# Analysis and evaluation

Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Papers are ordered by first public date. Read the original sources before using a claim.

For example: A researcher replaces an intermediate state with one taken from a different problem, then checks how the answer changes. This tests what information that state contributes to the solution.

Version 0.9.4; literature checked through 2026-10-18.

[Topic guide](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/) · [JSON](https://latent-implicit-thinking.github.io/data/topics/implicit-reasoning-evaluation.json)

## How the methods connect and differ

**Recovering information and testing its use**

Recovering an intermediate answer from hidden states is different from showing that the model uses it. The multi-hop study by Yang and colleagues separates recall of a bridge entity from its contribution to the final answer, including interventions on internal representations. Evidence was stronger for the first hop than for the complete two-hop computation and varied by relation type. That distinction matters when interpreting claims that a model reasons internally.

Sources: [Yang et al. (2024)](https://aclanthology.org/2024.acl-long.550/)

Paper details: [Do Large Language Models Latently Perform Multi-Hop Reasoning?](https://latent-implicit-thinking.github.io/papers/2402.16837/)

## Papers — oldest first

## Towards a Mechanistic Interpretation of Multi-Step Reasoning Capabilities of Language Models

Authors: Yifan Hou, Jiaoda Li, Yu Fei, Alessandro Stolfo, Wangchunshu Zhou, Guangtao Zeng, Antoine Bosselut, Mrinmaya Sachan.

Uses mechanistic analysis to identify internal components involved in multi-step reasoning and test their causal roles.

First public: 2023-10-23.
ArXiv initial submission: 2023-10-23.

[Original paper](https://arxiv.org/abs/2310.14491) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2310.14491/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2310.14491/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2310.14491/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2310.14491/record.json)

### Approaches

- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## A Mechanistic Analysis of a Transformer Trained on a Symbolic Multi-Step Reasoning Task

Authors: Jannik Brinkmann, Abhay Sheshadri, Victor Levoso, Paul Swoboda, Christian Bartelt.

Reverse-engineers a transformer trained on symbolic multi-step reasoning to characterize its learned internal algorithm.

First public: 2024-02-19.
ArXiv initial submission: 2024-02-19.

[Original paper](https://arxiv.org/abs/2402.11917) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2402.11917/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2402.11917/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2402.11917/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2402.11917/record.json)

### Approaches

- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Understanding and Patching Compositional Reasoning in LLMs

Authors: Zhaoyi Li, Gangwei Jiang, Hong Xie, Linqi Song, Defu Lian, Ying Wei.

Localizes internal representations involved in compositional reasoning and tests whether targeted interventions can repair failures.

First public: 2024-02-22.
ArXiv initial submission: 2024-02-22.

[Original paper](https://arxiv.org/abs/2402.14328) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2402.14328/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2402.14328/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2402.14328/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2402.14328/record.json)

### Approaches

- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Do Large Language Models Latently Perform Multi-Hop Reasoning?

Authors: Sohee Yang, Elena Gribovskaya, Nora Kassner, Mor Geva, Sebastian Riedel.

Probes whether language models internally compose facts across hops before producing an answer, separating internal computation from verbal explanation.

First public: 2024-02-26.
ArXiv initial submission: 2024-02-26.

[Original paper](https://arxiv.org/abs/2402.16837) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2402.16837/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2402.16837/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2402.16837/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2402.16837/record.json)

### Method comparisons

**Recovering information and testing its use**

Recovering an intermediate answer from hidden states is different from showing that the model uses it. The multi-hop study by Yang and colleagues separates recall of a bridge entity from its contribution to the final answer, including interventions on internal representations. Evidence was stronger for the first hop than for the complete two-hop computation and varied by relation type. That distinction matters when interpreting claims that a model reasons internally.

Sources: [Yang et al. (2024)](https://aclanthology.org/2024.acl-long.550/)

Paper details: [Do Large Language Models Latently Perform Multi-Hop Reasoning?](https://latent-implicit-thinking.github.io/papers/2402.16837/)


### Published version

Do Large Language Models Latently Perform Multi-Hop Reasoning?. Sohee Yang, Elena Gribovskaya, Nora Kassner, Mor Geva, Sebastian Riedel. Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), 2024.
[Publication](https://aclanthology.org/2024.acl-long.550/) · [BibTeX](https://latent-implicit-thinking.github.io/papers/2402.16837/publication.bib) · [CSL-JSON](https://latent-implicit-thinking.github.io/papers/2402.16837/publication.csl.json)
Metadata checked 2026-10-18 against [the publication record](https://aclanthology.org/2024.acl-long.550/).

### Approaches

- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Grokked Transformers are Implicit Reasoners: A Mechanistic Journey to the Edge of Generalization

Authors: Boshi Wang, Xiang Yue, Yu Su, Huan Sun.

Mechanistically studies transformers that learn implicit reasoning after grokking, focusing on how internal algorithms support out-of-distribution generalization.

First public: 2024-05-23.
ArXiv initial submission: 2024-05-23.

[Original paper](https://arxiv.org/abs/2405.15071) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2405.15071/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2405.15071/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2405.15071/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2405.15071/record.json)

### Approaches

- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Distributional Reasoning in LLMs: Parallel Reasoning Processes in Multi-Hop Reasoning

Authors: Yuval Shalev, Amir Feder, Ariel Goldstein.

Finds evidence for parallel internal processes during multi-hop reasoning rather than a single serial written-style chain.

