output and model confidence to search over candidate solutions with a frozen fine-tuned diffusion checkpoint. Evaluates logic and scheduling problems where global constraints can make irrevocable left-to-right commitments costly.","computation":["diffusion","search"],"venue":"arXiv","arxiv":"2609.38806","paper_url":"https://arxiv.org/abs/2609.38806","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Woosang Jeon","Jaeyeon Kim","Sham Kakade","Yilun Du","Amrit Singh Bedi","Arun Kumar Chithanar","Chul Lee","Taehyeong Kim","Sitan Chen"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.38806/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-38806","citation_date":"2026-09-30","json_url":"https://latent-implicit-thinking.github.io/papers/2609.38806/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.38806/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.38806/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.38806/citation.csl.json"},{"id":"2609.39740","title":"LatentHarness: Learning Latent Actions for Memory and Reasoning via Counterfactual Policy Distillation","authors":"Xiaoqiang Wang, Suyuchen Wang, Bang Liu","first_public":"2026-09-30","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.39740","paper_url":"https://arxiv.org/abs/2609.39740","lens":["continuous","recurrent"],"representation":["continuous-state","cache-memory"],"computation":["stateful","recurrent"],"training":["distillation"],"questions":["capability","efficiency","architecture"],"evidence":["empirical"],"modality":["language"],"summary":"Learns when to perform another internal reasoning step, recall stored evidence or intermediate states, or emit a token. Trains these choices by branching over alternative actions and measuring their effects on the next emitted token.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Xiaoqiang Wang","Suyuchen Wang","Bang Liu"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.39740/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-39740","citation_date":"2026-09-30","json_url":"https://latent-implicit-thinking.github.io/papers/2609.39740/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.39740/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.39740/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.39740/citation.csl.json"},{"id":"2609.39892","title":"Shared Weights, Selected Computations: How Looped Transformers Route What Each Loop Does","authors":"Jiaju Wu, Yi Hu, Muhan Zhang","first_public":"2026-09-30","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.39892","paper_url":"https://arxiv.org/abs/2609.39892","lens":["analysis","recurrent"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["analysis-only"],"questions":["interpretability","controllability"],"evidence":["empirical","mechanistic"],"modality":["symbolic"],"summary":"Uses graph-walk tasks to study how a looped transformer performs different computations with the same weights. Tests whether changing the state entering a loop can select its computation, using steering and activation-patching experiments.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Jiaju Wu","Yi Hu","Muhan Zhang"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.39892/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-39892","citation_date":"2026-09-30","json_url":"https://latent-implicit-thinking.github.io/papers/2609.39892/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.39892/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.39892/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.39892/citation.csl.json"},{"id":"2609.39967","title":"What Limits Recursive Reasoning Models: Optimization, Architecture and Test-Time Scaling","authors":"Yuliana Shakhvalieva, Dmitrii Kharchev, Viacheslav Bezrukov, Inessa Fedorova, Dmitry Bocharov, Ivan Oseledets, Valerii Ternovskii","first_public":"2026-09-30","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.39967","paper_url":"https://arxiv.org/abs/2609.39967","lens":["recurrent","analysis"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["supervised"],"questions":["architecture","generalization","limitations"],"evidence":["empirical"],"modality":["symbolic"],"summary":"Compares recursive reasoning models under a common training and evaluation setup. Isolates the effects of gradient propagation, batch size, state updates, and hierarchical structure on algorithmic tasks and generalization.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Yuliana Shakhvalieva","Dmitrii Kharchev","Viacheslav Bezrukov","Inessa Fedorova","Dmitry Bocharov","Ivan Oseledets","Valerii Ternovskii"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.39967/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-39967","citation_date":"2026-09-30","json_url":"https://latent-implicit-thinking.github.io/papers/2609.39967/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.39967/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.39967/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.39967/citation.csl.json"},{"id":"2609.40316","title":"Scaling Laws for Looped Mixture of Experts","authors":"Yanbei Chen, Anirudh Goyal, Raghuraman Krishnamoorthi","first_public":"2026-09-30","added_at":"2026-10-18","venue":"arXiv","arxiv":"2609.40316","paper_url":"https://arxiv.org/abs/2609.40316","lens":["recurrent","analysis"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["pretraining"],"questions":["scaling","architecture","efficiency"],"evidence":["empirical","scaling"],"modality":["language"],"summary":"Fits scaling laws that jointly account for recurrent depth, expert sparsity, model size, and training data in looped mixture-of-experts models. Uses them to study how to allocate resources under compute and memory constraints.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Yanbei Chen","Anirudh Goyal","Raghuraman Krishnamoorthi"],"record_url":"https://latent-implicit-thinking.github.io/papers/2609.40316/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2609-40316","citation_date":"2026-09-30","json_url":"https://latent-implicit-thinking.github.io/papers/2609.40316/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2609.40316/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2609.40316/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2609.40316/citation.csl.json"},{"id":"2610.00661","title":"Exploring More, Reasoning Better: Stepwise Risk-Sensitive GRPO for Diffusion Language Models","authors":"Yue Yu, Bowen Zuo, David Crandall, Yinglun Zhu, Dongruo Zhou","first_public":"2026-09-30","lens":["beyond-sequential"],"representation":["discrete-token"],"training":["reinforcement-learning"],"questions":["capability","scaling"],"evidence":["empirical","formal"],"modality":["language","symbolic"],"summary":"Changes how outcome rewards weight decisions at different denoising states during diffusion-model reinforcement learning. Derives the effect for binary rewards and uses matched-scale controls to test whether the schedule improves mathematical accuracy and reasoning-trace diversity.","computation":["diffusion","parallel"],"venue":"arXiv","arxiv":"2610.00661","paper_url":"https://arxiv.org/abs/2610.00661","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Yue Yu","Bowen Zuo","David Crandall","Yinglun Zhu","Dongruo Zhou"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.00661/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-00661","citation_date":"2026-09-30","json_url":"https://latent-implicit-thinking.github.io/papers/2610.00661/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.00661/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.00661/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.00661/citation.csl.json"},{"id":"2610.00673","title":"Closing the Loop: Practical Training Recipes for Looped Language Models","authors":"Andrei Marchenko, Viacheslav Bezrukov, Oleg Kashurin, Inessa Fedorova, Dmitry Bocharov, Yuliana Shakhvalieva, Maria Tikhonova, Valerii Ternovskii","first_public":"2026-09-30","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.00673","paper_url":"https://arxiv.org/abs/2610.00673","summary":"Gives training recipes for looped language models both from scratch and by converting pretrained models. Uses controlled data and compute comparisons to separate the benefit of recurrence from the training setup.","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["pretraining"],"questions":["architecture","efficiency","capability"],"evidence":["empirical"],"modality":["language"],"provenance":"Primary-source