{ "metadata": { "version": "0.9.4", "updated_at": "2026-10-18", "search_refreshed_at": "2026-10-18", "topic_id": "recurrent", "name": "Recurrent reasoning", "definition": "Repeat parts of the model or keep intermediate information in memory while working through a problem. Some methods also learn how many passes to run.", "record_count": 89, "topic_url": "https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/", "source_url": "https://latent-implicit-thinking.github.io/data/papers.json" }, "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" ] } ], "demos": [ ], "papers": [ { "id": "2310.10845", "title": "CoTFormer: A Chain-of-Thought Driven Architecture with Budget-Adaptive Computation Cost at Inference", "authors": "Amirkeivan Mohtashami, Matteo Pagliardini, Martin Jaggi", "first_public": "2023-10-16", "venue": "arXiv", "arxiv": "2310.10845", "paper_url": "https://arxiv.org/abs/2310.10845", "lens": [ "recurrent" ], "representation": [ "hidden-state" ], "computation": [ "recurrent", "depth-wise" ], "training": [ "supervised" ], "questions": [ "capability", "efficiency", "controllability" ], "evidence": [ "empirical" ], "modality": [ "language", "symbolic" ], "summary": "Runs shared transformer blocks repeatedly, keeping earlier passes available to attention. 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": "2502.05171", "title": "Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach", "authors": "Jonas Geiping, Sean McLeish, Neel Jain, John Kirchenbauer, Siddharth Singh, Brian R. 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": "2502.13842", "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": "2502.17416", "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": "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": "2505.13898", "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": "2505.19245", "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": "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": "2507.07996", "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": "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": "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": "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": "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": "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": "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": "2608.18222", "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": "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": "2609.04963", "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": "2609.15160", "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": "2609.16665", "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": "2609.21605", "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": "2609.23033", "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": "2609.27373", "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": "2609.33144", "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": "2609.34218", "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": "2609.34488", "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": "2609.35748", "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": "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": "2609.39740", "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": "2610.00673", "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": "2610.02185", "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": "2610.02383", "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": "2610.02741", "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": "2610.06949", "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": "2610.06833", "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": "2610.07591", "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": "2610.09876", "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": "2610.11570", "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": "2610.14252", "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": "2610.15218", "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": "2610.16427", "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": "2610.18127", "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": "2610.19220", "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": "2610.19768", "title": "Learning to Compute Is Not Learning to Retain or Reuse in Looped Transformers", "authors": "Peilong Zhou, Hongtao Zhang, Yulong Huang, Cangyuan Li, Mingyu Chen, Ying Wang", "first_public": "2026-10-14", "added_at": "2026-10-18", "venue": "arXiv", "arxiv": "2610.19768", "paper_url": "https://arxiv.org/abs/2610.19768", "summary": "Separates computing an answer, preserving it through additional loops, and keeping its hidden state usable for later steps. On state-machine and maze tasks, shows that training can improve one ability without securing the others.", "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": [ "Peilong Zhou", "Hongtao Zhang", "Yulong Huang", "Cangyuan Li", "Mingyu Chen", "Ying Wang" ], "record_url": "https://latent-implicit-thinking.github.io/papers/2610.19768/", "legacy_record_url": "https://latent-implicit-thinking.github.io/papers/#paper-2610-19768", "citation_date": "2026-10-14", "json_url": "https://latent-implicit-thinking.github.io/papers/2610.19768/record.json", "markdown_url": "https://latent-implicit-thinking.github.io/papers/2610.19768/index.md", "bibtex_url": "https://latent-implicit-thinking.github.io/papers/2610.19768/citation.bib", "csl_url": "https://latent-implicit-thinking.github.io/papers/2610.19768/citation.csl.json" }, { "id": "2610.21594", "title": "LoopAhead: Speculating Ahead for Faster Decoding in Looped Language Models", "authors": "Zixuan Liu, Nan Xue, Rui Bao, Yuhang Xu, Xiaofeng Cao, Jiangchao Yao, Zhiyong Chen", "first_public": "2026-10-15", "added_at": "2026-10-18", "venue": "arXiv", "arxiv": "2610.21594", "paper_url": "https://arxiv.org/abs/2610.21594", "summary": "Trains a small drafter to predict several future tokens from early-loop hidden states. Later loops decide which speculative branches to continue, and full-depth verification determines the final output.", "lens": [ "recurrent", "beyond-sequential" ], "representation": [ "hidden-state" ], "computation": [ "recurrent", "depth-wise", "parallel" ], "training": [ "distillation" ], "questions": [ "efficiency", "architecture" ], "evidence": [ "empirical", "formal" ], "modality": [ "language" ], "provenance": "Primary-source literature search, 2026-10-18", "author_names": [ "Zixuan Liu", "Nan Xue", "Rui Bao", "Yuhang Xu", "Xiaofeng Cao", "Jiangchao Yao", "Zhiyong Chen" ], "record_url": "https://latent-implicit-thinking.github.io/papers/2610.21594/", "legacy_record_url": "https://latent-implicit-thinking.github.io/papers/#paper-2610-21594", "citation_date": "2026-10-15", "json_url": "https://latent-implicit-thinking.github.io/papers/2610.21594/record.json", "markdown_url": "https://latent-implicit-thinking.github.io/papers/2610.21594/index.md", "bibtex_url": "https://latent-implicit-thinking.github.io/papers/2610.21594/citation.bib", "csl_url": "https://latent-implicit-thinking.github.io/papers/2610.21594/citation.csl.json" } ] }