First public: 2024-06-19.
ArXiv initial submission: 2024-06-19.

[Original paper](https://arxiv.org/abs/2406.13858) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2406.13858/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2406.13858/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2406.13858/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2406.13858/record.json)

### Approaches

- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process

Authors: Tian Ye, Zicheng Xu, Yuanzhi Li, Zeyuan Allen-Zhu.

Studies the internal computation behind grade-school mathematics, including when models learn robust procedures or rely on data shortcuts.

First public: 2024-07-29.
ArXiv initial submission: 2024-07-29.

[Original paper](https://arxiv.org/abs/2407.20311) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2407.20311/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2407.20311/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2407.20311/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2407.20311/record.json)

### Approaches

- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Uncovering Latent Chain of Thought Vectors in Language Models

Authors: Jason Zhang, Scott Viteri.

Searches hidden activations for directions that encode intermediate reasoning progress and tests how those directions affect behavior.

First public: 2024-09-21.
ArXiv initial submission: 2024-09-21.

[Original paper](https://arxiv.org/abs/2409.14026) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2409.14026/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2409.14026/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2409.14026/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2409.14026/record.json)

### Approaches

- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Latent Space Chain-of-Embedding Enables Output-free LLM Self-Evaluation

Authors: Yiming Wang, Pei Zhang, Baosong Yang, Derek F. Wong, Rui Wang.

Uses the sequence of hidden states produced during inference to estimate whether an answer is correct, without extra training or labeled correctness examples.

First public: 2024-10-17.
ArXiv initial submission: 2024-10-17.

[Original paper](https://arxiv.org/abs/2410.13640) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2410.13640/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2410.13640/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2410.13640/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2410.13640/record.json)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Do LLMs Really Think Step-by-step In Implicit Reasoning?

Authors: Yijiong Yu.

Tests whether successful implicit reasoning reflects an internal step-by-step procedure and documents where that interpretation fails.

First public: 2024-11-24.
ArXiv initial submission: 2024-11-24.

[Original paper](https://arxiv.org/abs/2411.15862) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2411.15862/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2411.15862/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2411.15862/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2411.15862/record.json)

### Approaches

- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Implicit Language Models are RNNs: Balancing Parallelization and Expressivity

Authors: Mark Schöne, Babak Rahmani, Heiner Kremer, Fabian Falck, Hitesh Ballani, Jannes Gladrow.

Connects implicit language models to recurrent computation and analyzes the trade-off between parallel training and expressive sequential depth.

First public: 2025-02-10.
ArXiv initial submission: 2025-02-10.

[Original paper](https://arxiv.org/abs/2502.07827) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2502.07827/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2502.07827/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2502.07827/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2502.07827/record.json)

### Method comparisons

**Recurrent depth and fixed points**

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.

Sources: [Recurrent-depth paper](https://proceedings.neurips.cc/paper_files/paper/2025/hash/3b01972cf31e6fa0fe29e4b8b5c2a0a1-Abstract-Conference.html) · [Implicit state-space paper](https://proceedings.mlr.press/v267/schone25a.html)

Paper details: [Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach](https://latent-implicit-thinking.github.io/papers/2502.05171/) · [Implicit Language Models are RNNs: Balancing Parallelization and Expressivity](https://latent-implicit-thinking.github.io/papers/2502.07827/)


### Published version

Implicit Language Models are RNNs: Balancing Parallelization and Expressivity. Mark Schöne, Babak Rahmani, Heiner Kremer, Fabian Falck, Hitesh Ballani, Jannes Gladrow. Proceedings of the 42nd International Conference on Machine Learning, 2025.
[Publication](https://proceedings.mlr.press/v267/schone25a.html) · [BibTeX](https://latent-implicit-thinking.github.io/papers/2502.07827/publication.bib) · [CSL-JSON](https://latent-implicit-thinking.github.io/papers/2502.07827/publication.csl.json)
Metadata checked 2026-10-18 against [the publication record](https://proceedings.mlr.press/v267/schone25a.html).

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Implicit Reasoning in Transformers is Reasoning through Shortcuts

Authors: Tianhe Lin, Jian Xie, Siyu Yuan, Deqing Yang.

Tests whether apparent implicit multi-step reasoning reflects compositional algorithms or learned shortcuts, emphasizing failure modes under distribution shift.

First public: 2025-03-10.
ArXiv initial submission: 2025-03-10.

[Original paper](https://arxiv.org/abs/2503.07604) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2503.07604/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2503.07604/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2503.07604/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2503.07604/record.json)

### Approaches

- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Beyond Chains of Thought: Benchmarking Latent-Space Reasoning Abilities in Large Language Models

Authors: Thilo Hagendorff, Sarah Fabi.

Encodes the answer in the language of the model's first response token, forcing a choice before any written explanation. Also tests whether successful answers could come from simple heuristics.

First public: 2025-04-14.
ArXiv initial submission: 2025-04-14.

[Original paper](https://arxiv.org/abs/2504.10615) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2504.10615/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2504.10615/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2504.10615/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2504.10615/record.json)

### Approaches

- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Do Language Models Use Their Depth Efficiently?

Authors: Róbert Csordás, Christopher D. Manning, Christopher Potts.

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.

First public: 2025-05-20.
ArXiv initial submission: 2025-05-20.