literature search, 2026-10-18","author_names":["Andrei Marchenko","Viacheslav Bezrukov","Oleg Kashurin","Inessa Fedorova","Dmitry Bocharov","Yuliana Shakhvalieva","Maria Tikhonova","Valerii Ternovskii"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.00673/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-00673","citation_date":"2026-09-30","json_url":"https://latent-implicit-thinking.github.io/papers/2610.00673/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.00673/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.00673/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.00673/citation.csl.json"},{"id":"2610.14030","title":"Rotate the Loop: Blockwise Conformality for Looped Transformers","authors":"Alexey Zemtsov, Albina Klepach, Vadim Lomshakov, Andrei Polubarov, Nikita Lyubaykin, Alexander Derevyagin, Vladislav Kurenkov, Alexander Nikulin","first_public":"2026-09-30","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.14030","paper_url":"https://arxiv.org/abs/2610.14030","summary":"Splits the recurrent residual into groups and rotates each group separately, aiming to preserve information across repeated transformer loops. Evaluates state tracking and language modeling.","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["pretraining","supervised"],"questions":["architecture","capability","generalization"],"evidence":["empirical"],"modality":["language","symbolic"],"provenance":"Primary-source literature search, 2026-10-18","author_names":["Alexey Zemtsov","Albina Klepach","Vadim Lomshakov","Andrei Polubarov","Nikita Lyubaykin","Alexander Derevyagin","Vladislav Kurenkov","Alexander Nikulin"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.14030/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-14030","citation_date":"2026-09-30","json_url":"https://latent-implicit-thinking.github.io/papers/2610.14030/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.14030/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.14030/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.14030/citation.csl.json"},{"id":"2610.01153","title":"Looping Beyond Twice: A Scalable Recipe for Looped Mixture-of-Experts","authors":"Di He, Pengxiang Li, Da Chang, Qingyan Meng, Lu Yin, Shiwei Liu","first_public":"2026-10-01","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.01153","paper_url":"https://arxiv.org/abs/2610.01153","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["pretraining"],"questions":["architecture","scaling","efficiency"],"evidence":["empirical","scaling"],"modality":["language"],"summary":"Studies how to train mixture-of-experts transformers with more than two recurrent passes. Combines stabilized residual updates, reintroduced input information, and loop-specific routing to support deeper reuse of the shared model.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Di He","Pengxiang Li","Da Chang","Qingyan Meng","Lu Yin","Shiwei Liu"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.01153/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-01153","citation_date":"2026-10-01","json_url":"https://latent-implicit-thinking.github.io/papers/2610.01153/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.01153/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.01153/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.01153/citation.csl.json"},{"id":"2610.01177","title":"Temporally-Resolved Token Attribution Reveals the Generation Dynamics of Diffusion Language Models","authors":"Darpan Aswal, Céline Hudelot","first_public":"2026-10-01","lens":["analysis","beyond-sequential"],"representation":["hidden-state","discrete-token"],"training":["analysis-only"],"questions":["interpretability","evaluation"],"evidence":["formal","empirical"],"modality":["language","symbolic"],"summary":"Extends integrated-gradient attribution across layers and denoising steps to examine which inputs influence a diffusion model's developing response. Includes multi-hop graph reasoning; the authors present attribution as a complement to, not a replacement for, causal intervention.","computation":["diffusion"],"venue":"arXiv","arxiv":"2610.01177","paper_url":"https://arxiv.org/abs/2610.01177","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Darpan Aswal","Céline Hudelot"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.01177/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-01177","citation_date":"2026-10-01","json_url":"https://latent-implicit-thinking.github.io/papers/2610.01177/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.01177/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.01177/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.01177/citation.csl.json"},{"id":"2610.02185","title":"Decoding Looped Transformers Better for (Almost) Free","authors":"Weihao Liu, Huangjie Zheng, Tianrong Chen, Rohit Dilip, Richard He Bai, Yizhu Jiao, Yuyang Wang, Ruixiang Zhang","first_public":"2026-10-01","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.02185","paper_url":"https://arxiv.org/abs/2610.02185","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["inference-only"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Compares a looped model's final prediction with predictions from earlier loops to improve decoding without additional training. Tests contrastive variants using either output logits or hidden states on mathematical reasoning and code generation.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Weihao Liu","Huangjie Zheng","Tianrong Chen","Rohit Dilip","Richard He Bai","Yizhu Jiao","Yuyang Wang","Ruixiang Zhang"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.02185/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-02185","citation_date":"2026-10-01","json_url":"https://latent-implicit-thinking.github.io/papers/2610.02185/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.02185/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.02185/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.02185/citation.csl.json"},{"id":"2610.02193","title":"Hierarchical Continuous Diffusion Language Models","authors":"Hui Ren, Zihan Li, Chang Liu, Huidong Liu, Alexander Schwing","first_public":"2026-10-01","lens":["continuous","beyond-sequential"],"representation":["continuous-state","discrete-token"],"training":["supervised"],"questions":["architecture","capability"],"evidence":["formal","empirical"],"modality":["language","symbolic"],"summary":"Keeps a continuous state throughout denoising while reading out tokens at each step and feeding them back into the next state update. Tests whether this coupling preserves dependencies during parallel generation on Sudoku, Countdown, and language modeling.","computation":["diffusion","parallel"],"venue":"arXiv","arxiv":"2610.02193","paper_url":"https://arxiv.org/abs/2610.02193","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Hui Ren","Zihan Li","Chang Liu","Huidong Liu","Alexander Schwing"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.02193/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-02193","citation_date":"2026-10-01","json_url":"https://latent-implicit-thinking.github.io/papers/2610.02193/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.02193/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.02193/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.02193/citation.csl.json"},{"id":"2610.02383","title":"The Surprising Effectiveness of Shared Memory in Looped Transformers","authors":"Giovanni Monea, Keshav Ramji, Yousef El-Kurdi, Luis A. Lastras, Yoav Artzi, Nathan Godey, Ramón Fernandez Astudillo","first_public":"2026-10-01","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.02383","paper_url":"https://arxiv.org/abs/2610.02383","lens":["recurrent"],"representation":["hidden-state","cache-memory"],"computation":["recurrent","depth-wise","stateful"],"training":["pretraining"],"questions":["architecture","efficiency","interpretability"],"evidence":["empirical","mechanistic"],"modality":["language"],"summary":"Shares a long-context KV memory written by the first loop across later loops, which also keep a short local memory. Studies this architecture during pretraining and examines how shared memory changes representations and gradient flow.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Giovanni Monea","Keshav Ramji","Yousef El-Kurdi","Luis A. Lastras","Yoav Artzi","Nathan Godey","Ramón Fernandez Astudillo"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.02383/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-02383","citation_date":"2026-10-01","json_url":"https://latent-implicit-thinking.github.io/papers/2610.02383/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.02383/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.02383/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.02383/citation.csl.json"},{"id":"2610.02665","title":"Large Language Continuous Diffusion Models","authors":"Zhihan Yang, Wei Guo, Jean-Marie Lemercier, Simon Welker, Yonggan Fu, Mohammad Mahdi Kamani, Sajad Norouzi, Julius Berner, Tomas Geffner, Karsten Kreis, Yongxin Chen, Molei Tao, John Thickstun, Pavlo Molchanov, Ante Jukić, Arash Vahdat, Morteza Mardani","first_public":"2026-10-02","lens":["continuous","beyond-sequential"],"representation":["continuous-state"],"training":["pretraining","supervised"],"questions":["architecture","capability","efficiency","controllability"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Sigma denoises learned continuous token embeddings in blocks, starting from autoregressive pretrained weights. Studies how guidance and temperature affect mathematical reasoning, coding, output diversity, and performance when fewer refinement steps are used.","computation":["diffusion","parallel"],"venue":"arXiv","arxiv":"2610.02665","paper_url":"https://arxiv.org/abs/2610.02665","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Zhihan Yang","Wei Guo","Jean-Marie Lemercier","Simon Welker","Yonggan Fu","Mohammad Mahdi Kamani","Sajad Norouzi","Julius Berner","Tomas Geffner","Karsten Kreis","Yongxin Chen","Molei Tao","John Thickstun","Pavlo Molchanov","Ante Jukić","Arash Vahdat","Morteza Mardani"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.02665/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-02665","citation_date":"2026-10-02","json_url":"https://latent-implicit-thinking.github.io/papers/2610.02665/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.02665/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.02665/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.02665/citation.csl.json"},{"id":"2610.02741","title":"On the Chain-of-Thought Monitorability of Looped Language Models","authors":"Han Wang, Ishwar B Balappanawar, Huan Zhang","first_public":"2026-10-02","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.02741","paper_url":"https://arxiv.org/abs/2610.02741","lens":["analysis","recurrent"],"representation":["hidden-state","text-latent-hybrid"],"computation":["recurrent","depth-wise"],"training":["analysis-only"],"questions":["evaluation","interpretability","limitations"],"evidence":["empirical","boundary"],"modality":["language","symbolic"],"summary":"Tests how recurrent depth affects the ability to monitor a language model through its written chain of thought. Finds task-dependent changes under stress tests, while matched comparisons do not show a general monitorability disadvantage for looped architectures.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Han Wang","Ishwar B Balappanawar","Huan Zhang"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.02741/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-02741","citation_date":"2026-10-02","json_url":"https://latent-implicit-thinking.github.io/papers/2610.02741/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.02741/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.02741/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.02741/citation.csl.json"},{"id":"2610.03665","title":"Pivot-SD: Efficient Self-Distillation for Masked Diffusion Language Models","authors":"Seo Hyun Kim, Sunwoo Hong, Younwoo Choi, Chen-Hao Chao, Se-Young Yun, Rahul G. Krishnan","first_public":"2026-10-02","lens":["beyond-sequential"],"representation":["discrete-token"],"training":["self-distillation"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Selects token commitments that most reduce uncertainty over the remaining output. Self-distillation reinforces these pivots from successful diffusion trajectories and discourages selected pivots from failed ones, rather than supervising every token equally.","computation":["diffusion"],"venue":"arXiv","arxiv":"2610.03665","paper_url":"https://arxiv.org/abs/2610.03665","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Seo Hyun Kim","Sunwoo Hong","Younwoo Choi","Chen-Hao Chao","Se-Young Yun","Rahul G. Krishnan"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.03665/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-03665","citation_date":"2026-10-02","json_url":"https://latent-implicit-thinking.github.io/papers/2610.03665/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.03665/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.03665/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.03665/citation.csl.json"},{"id":"2610.06949","title":"AdaLoop: Adaptive-Depth Latent Reasoning for Audio Language Models","authors":"Lee Seung-woo, Bowen Qi","first_public":"2026-10-03","venue":"arXiv","arxiv":"2610.06949","paper_url":"https://arxiv.org/abs/2610.06949","lens":["recurrent"],"representation":["hidden-state","multimodal-latent"],"computation":["recurrent","depth-wise"],"training":["supervised"],"questions":["architecture","capability","efficiency","controllability"],"evidence":["empirical"],"modality":["multimodal","language"],"summary":"Adds a shared recurrent block between an audio encoder and language model. A question-conditioned halting mechanism chooses how many refinement passes to apply, with deeper computation learned for tasks requiring finer acoustic distinctions.","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Lee Seung-woo","Bowen Qi"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.06949/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-06949","citation_date":"2026-10-03","json_url":"https://latent-implicit-thinking.github.io/papers/2610.06949/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.06949/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.06949/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.06949/citation.csl.json"},{"id":"2610.04864","title":"Enhancing Long-Video VLM Embeddings with Query-Aware Streaming Latent Reasoning","authors":"Haozhe Chi, Song Jin, Yang Jin, Yadong Mu","first_public":"2026-10-04","venue":"arXiv","arxiv":"2610.04864","paper_url":"https://arxiv.org/abs/2610.04864","lens":["continuous","recurrent"],"representation":["multimodal-latent"],"computation":["recurrent","stateful"],"training":["supervised","self-distillation"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["multimodal","vision"],"summary":"Processes selected video clips sequentially while persistent think tokens accumulate evidence for a fixed-size retrieval embedding. Intermediate retrieval supervision and self-distillation train partial-video readouts; the output is an embedding rather than a generated reasoning trace.","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Haozhe Chi","Song Jin","Yang Jin","Yadong Mu"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.04864/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-04864","citation_date":"2026-10-04","json_url":"https://latent-implicit-thinking.github.io/papers/2610.04864/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.04864/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.04864/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.04864/citation.csl.json"},{"id":"2610.06666","title":"What Matters for Latent Reasoning with Flow Matching","authors":"Yassine Ouali, Adrian Bulat, Georgios Tzimiropoulos","first_public":"2026-10-05","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.06666","paper_url":"https://arxiv.org/abs/2610.06666","lens":["continuous","beyond-sequential"],"representation":["continuous-state"],"computation":["parallel","diffusion"],"training":["supervised","self-training"],"questions":["capability","efficiency","interpretability","evaluation"],"evidence":["empirical","probing"],"modality":["language","symbolic"],"summary":"Compresses symbolic reasoning into latent codes and trains a flow model to refine a block of noise into a thought before decoding the answer. Studies training choices, self-training on verified thoughts, and tests of whether the answer actually uses those thoughts.