[Original paper](https://arxiv.org/abs/2505.13898) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2505.13898/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2505.13898/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2505.13898/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2505.13898/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Internal Chain-of-Thought: Empirical Evidence for Layer-wise Subtask Scheduling in LLMs

Authors: Zhipeng Yang, Junzhuo Li, Siyu Xia, Xuming Hu.

Presents evidence that transformer layers schedule intermediate subtasks internally, offering a layer-wise view of implicit reasoning.

First public: 2025-05-20.
ArXiv initial submission: 2025-05-20.

[Original paper](https://arxiv.org/abs/2505.14530) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2505.14530/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2505.14530/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2505.14530/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2505.14530/record.json)
[Code](https://github.com/yzp11/Internal-Chain-of-Thought)

### Approaches

- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Reasoning Beyond Language: A Comprehensive Survey on Latent Chain-of-Thought Reasoning

Authors: Xinghao Chen, Anhao Zhao, Heming Xia, Xuan Lu, Hanlin Wang, Yanjun Chen, Wei Zhang, Jian Wang, Wenjie Li, Xiaoyu Shen.

Surveys latent chain-of-thought methods and organizes a broad, continuously updated bibliography spanning token-wise, structural, representational, and analytical work.

First public: 2025-05-22.
ArXiv initial submission: 2025-05-22.

[Original paper](https://arxiv.org/abs/2505.16782) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2505.16782/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2505.16782/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2505.16782/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2505.16782/record.json)
[Code](https://github.com/EIT-NLP/Awesome-Latent-CoT)

### Approaches

- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Language Models Can Learn Implicit Multi-Hop Reasoning, but Only If They Have Lots of Training Data

Authors: Yuekun Yao, Yupei Du, Dawei Zhu, Michael Hahn, Alexander Koller.

Studies the data requirements for learning implicit multi-hop reasoning and identifies sharp limitations in low-data regimes.

First public: 2025-05-23.
ArXiv initial submission: 2025-05-23.

[Original paper](https://arxiv.org/abs/2505.17923) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2505.17923/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2505.17923/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2505.17923/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2505.17923/record.json)

### Approaches

- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## To CoT or To Loop? A Formal Comparison Between Chain-of-Thought and Looped Transformers

Authors: Kevin Xu, Issei Sato.

Formally compares explicit chain-of-thought computation with repeated internal transformations in looped transformer architectures.

First public: 2025-05-25.
ArXiv initial submission: 2025-05-25.

[Original paper](https://arxiv.org/abs/2505.19245) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2505.19245/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2505.19245/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2505.19245/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2505.19245/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Continuous Chain of Thought Enables Parallel Exploration and Reasoning

Authors: Halil Alperen Gozeten, M. Emrullah Ildiz, Xuechen Zhang, Hrayr Harutyunyan, Ankit Singh Rawat, Samet Oymak.

Analyzes and demonstrates how continuous intermediate states can explore several candidate reasoning paths in parallel.

First public: 2025-05-29.
ArXiv initial submission: 2025-05-29.

[Original paper](https://arxiv.org/abs/2505.23648) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2505.23648/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2505.23648/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2505.23648/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2505.23648/record.json)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Latent Chain-of-Thought? Decoding the Depth-Recurrent Transformer

Authors: Wenquan Lu, Yuechuan Yang, Kyle Lee, Yanshu Li, Enqi Liu.

Probes a depth-recurrent transformer to test what its repeated hidden-state computation represents and whether it behaves like a latent chain of thought.

First public: 2025-07-02.
ArXiv initial submission: 2025-07-02.

[Original paper](https://arxiv.org/abs/2507.02199) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2507.02199/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2507.02199/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2507.02199/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2507.02199/record.json)
[Code](https://github.com/wenquanlu/huginn-latent-cot)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## A Survey on Latent Reasoning

Authors: Rui-Jie Zhu, Tianhao Peng, Tianhao Cheng, Xingwei Qu, Jinfa Huang, Dawei Zhu, Hao Wang, Kaiwen Xue, Xuanliang Zhang, Yong Shan, Tianle Cai, Taylor Kergan, Assel Kembay, Andrew Smith, Chenghua Lin, Binh Nguyen, Yuqi Pan, Yuhong Chou, Zefan Cai, Zhenhe Wu, Yongchi Zhao, Tianyu Liu, Jian Yang, Wangchunshu Zhou, Chujie Zheng, Chongxuan Li, Yuyin Zhou, Zhoujun Li, Zhaoxiang Zhang, Jiaheng Liu, Ge Zhang, Wenhao Huang, Jason Eshraghian.

Surveys latent-reasoning methods, evaluation, and applications and accompanies a maintained research bibliography.

First public: 2025-07-08.
ArXiv initial submission: 2025-07-08.

[Original paper](https://arxiv.org/abs/2507.06203) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2507.06203/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2507.06203/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2507.06203/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2507.06203/record.json)
[Code](https://github.com/multimodal-art-projection/LatentCoT-Horizon)

### Approaches

- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## LLMs are Single-threaded Reasoners: Demystifying the Working Mechanism of Soft Thinking

Authors: Junhong Wu, Jinliang Lu, Zixuan Ren, Gangqiang Hu, Zhi Wu, Dai Dai, Hua Wu.

Probes soft-token reasoning and finds that tested models often follow the highest-probability component rather than exploring several paths at once. Introduces stochastic soft thinking, including Gumbel-Softmax sampling, to reduce this greedy behavior.

First public: 2025-08-05.
ArXiv initial submission: 2025-08-05.