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Yassine Ouali","Adrian Bulat","Georgios Tzimiropoulos"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.06666/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-06666","citation_date":"2026-10-05","json_url":"https://latent-implicit-thinking.github.io/papers/2610.06666/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.06666/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.06666/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.06666/citation.csl.json"},{"id":"2610.06833","title":"Towards Looped Models Done Right, Part II: Rethinking at Fixed Points","authors":"Benhao Huang, Chufan Shi, Junlin Chen, Shicheng Wen, Zhengzhong Liu, Eric Xing, Xuezhe Ma","first_public":"2026-10-05","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.06833","paper_url":"https://arxiv.org/abs/2610.06833","summary":"Uses near-fixed-point recurrent states to reduce the cost of training, key/value caching, and prefill. Learns how to sample loop depths and changes how the input is reintroduced on each loop.","lens":["recurrent"],"representation":["hidden-state","cache-memory"],"computation":["recurrent","depth-wise"],"training":["pretraining","distillation","reinforcement-learning"],"questions":["architecture","efficiency","scaling"],"evidence":["empirical","scaling"],"modality":["language"],"provenance":"Primary-source literature search, 2026-10-18","author_names":["Benhao Huang","Chufan Shi","Junlin Chen","Shicheng Wen","Zhengzhong Liu","Eric Xing","Xuezhe Ma"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.06833/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-06833","citation_date":"2026-10-05","json_url":"https://latent-implicit-thinking.github.io/papers/2610.06833/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.06833/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.06833/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.06833/citation.csl.json"},{"id":"2610.07175","title":"CALR: Continuous Anchored Latent Reasoning via Render-of-Thought Compression","authors":"Zhaoyang Wei, Bowen Jiang, Yanchao Hao, Wenchao Ding, Zheng Wei, Shaocheng Wu, Zhenjun Han, Jianbin Jiao","first_public":"2026-10-05","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.07175","paper_url":"https://arxiv.org/abs/2610.07175","lens":["continuous"],"representation":["continuous-state","multimodal-latent"],"computation":["token-wise"],"training":["supervised","curriculum"],"questions":["capability","efficiency","interpretability"],"evidence":["empirical","probing"],"modality":["language","symbolic","vision"],"summary":"Compresses images of written derivations into continuous states, training both the answers they support and the reasoning that can be recovered from them. Gradually shifts from generating latent blocks in parallel to generating them in sequence.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Zhaoyang Wei","Bowen Jiang","Yanchao Hao","Wenchao Ding","Zheng Wei","Shaocheng Wu","Zhenjun Han","Jianbin Jiao"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.07175/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-07175","citation_date":"2026-10-05","json_url":"https://latent-implicit-thinking.github.io/papers/2610.07175/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.07175/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.07175/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.07175/citation.csl.json"},{"id":"2610.07591","title":"Recurrent Looped Transformer","authors":"Yifan Zhang, Jichen Feng, Shihan Qin, Sun-Yuan Kung, Mengdi Wang","first_public":"2026-10-06","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.07591","paper_url":"https://arxiv.org/abs/2610.07591","summary":"Passes each token's final decoder state to the next token, alongside a causal encoder representation. Tests whether this growing computation path supports state tracking on sequences longer than those seen during training.","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent","token-wise","stateful"],"training":["supervised"],"questions":["architecture","capability","generalization"],"evidence":["empirical"],"modality":["symbolic"],"provenance":"Primary-source literature search, 2026-10-18","author_names":["Yifan Zhang","Jichen Feng","Shihan Qin","Sun-Yuan Kung","Mengdi Wang"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.07591/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-07591","citation_date":"2026-10-06","json_url":"https://latent-implicit-thinking.github.io/papers/2610.07591/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.07591/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.07591/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.07591/citation.csl.json"},{"id":"2610.07730","title":"SanSi: A Looped Typed Decision Model for System 1.5 Thinking","authors":"Shuyu Gan, Young-Jun Lee, Dongyeop Kang","first_public":"2026-10-06","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.07730","paper_url":"https://arxiv.org/abs/2610.07730","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["supervised"],"questions":["capability","controllability","generalization"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Refines an internal state across loops to choose among typed answer options without generating a written reasoning trace. Supervises decisions at multiple depths and evaluates how prediction quality changes with the available computation budget.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Shuyu Gan","Young-Jun Lee","Dongyeop Kang"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.07730/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-07730","citation_date":"2026-10-06","json_url":"https://latent-implicit-thinking.github.io/papers/2610.07730/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.07730/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.07730/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.07730/citation.csl.json"},{"id":"2610.07907","title":"Continuous Memory Machines","authors":"Ciaran Regan, Kai Arulkumaran, Luke Darlow, Stefania Druga, Sebastian Risi, Llion Jones","first_public":"2026-10-06","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.07907","paper_url":"https://arxiv.org/abs/2610.07907","summary":"Keeps separate short- and long-term matrix memories and lets a transformer update both through bidirectional reads and writes. Tests this recurrent architecture on algorithmic, in-context learning, and reasoning tasks.","lens":["recurrent"],"representation":["hidden-state","cache-memory"],"computation":["recurrent","stateful"],"training":["supervised"],"questions":["architecture","capability","generalization"],"evidence":["empirical"],"modality":["symbolic"],"provenance":"Primary-source literature search, 2026-10-18","author_names":["Ciaran Regan","Kai Arulkumaran","Luke Darlow","Stefania Druga","Sebastian Risi","Llion Jones"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.07907/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-07907","citation_date":"2026-10-06","json_url":"https://latent-implicit-thinking.github.io/papers/2610.07907/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.07907/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.07907/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.07907/citation.csl.json"},{"id":"2610.09145","title":"Noise Your Prompt: Noising Conditioning Tokens in Continuous Diffusion Language Models","authors":"Justin Jung","first_public":"2026-10-06","lens":["continuous","beyond-sequential"],"representation":["continuous-state"],"training":["supervised"],"questions":["generalization","capability","limitations"],"evidence":["empirical","boundary"],"modality":["language","symbolic"],"summary":"Adds noise to conditioning tokens during training instead of keeping the prompt clean. Tests improvements in Sudoku and N-Queens generalization and solution diversity, while reporting that the gains do not transfer to every language-generation task.","computation":["diffusion"],"venue":"arXiv","arxiv":"2610.09145","paper_url":"https://arxiv.org/abs/2610.09145","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Justin Jung"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.09145/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-09145","citation_date":"2026-10-06","json_url":"https://latent-implicit-thinking.github.io/papers/2610.09145/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.09145/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.09145/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.09145/citation.csl.json"},{"id":"2610.09416","title":"Efficient Reasoning with Flow Language Models","authors":"Hanru Bai, Faissal Izermine, Oscar Davis, T. Konstantin Rusch","first_public":"2026-10-07","lens":["analysis","continuous","beyond-sequential"],"representation":["continuous-state"],"training":["analysis-only","supervised"],"questions":["theory","interpretability","efficiency"],"evidence":["formal","empirical","mechanistic"],"modality":["symbolic"],"summary":"Compares continuous flow and discrete diffusion models at matched sizes and denoising steps. A theoretical account and intermediate-state interventions examine whether retaining information about several candidates helps solve mazes and Sudoku before final discretization.","computation":["diffusion","parallel"],"venue":"arXiv","arxiv":"2610.09416","paper_url":"https://arxiv.org/abs/2610.09416","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Hanru Bai","Faissal Izermine","Oscar Davis","T. Konstantin Rusch"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.09416/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-09416","citation_date":"2026-10-07","json_url":"https://latent-implicit-thinking.github.io/papers/2610.09416/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.09416/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.09416/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.09416/citation.csl.json"},{"id":"2610.09876","title":"Think Before You Paint: Recursive Latent Reasoning for Diffusion Models","authors":"Paweł Skierś, Małgorzata Grzanka, Wojciech Masarczyk, Jan-Willem van de Meent, Kamil Deja","first_public":"2026-10-07","venue":"arXiv","arxiv":"2610.09876","paper_url":"https://arxiv.org/abs/2610.09876","lens":["recurrent","continuous","beyond-sequential"],"representation":["multimodal-latent","continuous-state"],"computation":["recurrent","diffusion"],"training":["supervised"],"questions":["architecture","capability","generalization"],"evidence":["empirical"],"modality":["vision","symbolic"],"summary":"PaTh uses a small recursive network to refine learned image-state tokens inside each denoising step and steer a frozen diffusion model through adapters. It learns visual puzzles from reconstruction targets without symbolic solutions or an external verifier.","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Paweł Skierś","Małgorzata Grzanka","Wojciech Masarczyk","Jan-Willem van de Meent","Kamil Deja"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.09876/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-09876","citation_date":"2026-10-07","json_url":"https://latent-implicit-thinking.github.io/papers/2610.09876/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.09876/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.09876/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.09876/citation.csl.json"},{"id":"2610.10623","title":"Recurrent Self-Improvement: Dynamic Cross-Loop On-Policy Distillation for Looped Language Models","authors":"Yi Wang, Rui Qian, Yu Li, Haoyang Yao, Wenjie Wang","first_public":"2026-10-07","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.10623","paper_url":"https://arxiv.org/abs/2610.10623","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["self-distillation"],"questions":["capability","architecture","theory"],"evidence":["empirical","formal"],"modality":["language","symbolic"],"summary":"Trains an intermediate loop using a deeper loop of the same language model as its teacher on student-generated outputs. A dynamic variant refreshes the teacher during training, turning additional recurrent computation into a source of supervision.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Yi Wang","Rui Qian","Yu Li","Haoyang Yao","Wenjie Wang"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.10623/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-10623","citation_date":"2026-10-07","json_url":"https://latent-implicit-thinking.github.io/papers/2610.10623/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.10623/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.10623/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.10623/citation.csl.json"},{"id":"2610.10625","title":"Safe at One Loop, Risky at Another: Aligning Safety Across Recurrent Depths in Looped Language Models","authors":"Yi Wang, Xiuyuan Qi, Dongqi Han, Dongsheng Li, Wenjie Wang","first_public":"2026-10-07","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.10625","paper_url":"https://arxiv.org/abs/2610.10625","lens":["recurrent","analysis"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["supervised"],"questions":["evaluation","controllability","limitations"],"evidence":["empirical"],"modality":["language"],"summary":"Evaluates harmful-query and jailbreak behavior at different recurrent depths of looped language models. Proposes depth-specific control, state sharing, and joint supervision to align safety behavior across depths.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Yi Wang","Xiuyuan Qi","Dongqi Han","Dongsheng Li","Wenjie Wang"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.10625/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-10625","citation_date":"2026-10-07","json_url":"https://latent-implicit-thinking.github.io/papers/2610.10625/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.10625/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.10625/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.10625/citation.csl.json"},{"id":"2610.10996","title":"Invariant-Measure Reasoners: Stable Representations for Latent Reasoning","authors":"Yuto Inui, Takuya Konishi, Yoshinobu Kawahara","first_public":"2026-10-07","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.10996","paper_url":"https://arxiv.org/abs/2610.10996","summary":"Predicts by averaging over the long-run distribution of recurrent hidden states instead of reading a single final state. This lets the model use changing hidden states without requiring them to settle at one fixed point.","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent"],"training":["supervised"],"questions":["architecture","capability","generalization"],"evidence":["empirical"],"modality":["symbolic"],"provenance":"Primary-source literature search, 2026-10-18","author_names":["Yuto Inui","Takuya Konishi","Yoshinobu Kawahara"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.10996/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-10996","citation_date":"2026-10-07","json_url":"https://latent-implicit-thinking.github.io/papers/2610.10996/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.10996/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.10996/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.10996/citation.csl.json"},{"id":"2610.20641","title":"AbridgeKV: Compressing Long Reasoning into the KV Cache of Learned Pause Tokens","authors":"Jack Cai, Lijie Yang, Vasilis Kontonis, Dimitris Papailiopoulos, Shivam Garg","first_public":"2026-10-07","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.20641","paper_url":"https://arxiv.org/abs/2610.20641","summary":"Compresses each completed block of generated reasoning into the key/value cache of learned pause tokens, then discards the block's original cache. Later tokens attend to the compact replacement.","lens":["learned-tokens"],"representation":["cache-memory","text-latent-hybrid"],"computation":["token-wise","stateful"],"training":["supervised"],"questions":["efficiency","architecture"],"evidence":["empirical"],"modality":["language","symbolic"],"provenance":"Primary-source literature search, 2026-10-18","author_names":["Jack Cai","Lijie Yang","Vasilis Kontonis","Dimitris Papailiopoulos","Shivam Garg"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.20641/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-20641","citation_date":"2026-10-07","json_url":"https://latent-implicit-thinking.github.io/papers/2610.20641/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.20641/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.20641/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.20641/citation.csl.json"},{"id":"2610.11570","title":"Scaling to Tens of Thousands of Test-Time Iterations with Loop-Native Attention Residuals","authors":"Pengxiang Li, Dilxat Muhtar, Di He, Guinan Su, Lu Yin, Shiwei Liu","first_public":"2026-10-08","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.11570","paper_url":"https://arxiv.org/abs/2610.11570","lens":["recurrent"],"representation":["hidden-state","continuous-state"],"computation":["recurrent","depth-wise","stateful"],"training":["supervised"],"questions":["architecture","scaling","generalization"],"evidence":["empirical","scaling"],"modality":["symbolic"],"summary":"Adds a learned running summary of previous recurrent states so that each update can retain useful earlier work. Uses content-based weighting and temporal decay with constant aggregation memory, and tests whether puzzle-solving improves over much longer inference runs.