[Original paper](https://arxiv.org/abs/2508.03440) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2508.03440/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2508.03440/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2508.03440/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2508.03440/record.json)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Implicit Reasoning in Large Language Models: A Comprehensive Survey

Authors: Jindong Li, Yali Fu, Li Fan, Jiahong Liu, Yao Shu, Chengwei Qin, Menglin Yang, Irwin King, Rex Ying.

Organizes implicit-reasoning research across model mechanisms, training methods, evaluation, and applications.

First public: 2025-09-02.
ArXiv initial submission: 2025-09-02.

[Original paper](https://arxiv.org/abs/2509.02350) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2509.02350/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2509.02350/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2509.02350/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2509.02350/record.json)
[Code](https://github.com/digailab/awesome-llm-implicit-reasoning)

### Approaches

- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Do Latent Tokens Think? A Causal and Adversarial Analysis of Chain-of-Continuous-Thought

Authors: Yuyi Zhang, Boyu Tang, Tianjie Ju, Sufeng Duan, Gongshen Liu.

Tests COCONUT with latent-state interventions and deliberately biased examples on MMLU and HotpotQA. Finds weak sensitivity to steering and dependence on dataset shortcuts in the evaluated models, challenging whether their intermediate states faithfully carry the reasoning.

First public: 2025-12-25.
ArXiv initial submission: 2025-12-25.

[Original paper](https://arxiv.org/abs/2512.21711) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2512.21711/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2512.21711/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2512.21711/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2512.21711/record.json)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Chain Of Thought Compression: A Theoretical Analysis

Authors: Juncai Li, Ru Li, Yuxiang Zhou, Boxiang Ma, Jeff Z. Pan.

Analyzes how skipping intermediate steps weakens learning signals in a simplified parity-task model. Introduces NatBool-DAG to test logical dependencies and ALiCoT, which supervises learned token states with intermediate logical labels or explicit-CoT representations.

First public: 2026-01-29.
ArXiv initial submission: 2026-01-29.

[Original paper](https://arxiv.org/abs/2601.21576) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2601.21576/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2601.21576/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2601.21576/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2601.21576/record.json)

### Approaches

- [Internalized reasoning](https://latent-implicit-thinking.github.io/topics/internalized-reasoning/): Learn from worked solutions so that some or all of the reasoning can later happen without writing those steps. Training may use a separate teacher model or progressively remove written steps from the model being trained.
- [Thinking tokens](https://latent-implicit-thinking.github.io/topics/thinking-tokens/): Give a model extra tokens for computation, such as pauses, filler symbols, or learned planning tokens. These tokens need not spell out the solution.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Do Latent-CoT Models Think Step-by-Step? A Mechanistic Study on Sequential Reasoning Tasks

Authors: Jia Liang, Liangming Pan.

Uses mechanistic interventions on sequential tasks to test whether latent chain-of-thought models actually execute stepwise internal procedures.

First public: 2026-01-31.
ArXiv initial submission: 2026-01-31.

[Original paper](https://arxiv.org/abs/2602.00449) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2602.00449/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2602.00449/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2602.00449/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2602.00449/record.json)
[Code](https://github.com/jialiang19/latent-cot-thinking)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Capabilities and Fundamental Limits of Latent Chain-of-Thought

Authors: Jiaxuan Zou, Yaozhong Xiong, Yong Liu.

Characterizes tasks that latent chain-of-thought can express and identifies theoretical and empirical limits of the approach.

First public: 2026-02-01.
ArXiv initial submission: 2026-02-01.

[Original paper](https://arxiv.org/abs/2602.01148) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2602.01148/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2602.01148/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2602.01148/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2602.01148/record.json)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Transformers Provably Learn to Internalize Chain-of-Thought

Authors: Yixiao Huang, Hanlin Zhu, Zixuan Wang, Jiantao Jiao, Stuart Russell, Somayeh Sojoudi, Song Mei.

Provides theoretical and empirical results on when transformers trained with a curriculum learn to internalize explicit reasoning steps.

First public: 2026-05-27.
ArXiv initial submission: 2026-05-27.

[Original paper](https://arxiv.org/abs/2605.28600) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2605.28600/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2605.28600/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2605.28600/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2605.28600/record.json)

### Approaches

- [Internalized reasoning](https://latent-implicit-thinking.github.io/topics/internalized-reasoning/): Learn from worked solutions so that some or all of the reasoning can later happen without writing those steps. Training may use a separate teacher model or progressively remove written steps from the model being trained.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Unlocking the Black Box of Latent Reasoning: An Interpretability-Guided Approach to Intervention

Authors: Shuochen Chang, Tong Bai, Xiaofeng Zhang, Qianli Ma, Qingyang Liu, Zhaohe Liao, Yibo Miao, Li Niu.

Uses probes, ablations, and targeted edits to study how continuous reasoning states affect answers. Builds interventions from learned semantic mappings and geometric constraints, improving the evaluated models by editing their latent states without updating base-model weights.

First public: 2026-05-31.
ArXiv initial submission: 2026-05-31.

[Original paper](https://arxiv.org/abs/2606.01243) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2606.01243/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2606.01243/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2606.01243/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2606.01243/record.json)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Observable Patterns Are Not Explanations: A Causal-Geometric Analysis of Latent Reasoning Models

Authors: Darpan Aswal, Thomas Palmeira Ferraz, Yongxin Zhou, Maxime Peyrard.