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Pengxiang Li","Dilxat Muhtar","Di He","Guinan Su","Lu Yin","Shiwei Liu"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.11570/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-11570","citation_date":"2026-10-08","json_url":"https://latent-implicit-thinking.github.io/papers/2610.11570/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.11570/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.11570/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.11570/citation.csl.json"},{"id":"2610.12582","title":"One Model to Loop Them All: Elastic Latent Recurrence for Language Models","authors":"Faisal Ladhak, Shantanu Acharya, Santiago Akle Serano, Simeng Sun, Boris Ginsburg, Krishna C Puvvada","first_public":"2026-10-08","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.12582","paper_url":"https://arxiv.org/abs/2610.12582","summary":"Trains one language model to operate at different loop counts by mixing depths during training and conditioning each pass on its index and budget. A learned gate controls each recurrent update.","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["pretraining","supervised"],"questions":["architecture","efficiency","scaling","controllability"],"evidence":["empirical","scaling"],"modality":["language"],"provenance":"Primary-source literature search, 2026-10-18","author_names":["Faisal Ladhak","Shantanu Acharya","Santiago Akle Serano","Simeng Sun","Boris Ginsburg","Krishna C Puvvada"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.12582/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-12582","citation_date":"2026-10-08","json_url":"https://latent-implicit-thinking.github.io/papers/2610.12582/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.12582/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.12582/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.12582/citation.csl.json"},{"id":"2610.13330","title":"Masked Diffusion Language Agents for Tool-Integrated Chemical Reasoning","authors":"Mengdi Liu, Chenghao Jia, Hong Chang, Shiguang Shan","first_public":"2026-10-09","lens":["beyond-sequential"],"representation":["discrete-token"],"training":["supervised","reinforcement-learning"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"ChemDiffAgent denoises interleaved textual reasoning and tool-use trajectories, letting tool decisions depend on context across the trajectory. A chemistry benchmark and matched-budget comparisons test this alternative to left-to-right agent generation.","computation":["diffusion","parallel"],"venue":"arXiv","arxiv":"2610.13330","paper_url":"https://arxiv.org/abs/2610.13330","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Mengdi Liu","Chenghao Jia","Hong Chang","Shiguang Shan"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.13330/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-13330","citation_date":"2026-10-09","json_url":"https://latent-implicit-thinking.github.io/papers/2610.13330/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.13330/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.13330/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.13330/citation.csl.json"},{"id":"2610.13527","title":"S-Space: Exploring Spatial Workspace in Multimodal Language Models","authors":"Zhiyuan Shi, Xiang Li, Xingzhuo Guo, Shangchen Miao, Weiliang Chen, Qiyu Dai, Jinshan Ren, Jiangran Lyu, Fangfu Liu, Mingsheng Long, Jialong Wu","first_public":"2026-10-09","venue":"arXiv","arxiv":"2610.13527","paper_url":"https://arxiv.org/abs/2610.13527","lens":["analysis"],"representation":["hidden-state","multimodal-latent"],"computation":["depth-wise"],"training":["analysis-only"],"questions":["interpretability","evaluation","limitations"],"evidence":["empirical","mechanistic","probing"],"modality":["multimodal","vision"],"summary":"Identifies spatial-coordinate directions in multimodal model activations and tests them through causal interventions. Separating perception from viewpoint transformation reveals cases where a model represents object locations but fails to perform the required spatial computation.","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Zhiyuan Shi","Xiang Li","Xingzhuo Guo","Shangchen Miao","Weiliang Chen","Qiyu Dai","Jinshan Ren","Jiangran Lyu","Fangfu Liu","Mingsheng Long","Jialong Wu"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.13527/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-13527","citation_date":"2026-10-09","json_url":"https://latent-implicit-thinking.github.io/papers/2610.13527/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.13527/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.13527/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.13527/citation.csl.json"},{"id":"2610.14252","title":"Adaptive-Depth Is a Finishing Stage","authors":"Andrei Piterbarg, Sean McLeish, Dhruv Pai, Benjamin Keigwin","first_public":"2026-10-09","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.14252","paper_url":"https://arxiv.org/abs/2610.14252","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["pretraining","curriculum"],"questions":["efficiency","architecture","scaling"],"evidence":["empirical","scaling"],"modality":["language"],"summary":"Trains a looped language model at a fixed depth first, then introduces varying depths only near the end of training. Compares the resulting training cost and performance across inference depths with varying depth throughout training.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Andrei Piterbarg","Sean McLeish","Dhruv Pai","Benjamin Keigwin"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.14252/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-14252","citation_date":"2026-10-09","json_url":"https://latent-implicit-thinking.github.io/papers/2610.14252/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.14252/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.14252/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.14252/citation.csl.json"},{"id":"2610.14456","title":"Learning to Extrapolate in Depth with Looped Transformers","authors":"Huitao Yang, Jianhao Huang, Zixuan Wang, Baharan Mirzasoleiman","first_public":"2026-10-10","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.14456","paper_url":"https://arxiv.org/abs/2610.14456","summary":"Analyzes how many extra loops a model trained on graph connectivity can safely run. Derives a finite range where added depth solves harder graphs before further loops create false connections.","lens":["analysis","recurrent"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["supervised","analysis-only"],"questions":["theory","generalization","limitations"],"evidence":["formal","empirical","boundary"],"modality":["symbolic"],"provenance":"Primary-source literature search, 2026-10-18","author_names":["Huitao Yang","Jianhao Huang","Zixuan Wang","Baharan Mirzasoleiman"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.14456/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-14456","citation_date":"2026-10-10","json_url":"https://latent-implicit-thinking.github.io/papers/2610.14456/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.14456/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.14456/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.14456/citation.csl.json"},{"id":"2610.15081","title":"Knowledge transfer between simple discrete worlds","authors":"Silvère Gangloff, Jan Hula","first_public":"2026-10-10","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.15081","paper_url":"https://arxiv.org/abs/2610.15081","lens":["recurrent","analysis"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["supervised"],"questions":["generalization","evaluation"],"evidence":["empirical"],"modality":["symbolic"],"summary":"Evaluates a depth-recurrent model on Sudoku-like worlds with different rule combinations. Compares symbolic rule descriptions with solved examples when the test world contains new puzzles, new combinations, or unfamiliar rule instances.