Compares Coconut and CODI with controls lacking their proposed reasoning recurrence or curriculum. Finds that decodable patterns can also appear in controls, while interventions reveal varying causal use of latent states concentrated in low-dimensional directions.

First public: 2026-06-10.
ArXiv initial submission: 2026-06-10.

[Original paper](https://arxiv.org/abs/2606.12689) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2606.12689/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2606.12689/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2606.12689/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2606.12689/record.json)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## 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.

Trains switchable hidden-state recurrence with on-policy reinforcement learning and analyzes how the internal loop contributes to reasoning.

First public: 2026-06-11.
ArXiv initial submission: 2026-06-11.

[Original paper](https://arxiv.org/abs/2606.13106) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2606.13106/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2606.13106/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2606.13106/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2606.13106/record.json)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## What Makes Effective Supervision in Latent Chain-of-Thought: An Information-Theoretic Analysis

Authors: Xinghao Chen, Chak Tou Leong, Wenjin Guo, Jian Wang, Wenjie Li, Xiaoyu Shen.

Uses information-theoretic analysis to study which supervision signals make latent chain-of-thought training effective.

First public: 2026-06-18.
ArXiv initial submission: 2026-06-18.

[Original paper](https://arxiv.org/abs/2606.20075) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2606.20075/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2606.20075/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2606.20075/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2606.20075/record.json)
[Code](https://github.com/EIT-NLP/Supervision-in-Latent-CoT)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Think in Latent, Explain in Language: Self-Explainable Latent Reasoning

Authors: Dayuan Zhao, Shengcao Cao, Yu-Xiong Wang, Liang-Yan Gui.

Jointly trains latent states for answer prediction and for decoding back into readable reasoning, using one model rather than a separate post-hoc explanation decoder.

First public: 2026-07-01.
ArXiv initial submission: 2026-07-01.

[Original paper](https://arxiv.org/abs/2608.13570) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2608.13570/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2608.13570/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2608.13570/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2608.13570/record.json)
[Code](https://jasondayuan.github.io/SELR/)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Final Checkpoints Are Not Enough: Analyzing Latent Reasoning Faithfulness Along Training Trajectories

Authors: Hengyu Jin, Shu Yang, Di Wang.

Tests how answers respond to changed inputs and altered hidden reasoning states throughout training. These responses can change even while accuracy remains high.

First public: 2026-07-07.
ArXiv initial submission: 2026-07-07.

[Original paper](https://arxiv.org/abs/2607.06648) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2607.06648/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2607.06648/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2607.06648/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2607.06648/record.json)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Training Continuous Chain of Thought Models: A Tale of Two Regimes

Authors: Varun Yerram, He He, Eunsol Choi.

Introduces direct latent supervision through averaged trace embeddings and finds that both direct and indirect continuous-CoT training degrade sharply on tasks with substantially longer reasoning traces.

First public: 2026-07-18.
ArXiv initial submission: 2026-07-18.

[Original paper](https://arxiv.org/abs/2607.16972) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2607.16972/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2607.16972/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2607.16972/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2607.16972/record.json)
[Code](https://github.com/Varun221/cmtp_research)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Does Out-of-Sight Equal Out-of-Mind in CoT Monitorability?

Authors: Pedro Ferreira, Wilker Aziz, Ivan Titov.

Compares monitoring from explicit traces, latent-state probes, and latent verbalizations, finding that monitorability depends strongly on task structure and level of internal access.

First public: 2026-08-05.
ArXiv initial submission: 2026-08-05.

[Original paper](https://arxiv.org/abs/2608.04928) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2608.04928/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2608.04928/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2608.04928/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2608.04928/record.json)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## 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.

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.

First public: 2026-08-18.
ArXiv initial submission: 2026-08-18.

[Original paper](https://arxiv.org/abs/2608.18222) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2608.18222/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2608.18222/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2608.18222/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2608.18222/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Allocating Recurrent Compute in Looped Language Models

Authors: Ruhai Lin, Yiyang Guo, Rui-Jie Zhu, Hao Ye, Jason K. Eshraghian.

Studies which transformer components should recur and introduces MixerLoop, which repeats the sequence mixer while applying the dense feed-forward component once.

First public: 2026-08-18.
ArXiv initial submission: 2026-08-18.

[Original paper](https://arxiv.org/abs/2608.18230) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2608.18230/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2608.18230/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2608.18230/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2608.18230/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Detecting Hidden Chain-of-Thought in Large Language Models with Linguistic, Behavioral, and Mechanistic Indicators

Authors: Armaan Singh, Ryan Trinh Le, Jasmine Kaur, Abdullah Sultan, Edward Lue Chee Lip, Kiran Nijjer, Adnan Ahmed, Vasu Sharma.

Compares behavior under neutral, explicit-CoT, and no-CoT prompts using linguistic and internal-state measurements. Its score measures resemblance to CoT behavior, not direct evidence of a hidden reasoning trace; calibration controls expose important confounds.

First public: 2026-08-30.
ArXiv initial submission: 2026-08-30.

[Original paper](https://arxiv.org/abs/2608.29956) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2608.29956/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2608.29956/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2608.29956/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2608.29956/record.json)

### Approaches

- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Dissecting Hierarchical Reasoning Models: A Mechanistic Study

Authors: Leo Raphael Rodrigues, Jian Kang.

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.

First public: 2026-08-30.
ArXiv initial submission: 2026-08-30.