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Silvère Gangloff","Jan Hula"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.15081/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-15081","citation_date":"2026-10-10","json_url":"https://latent-implicit-thinking.github.io/papers/2610.15081/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.15081/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.15081/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.15081/citation.csl.json"},{"id":"2610.15097","title":"Anchors Enhance Controllability and Reasoning of Diffusion Language Models","authors":"Feiyu Qu, Zheng Huang, Andrea Zanette","first_public":"2026-10-10","lens":["beyond-sequential"],"representation":["discrete-token"],"training":["reinforcement-learning"],"questions":["controllability","capability"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Trains an anchor generator to choose a short text fragment and its position in a frozen diffusion model's output. These visible control tokens guide subsequent denoising, with rewards for correct answers and satisfied constraints.","computation":["diffusion"],"venue":"arXiv","arxiv":"2610.15097","paper_url":"https://arxiv.org/abs/2610.15097","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Feiyu Qu","Zheng Huang","Andrea Zanette"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.15097/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-15097","citation_date":"2026-10-10","json_url":"https://latent-implicit-thinking.github.io/papers/2610.15097/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.15097/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.15097/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.15097/citation.csl.json"},{"id":"2610.15218","title":"Running Fewer Loops Removes Refusal Behaviour in Recurrent-Depth Language Models","authors":"Seyedarmin Azizi, Erfan Baghaei Potraghloo, Arya Fayyazi, Saeid Shokoufa, Massoud Pedram","first_public":"2026-10-10","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.15218","paper_url":"https://arxiv.org/abs/2610.15218","lens":["analysis","recurrent"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["analysis-only","supervised"],"questions":["evaluation","interpretability","limitations"],"evidence":["empirical","mechanistic","probing"],"modality":["language"],"summary":"Studies how reducing recurrent depth changes refusal behavior in two looped language-model families. Uses probes and interventions to distinguish recognizing a harmful request from refusing it, and tests safety training across randomly selected depths.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Seyedarmin Azizi","Erfan Baghaei Potraghloo","Arya Fayyazi","Saeid Shokoufa","Massoud Pedram"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.15218/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-15218","citation_date":"2026-10-10","json_url":"https://latent-implicit-thinking.github.io/papers/2610.15218/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.15218/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.15218/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.15218/citation.csl.json"},{"id":"2610.15501","title":"Large Decision Models: Repurposing Large Language Models as Single-Pass Decision Makers","authors":"Ziyi Chen, Yan Zhang, Jianhui Wei, Jianing Yin, Daoan Zhang","first_public":"2026-10-11","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.15501","paper_url":"https://arxiv.org/abs/2610.15501","lens":["internalized"],"representation":["hidden-state"],"computation":["depth-wise"],"training":["distillation","supervised"],"questions":["capability","efficiency","generalization"],"evidence":["empirical"],"modality":["language"],"summary":"Trains a language model to score labels supplied at inference in one forward pass, without generating a reasoning trace. Distills label distributions from repeated teacher reasoning and studies routing uncertain decisions back to explicit reasoning.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Ziyi Chen","Yan Zhang","Jianhui Wei","Jianing Yin","Daoan Zhang"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.15501/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-15501","citation_date":"2026-10-11","json_url":"https://latent-implicit-thinking.github.io/papers/2610.15501/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.15501/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.15501/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.15501/citation.csl.json"},{"id":"2610.16427","title":"Resample the Answer: Where to Spend Test-Time Compute in Recursive Reasoning","authors":"Maxime Illouz","first_public":"2026-10-12","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.16427","paper_url":"https://arxiv.org/abs/2610.16427","lens":["recurrent","analysis"],"representation":["hidden-state"],"computation":["recurrent","search"],"training":["inference-only"],"questions":["efficiency","scaling","interpretability"],"evidence":["empirical","mechanistic"],"modality":["symbolic"],"summary":"Separately perturbs the answer state and the reasoning state of a recursive puzzle solver to study where extra search is useful. Uses the model's halting prediction to trigger restarts that resample the answer state.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Maxime Illouz"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.16427/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-16427","citation_date":"2026-10-12","json_url":"https://latent-implicit-thinking.github.io/papers/2610.16427/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.16427/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.16427/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.16427/citation.csl.json"},{"id":"2610.17679","title":"Dynamic K-Head: Difficulty-Supervised Budget Selection for Continuous Latent Reasoning","authors":"Ying Li, Yuqi Chen, Sixuan Li, Yunfeng Cai","first_public":"2026-10-13","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.17679","paper_url":"https://arxiv.org/abs/2610.17679","lens":["continuous"],"representation":["continuous-state"],"computation":["token-wise"],"training":["supervised"],"questions":["capability","efficiency","controllability","evaluation"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Predicts from the question how many continuous reasoning updates to perform. Evaluates total cost including latent updates, special tokens, and any written continuation rather than counting latent steps alone.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Ying Li","Yuqi Chen","Sixuan Li","Yunfeng Cai"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.17679/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-17679","citation_date":"2026-10-13","json_url":"https://latent-implicit-thinking.github.io/papers/2610.17679/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.17679/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.17679/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.17679/citation.csl.json"},{"id":"2610.18127","title":"Monitoring latent reasoning in looped language models","authors":"Pawel Olszowiec, Paulina Tomaszewska, Maciej Żelaszczyk, Michal Byra, Neo Christopher Chung","first_public":"2026-10-13","venue":"arXiv","arxiv":"2610.18127","paper_url":"https://arxiv.org/abs/2610.18127","lens":["analysis","recurrent"],"representation":["hidden-state"],"computation":["recurrent","depth-wise"],"training":["analysis-only"],"questions":["interpretability","evaluation","limitations","architecture"],"evidence":["empirical","mechanistic"],"modality":["language"],"summary":"Inspects eight looped language models for state convergence, token decisions, readout quality, attention behavior, and sensitivity to injected noise. Finds important differences between models that receive the prompt once and those that reintroduce it at each loop.","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Pawel Olszowiec","Paulina Tomaszewska","Maciej Żelaszczyk","Michal Byra","Neo Christopher Chung"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.18127/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-18127","citation_date":"2026-10-13","json_url":"https://latent-implicit-thinking.github.io/papers/2610.18127/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.18127/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.18127/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.18127/citation.csl.json"},{"id":"2610.18162","title":"LoOPSD: On-Policy Self-Distillation with Looped Teachers","authors":"Wei Fan, Qingyue Yang, Chao-Hong Tan, Qian Chen, Wen Wang, Xiangang Li, Kejiang Chen, Weiming Zhang, Nenghai Yu","first_public":"2026-10-13","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.18162","paper_url":"https://arxiv.org/abs/2610.18162","summary":"Searches