[Original paper](https://arxiv.org/abs/2609.22197) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.22197/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.22197/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.22197/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.22197/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## A Score Is Not a Policy: Measuring the Value of Adaptive Revision

Authors: Ayushi Chadha.

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.

First public: 2026-09-01.
ArXiv initial submission: 2026-09-01.

[Original paper](https://arxiv.org/abs/2609.00874) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.00874/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.00874/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.00874/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.00874/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## 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.

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.

First public: 2026-09-01.
ArXiv initial submission: 2026-09-01.

[Original paper](https://arxiv.org/abs/2609.01343) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.01343/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.01343/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.01343/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.01343/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Looped Transformers under the Jacobian Lens: Does the Global Workspace Survive Recurrence?

Authors: Wenlong Wang, Fergal Reid.

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.

First public: 2026-09-01.
ArXiv initial submission: 2026-09-01.

[Original paper](https://arxiv.org/abs/2609.01924) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.01924/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.01924/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.01924/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.01924/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Towards Understanding Pause Token Fine-Tuning Dynamics: A Mode Retention Perspective

Authors: Jaehyeon Kim, Suhwan Kim, Nakyung Lee, Yeongoon Kim, Jimin Seo, Giho Lee, Jungwoo Lee.

Places pause tokens at reasoning-step boundaries and masks their training loss. Studies how this affects learning new tasks while retaining earlier capabilities, including during reinforcement learning.

First public: 2026-09-03.
ArXiv initial submission: 2026-09-03.

[Original paper](https://arxiv.org/abs/2609.04489) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.04489/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.04489/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.04489/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.04489/record.json)

### Approaches

- [Thinking tokens](https://latent-implicit-thinking.github.io/topics/thinking-tokens/): Give a model extra tokens for computation, such as pauses, filler symbols, or learned planning tokens. These tokens need not spell out the solution.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Fractal basins trap latent reasoning

Authors: Jeffrey Lai, Anthony Bao, John Quinn, William Gilpin.

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.

First public: 2026-09-04.
ArXiv initial submission: 2026-09-04.

[Original paper](https://arxiv.org/abs/2609.04963) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.04963/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.04963/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.04963/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.04963/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## 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.

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.

First public: 2026-09-15.
ArXiv initial submission: 2026-09-15.

[Original paper](https://arxiv.org/abs/2609.16665) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.16665/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.16665/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.16665/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.16665/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## How Model Growth, Recursion, and Boundary Operators Influence Scaling Exponents

Authors: Zixi Chen, Akshay Vegesna, Samip Dahal, Andrew Gordon Wilson.

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.

First public: 2026-09-16.
ArXiv initial submission: 2026-09-16.

[Original paper](https://arxiv.org/abs/2609.19107) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.19107/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.19107/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.19107/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.19107/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Storing Is Not Remembering: LSTM-UT and Bounded Gated Memory for Looped Transformers

Authors: Aras Kavuncu, Muhammad Burhan Hafez.

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.

First public: 2026-09-17.
ArXiv initial submission: 2026-09-17.

[Original paper](https://arxiv.org/abs/2609.19521) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.19521/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.19521/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.19521/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.19521/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## When Steering Fails in Latent Reasoning: A Latent-to-Language Transition Gap

Authors: Gaoxiang Huang, Lei Qi.

Tests whether changing continuous reasoning states changes the model's later text output. Finds weaker steering effects than in explicit chain-of-thought, despite comparable changes to the hidden representations.

First public: 2026-09-18.
ArXiv initial submission: 2026-09-18.

[Original paper](https://arxiv.org/abs/2609.21662) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.21662/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.21662/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.21662/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.21662/record.json)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## LOCKR: A Hidden-State Trajectory-Guided Planner for Detecting and Repairing Stable-but-Wrong Lock-In in Diffusion Language Models

Authors: Guoshenghui Zhao, Tan Yu, Weijie Zhao.

Uses the history of diffusion hidden states to detect answers that become stable but remain wrong. A planner selects targeted repair branches and verifies continuations, testing whether these internal trajectories support better repair decisions than confidence or a single snapshot.

First public: 2026-09-23.
ArXiv initial submission: 2026-09-23.

[Original paper](https://arxiv.org/abs/2609.27220) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.27220/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.27220/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.27220/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.27220/record.json)

### Approaches

- [Alternative generation methods](https://latent-implicit-thinking.github.io/topics/alternative-reasoning-schedules/): Change how intermediate steps are generated, revised, or searched—for example, by refining several steps in parallel. These are related approaches: some still produce written chains of thought.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Attention Routing Stabilizes Early: Working-Set Inference for Recurrent Language Models

Authors: Ke Wan, Chen Chen.

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.

First public: 2026-09-23.
ArXiv initial submission: 2026-09-23.

[Original paper](https://arxiv.org/abs/2609.27373) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.27373/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.27373/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.27373/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.27373/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Ceiling of a Task: When Can a Transformer Succeed Without Its Chain of Thought?

Authors: Jiashu He, Jinxuan Fan, Xiao Xiao, Radu Marculescu, Alejandro Ribeiro.

Analyzes tasks for which a fixed-depth transformer needs an informative chain of thought to exceed a task-specific accuracy limit. Combines circuit-based results with experiments that replace, erase, or shuffle reasoning tokens, including comparisons with filler tokens.

First public: 2026-09-27.
ArXiv initial submission: 2026-09-27.

[Original paper](https://arxiv.org/abs/2609.33134) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.33134/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.33134/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.33134/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.33134/record.json)

### Approaches

- [Thinking tokens](https://latent-implicit-thinking.github.io/topics/thinking-tokens/): Give a model extra tokens for computation, such as pauses, filler symbols, or learned planning tokens. These tokens need not spell out the solution.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Beyond the Training Horizon: Mechanisms and Limits of Length Generalization in Looped Transformers

Authors: Jia Liang, Xi Jin, Liangming Pan.

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.

First public: 2026-09-27.
ArXiv initial submission: 2026-09-27.

[Original paper](https://arxiv.org/abs/2609.33144) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.33144/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.33144/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.33144/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.33144/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Why Deterministic PRM Guidance Underperforms in Discrete Diffusion Reasoning

Authors: Yan Zhan, Shaobo Liu, Zhijun Gao.

Compares process-reward guidance with independent sampling and final-answer reranking at matched forward-pass budgets. In the tested diffusion models, early pruning removes promising candidates and intermediate-state scorers can be poor final judges; the generated solutions remain textual.

First public: 2026-09-28.
ArXiv initial submission: 2026-09-28.

[Original paper](https://arxiv.org/abs/2609.35472) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.35472/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.35472/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.35472/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.35472/record.json)

### Approaches

- [Alternative generation methods](https://latent-implicit-thinking.github.io/topics/alternative-reasoning-schedules/): Change how intermediate steps are generated, revised, or searched—for example, by refining several steps in parallel. These are related approaches: some still produce written chains of thought.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Reliable Parallel Decoding in Masked Diffusion Language Models

Authors: Zhenghao He, Bohan Liu, Guangzhi Xiong, Aidong Zhang.

Studies when simultaneously committing several predicted tokens breaks their reasoning dependencies. RPD combines stability across final layers with confidence and uncertainty in preceding positions to defer unsupported predictions while retaining parallel text generation.

First public: 2026-09-29.
ArXiv initial submission: 2026-09-29.

[Original paper](https://arxiv.org/abs/2609.36452) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.36452/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.36452/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.36452/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.36452/record.json)

### Approaches

- [Alternative generation methods](https://latent-implicit-thinking.github.io/topics/alternative-reasoning-schedules/): Change how intermediate steps are generated, revised, or searched—for example, by refining several steps in parallel. These are related approaches: some still produce written chains of thought.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## What Makes Recurrence Effective in Looped Language Models?

Authors: Xinlin Zhuang, Siyuan Wang, Imran Razzak, Weiyang Liu.

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.

First public: 2026-09-29.
ArXiv initial submission: 2026-09-29.

[Original paper](https://arxiv.org/abs/2609.36636) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.36636/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.36636/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.36636/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.36636/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Scheduling Recursive Reasoning in Looped Transformers

Authors: Boyuan Wang, Chengyao Yu, Jiaxi Ren, Hongxin Wei, Bingyi Jing, Yuxin Tao.

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.

First public: 2026-09-29.
ArXiv initial submission: 2026-09-29.

[Original paper](https://arxiv.org/abs/2609.36653) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.36653/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.36653/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.36653/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.36653/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Looped Transformers as Optimizers

Authors: Yulong Huang, Chen Jiang, Zhanpeng Zhou, Hongtao Zhang, Tianyu Li, Tianyu He, Xiangyu Zhang, Bojun Cheng.

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.

First public: 2026-09-29.
ArXiv initial submission: 2026-09-29.

[Original paper](https://arxiv.org/abs/2609.37379) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.37379/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.37379/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.37379/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.37379/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Shared Weights, Selected Computations: How Looped Transformers Route What Each Loop Does

Authors: Jiaju Wu, Yi Hu, Muhan Zhang.

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.

First public: 2026-09-30.
ArXiv initial submission: 2026-09-30.

[Original paper](https://arxiv.org/abs/2609.39892) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.39892/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.39892/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.39892/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.39892/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## 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.

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.

First public: 2026-09-30.
ArXiv initial submission: 2026-09-30.

[Original paper](https://arxiv.org/abs/2609.39967) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.39967/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.39967/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.39967/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.39967/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Scaling Laws for Looped Mixture of Experts

Authors: Yanbei Chen, Anirudh Goyal, Raghuraman Krishnamoorthi.

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.

First public: 2026-09-30.
ArXiv initial submission: 2026-09-30.

[Original paper](https://arxiv.org/abs/2609.40316) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.40316/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.40316/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.40316/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.40316/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Temporally-Resolved Token Attribution Reveals the Generation Dynamics of Diffusion Language Models

Authors: Darpan Aswal, Céline Hudelot.

Extends integrated-gradient attribution across layers and denoising steps to examine which inputs influence a diffusion model's developing response. Includes multi-hop graph reasoning; the authors present attribution as a complement to, not a replacement for, causal intervention.

First public: 2026-10-01.
ArXiv initial submission: 2026-10-01.

[Original paper](https://arxiv.org/abs/2610.01177) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.01177/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.01177/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.01177/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.01177/record.json)

### Approaches

- [Alternative generation methods](https://latent-implicit-thinking.github.io/topics/alternative-reasoning-schedules/): Change how intermediate steps are generated, revised, or searched—for example, by refining several steps in parallel. These are related approaches: some still produce written chains of thought.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## On the Chain-of-Thought Monitorability of Looped Language Models

Authors: Han Wang, Ishwar B Balappanawar, Huan Zhang.