for layers to repeat to make a stronger teacher from the current model, then distills its predictions into the original student. Repeats search and distillation as the student improves.","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent","depth-wise","search"],"training":["self-distillation"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["language","symbolic"],"provenance":"Primary-source literature search, 2026-10-18","author_names":["Wei Fan","Qingyue Yang","Chao-Hong Tan","Qian Chen","Wen Wang","Xiangang Li","Kejiang Chen","Weiming Zhang","Nenghai Yu"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.18162/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-18162","citation_date":"2026-10-13","json_url":"https://latent-implicit-thinking.github.io/papers/2610.18162/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.18162/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.18162/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.18162/citation.csl.json"},{"id":"2610.18174","title":"Looped Reasoning Finishes Earlier Than You Think","authors":"Sumin Park, T. Konstantin Rusch","first_public":"2026-10-13","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.18174","paper_url":"https://arxiv.org/abs/2610.18174","lens":["recurrent","analysis"],"representation":["hidden-state","continuous-state"],"computation":["recurrent","depth-wise"],"training":["supervised"],"questions":["architecture","theory","efficiency"],"evidence":["formal","empirical"],"modality":["symbolic"],"summary":"Studies how oscillations can slow convergence in recurrent reasoning models. Proposes an architecture whose rotational state changes are separated from the representation used for reasoning, and tests convergence on puzzle-solving tasks.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Sumin Park","T. Konstantin Rusch"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.18174/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-18174","citation_date":"2026-10-13","json_url":"https://latent-implicit-thinking.github.io/papers/2610.18174/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.18174/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.18174/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.18174/citation.csl.json"},{"id":"2610.18547","title":"Input-Conditioned Search for Efficient Test-Time Scaling of Recursive Reasoners","authors":"Haochen Shi, Tianwen Fu, Qianggang Ding, Yinhan Lu, Yizhan Li, Huan Zhang, Yajie Zhao, Xingdi Yuan, Hengyang Lu, Bang Liu","first_public":"2026-10-13","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.18547","paper_url":"https://arxiv.org/abs/2610.18547","lens":["recurrent"],"representation":["hidden-state"],"computation":["recurrent","search"],"training":["inference-only"],"questions":["efficiency","theory","capability"],"evidence":["empirical","formal"],"modality":["symbolic"],"summary":"Searches over input conditions to change a recursive reasoner's update rule without retraining it. Tests whether these alternative updates can redirect a trajectory away from an incorrect solution, rather than only adding more steps or perturbing its state.","provenance":"Primary-source literature search, 2026-10-18","author_names":["Haochen Shi","Tianwen Fu","Qianggang Ding","Yinhan Lu","Yizhan Li","Huan Zhang","Yajie Zhao","Xingdi Yuan","Hengyang Lu","Bang Liu"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.18547/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-18547","citation_date":"2026-10-13","json_url":"https://latent-implicit-thinking.github.io/papers/2610.18547/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.18547/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.18547/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.18547/citation.csl.json"},{"id":"2610.19080","title":"Backpropagating Verifier Rewards Through Continuous Flow Language Models","authors":"Xu Han, Jiajing Hu, Li-Ping Liu","first_public":"2026-10-13","lens":["continuous","beyond-sequential"],"representation":["continuous-state"],"training":["reinforcement-learning"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Trains a critic to score intermediate continuous token representations, enabling reward gradients through the denoising trajectory before final discrete decoding. Evaluates this post-training approach on four reasoning tasks.","computation":["diffusion"],"venue":"arXiv","arxiv":"2610.19080","paper_url":"https://arxiv.org/abs/2610.19080","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Xu Han","Jiajing Hu","Li-Ping Liu"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.19080/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-19080","citation_date":"2026-10-13","json_url":"https://latent-implicit-thinking.github.io/papers/2610.19080/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.19080/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.19080/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.19080/citation.csl.json"},{"id":"2610.19220","title":"Riding the Fixed-Point Curve: Image Classification in the Continuous Thought Machine","authors":"Thomas Hannagan","first_public":"2026-10-13","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.19220","paper_url":"https://arxiv.org/abs/2610.19220","summary":"Analyzes the Continuous Thought Machine's repeated updates during image classification. Finds that its hidden states follow moving fixed points and that much of its attention schedule is shared across images.","lens":["analysis","recurrent"],"representation":["hidden-state"],"computation":["recurrent"],"training":["analysis-only"],"questions":["interpretability","theory","limitations"],"evidence":["formal","empirical","mechanistic"],"modality":["vision"],"provenance":"Primary-source literature search, 2026-10-18","author_names":["Thomas Hannagan"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.19220/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-19220","citation_date":"2026-10-13","json_url":"https://latent-implicit-thinking.github.io/papers/2610.19220/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.19220/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.19220/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.19220/citation.csl.json"},{"id":"2610.19408","title":"ForkGRPO: Efficient Exploration and Fine-Grained Credit Assignment for Diffusion Language Models","authors":"Zhaoyan Jia, Chengwei Zhou, Gourav Datta, Massoud Pedram","first_public":"2026-10-14","lens":["beyond-sequential"],"representation":["discrete-token"],"training":["reinforcement-learning"],"questions":["capability","efficiency"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Branches rollouts from uncertain intermediate states and reuses their shared textual prefixes. Local outcome comparisons assign credit to reasoning segments, testing whether more targeted exploration improves diffusion-model reasoning with fewer generated training tokens.","computation":["diffusion","search"],"venue":"arXiv","arxiv":"2610.19408","paper_url":"https://arxiv.org/abs/2610.19408","provenance":"Primary-source literature search, 2026-10-18","added_at":"2026-10-18","author_names":["Zhaoyan Jia","Chengwei Zhou","Gourav Datta","Massoud Pedram"],"record_url":"https://latent-implicit-thinking.github.io/papers/2610.19408/","legacy_record_url":"https://latent-implicit-thinking.github.io/papers/#paper-2610-19408","citation_date":"2026-10-14","json_url":"https://latent-implicit-thinking.github.io/papers/2610.19408/record.json","markdown_url":"https://latent-implicit-thinking.github.io/papers/2610.19408/index.md","bibtex_url":"https://latent-implicit-thinking.github.io/papers/2610.19408/citation.bib","csl_url":"https://latent-implicit-thinking.github.io/papers/2610.19408/citation.csl.json"},{"id":"2610.19568","title":"INTACT: Inducing Latent Reasoning on a Frozen Backbone","authors":"Kutay Tire, Atula Tejaswi, Haris Vikalo, Sujay Sanghavi","first_public":"2026-10-14","added_at":"2026-10-18","venue":"arXiv","arxiv":"2610.19568","paper_url":"https://arxiv.org/abs/2610.19568","lens":["continuous"],"representation":["text-latent-hybrid"],"computation":["token-wise"],"training":["distillation","reinforcement-learning"],"questions":["capability","efficiency","generalization"],"evidence":["empirical"],"modality":["language","symbolic"],"summary":"Trains a small encoder to turn a frozen model's hidden states into successive blocks of continuous thoughts. 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