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.

First public: 2026-10-02.
ArXiv initial submission: 2026-10-02.

[Original paper](https://arxiv.org/abs/2610.02741) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.02741/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.02741/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.02741/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.02741/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Efficient Reasoning with Flow Language Models

Authors: Hanru Bai, Faissal Izermine, Oscar Davis, T. Konstantin Rusch.

Compares continuous flow and discrete diffusion models at matched sizes and denoising steps. A theoretical account and intermediate-state interventions examine whether retaining information about several candidates helps solve mazes and Sudoku before final discretization.

First public: 2026-10-07.
ArXiv initial submission: 2026-10-07.

[Original paper](https://arxiv.org/abs/2610.09416) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.09416/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.09416/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.09416/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.09416/record.json)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Alternative generation methods](https://latent-implicit-thinking.github.io/topics/alternative-reasoning-schedules/): Change how intermediate steps are generated, revised, or searched—for example, by refining several steps in parallel. These are related approaches: some still produce written chains of thought.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## 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.

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.

First public: 2026-10-07.
ArXiv initial submission: 2026-10-07.

[Original paper](https://arxiv.org/abs/2610.10625) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.10625/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.10625/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.10625/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.10625/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## S-Space: Exploring Spatial Workspace in Multimodal Language Models

Authors: Zhiyuan Shi, Xiang Li, Xingzhuo Guo, Shangchen Miao, Weiliang Chen, Qiyu Dai, Jinshan Ren, Jiangran Lyu, Fangfu Liu, Mingsheng Long, Jialong Wu.

Identifies spatial-coordinate directions in multimodal model activations and tests them through causal interventions. Separating perception from viewpoint transformation reveals cases where a model represents object locations but fails to perform the required spatial computation.

First public: 2026-10-09.
ArXiv initial submission: 2026-10-09.

[Original paper](https://arxiv.org/abs/2610.13527) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.13527/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.13527/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.13527/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.13527/record.json)

### Approaches

- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Learning to Extrapolate in Depth with Looped Transformers

Authors: Huitao Yang, Jianhao Huang, Zixuan Wang, Baharan Mirzasoleiman.

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.

First public: 2026-10-10.
ArXiv initial submission: 2026-10-10.

[Original paper](https://arxiv.org/abs/2610.14456) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.14456/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.14456/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.14456/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.14456/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Knowledge transfer between simple discrete worlds

Authors: Silvère Gangloff, Jan Hula.

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.

First public: 2026-10-10.
ArXiv initial submission: 2026-10-10.

[Original paper](https://arxiv.org/abs/2610.15081) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.15081/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.15081/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.15081/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.15081/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Running Fewer Loops Removes Refusal Behaviour in Recurrent-Depth Language Models

Authors: Seyedarmin Azizi, Erfan Baghaei Potraghloo, Arya Fayyazi, Saeid Shokoufa, Massoud Pedram.

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.

First public: 2026-10-10.
ArXiv initial submission: 2026-10-10.

[Original paper](https://arxiv.org/abs/2610.15218) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.15218/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.15218/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.15218/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.15218/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Resample the Answer: Where to Spend Test-Time Compute in Recursive Reasoning

Authors: Maxime Illouz.

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.

First public: 2026-10-12.
ArXiv initial submission: 2026-10-12.

[Original paper](https://arxiv.org/abs/2610.16427) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.16427/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.16427/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.16427/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.16427/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Monitoring latent reasoning in looped language models

Authors: Pawel Olszowiec, Paulina Tomaszewska, Maciej Żelaszczyk, Michal Byra, Neo Christopher Chung.

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.

First public: 2026-10-13.
ArXiv initial submission: 2026-10-13.

[Original paper](https://arxiv.org/abs/2610.18127) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.18127/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.18127/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.18127/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.18127/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Looped Reasoning Finishes Earlier Than You Think

Authors: Sumin Park, T. Konstantin Rusch.

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.

First public: 2026-10-13.
ArXiv initial submission: 2026-10-13.

[Original paper](https://arxiv.org/abs/2610.18174) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.18174/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.18174/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.18174/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.18174/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Riding the Fixed-Point Curve: Image Classification in the Continuous Thought Machine

Authors: Thomas Hannagan.

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.

First public: 2026-10-13.
ArXiv initial submission: 2026-10-13.

[Original paper](https://arxiv.org/abs/2610.19220) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.19220/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.19220/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.19220/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.19220/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## 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.

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.

First public: 2026-10-14.
ArXiv initial submission: 2026-10-14.

[Original paper](https://arxiv.org/abs/2610.19768) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.19768/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.19768/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.19768/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.19768/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): 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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.


## Does Latent Chain-of-Thought Actually Reason? A Single, Unifying Taxonomy for Latent Reasoning

Authors: Jingjie Qiu, Sheldon Yu, Xunyi Jiang, Jiajin Liu, Zihan Huang, Zhendong Chu, Tong Yu, Julian McAuley, Junda Wu.

Uses chain deletion, content replacement, probes, and trajectory analysis across 21 model-task configurations. Separates what continuous states encode from whether the model uses their content, finding that dependence on the chain varies with task and training recipe.

First public: 2026-10-15.
ArXiv initial submission: 2026-10-15.

[Original paper](https://arxiv.org/abs/2610.21182) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.21182/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.21182/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.21182/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.21182/record.json)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.4; literature checked through 2026-10-18.