# 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.

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

For example: A model runs the same layers several times, updating the information it keeps between passes. If it has learned a stopping rule, it can decide when to produce its answer.

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

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

## How the methods connect and differ

**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/)

## Papers — oldest first

## CoTFormer: A Chain-of-Thought Driven Architecture with Budget-Adaptive Computation Cost at Inference

Authors: Amirkeivan Mohtashami, Matteo Pagliardini, Martin Jaggi.

Runs shared transformer blocks repeatedly, keeping earlier passes available to attention. A learned router chooses how many passes each token receives.

First public: 2023-10-16.
ArXiv initial submission: 2023-10-16.

[Original paper](https://arxiv.org/abs/2310.10845) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2310.10845/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2310.10845/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2310.10845/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2310.10845/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.

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 up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach

Authors: Jonas Geiping, Sean McLeish, Neel Jain, John Kirchenbauer, Siddharth Singh, Brian R. Bartoldson, Bhavya Kailkhura, Abhinav Bhatele, Tom Goldstein.

Pretrains a depth-recurrent language model whose computation can be extended at inference time, separating test-time compute from generated token length.

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

[Original paper](https://arxiv.org/abs/2502.05171) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2502.05171/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2502.05171/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2502.05171/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2502.05171/record.json)
[Code](https://github.com/seal-rg/recurrent-pretraining)

### 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

Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach. Jonas Geiping, Sean McLeish, Neel Jain, John Kirchenbauer, Siddharth Singh, Brian Bartoldson, Bhavya Kailkhura, Abhinav Bhatele, Tom Goldstein. Advances in Neural Information Processing Systems, 2025.
[Publication](https://proceedings.neurips.cc/paper_files/paper/2025/hash/3b01972cf31e6fa0fe29e4b8b5c2a0a1-Abstract-Conference.html) · [BibTeX](https://latent-implicit-thinking.github.io/papers/2502.05171/publication.bib) · [CSL-JSON](https://latent-implicit-thinking.github.io/papers/2502.05171/publication.csl.json)
Metadata checked 2026-10-18 against [the publication record](https://proceedings.neurips.cc/paper_files/paper/2025/hash/3b01972cf31e6fa0fe29e4b8b5c2a0a1-Abstract-Conference.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.

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.


## Inner Thinking Transformer: Leveraging Dynamic Depth Scaling to Foster Adaptive Internal Thinking

Authors: Yilong Chen, Junyuan Shang, Zhenyu Zhang, Yanxi Xie, Jiawei Sheng, Tingwen Liu, Shuohuan Wang, Yu Sun, Hua Wu, Haifeng Wang.

Routes selected tokens through extra computation while reusing model parameters. Marks successive thinking steps so the model can distinguish one pass from the next.

First public: 2025-02-19.
ArXiv initial submission: 2025-02-19.

[Original paper](https://arxiv.org/abs/2502.13842) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2502.13842/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2502.13842/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2502.13842/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2502.13842/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.

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 with Latent Thoughts: On the Power of Looped Transformers

Authors: Nikunj Saunshi, Nishanth Dikkala, Zhiyuan Li, Sanjiv Kumar, Sashank J. Reddi.

Analyzes the expressive power of transformers that repeatedly apply shared layers, treating recurrent depth as a form of internal reasoning.

First public: 2025-02-24.
ArXiv initial submission: 2025-02-24.

[Original paper](https://arxiv.org/abs/2502.17416) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2502.17416/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2502.17416/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2502.17416/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2502.17416/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.

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 Pretraining Length Scaling

Authors: Bohong Wu, Shen Yan, Sijun Zhang, Jianqiao Lu, Yutao Zeng, Ya Wang, Xun Zhou.

Adds hidden decoding tokens during pretraining, then discards their key/value cache entries after use. Keeps the original tokens' entries to preserve longer-range context.

First public: 2025-04-21.
ArXiv initial submission: 2025-04-21.

[Original paper](https://arxiv.org/abs/2504.14992) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2504.14992/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2504.14992/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2504.14992/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2504.14992/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.
- [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.

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.


## 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.


## PonderLM: Pretraining Language Models to Ponder in Continuous Space

Authors: Boyi Zeng, Shixiang Song, Siyuan Huang, Yixuan Wang, He Li, Ziwei He, Xinbing Wang, Zhiyu Li, Zhouhan Lin.

Pretrains language models with repeated continuous-space pondering steps before token prediction.

First public: 2025-05-27.
ArXiv initial submission: 2025-05-27.

[Original paper](https://arxiv.org/abs/2505.20674) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2505.20674/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2505.20674/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2505.20674/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2505.20674/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.

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.


## Hierarchical Reasoning Model

Authors: Guan Wang, Jin Li, Yuhao Sun, Xing Chen, Changling Liu, Yue Wu, Meng Lu, Sen Song, Yasin Abbasi Yadkori.

Uses coupled recurrent modules operating at different timescales to perform iterative internal computation on difficult reasoning tasks.

First public: 2025-06-26.
ArXiv initial submission: 2025-06-26.

[Original paper](https://arxiv.org/abs/2506.21734) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2506.21734/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2506.21734/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2506.21734/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2506.21734/record.json)
[Code](https://github.com/sapientinc/HRM)

### 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.

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.


## Skip a Layer or Loop it? Test-Time Depth Adaptation of Pretrained LLMs

Authors: Ziyue Li, Yang Li, Tianyi Zhou.

Adapts the depth of pretrained language models at test time by selectively skipping or repeating layers.

First public: 2025-07-10.
ArXiv initial submission: 2025-07-10.

[Original paper](https://arxiv.org/abs/2507.07996) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2507.07996/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2507.07996/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2507.07996/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2507.07996/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.

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.


## Mixture-of-Recursions: Learning Dynamic Recursive Depths for Adaptive Token-Level Computation

Authors: Sangmin Bae, Yujin Kim, Reza Bayat, Sungnyun Kim, Jiyoun Ha, Tal Schuster, Adam Fisch, Hrayr Harutyunyan, Ziwei Ji, Aaron Courville, Se-Young Yun.

Learns token-level routing across recursive depths so different positions can receive different amounts of internal computation.

First public: 2025-07-14.
ArXiv initial submission: 2025-07-14.

[Original paper](https://arxiv.org/abs/2507.10524) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2507.10524/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2507.10524/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2507.10524/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2507.10524/record.json)
[Code](https://github.com/raymin0223/mixture_of_recursions)

### 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.

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 Latent Reasoning via Looped Language Models

Authors: Rui-Jie Zhu, Zixuan Wang, Kai Hua, Tianyu Zhang, Ziniu Li, Haoran Que, Boyi Wei, Zixin Wen, Fan Yin, He Xing, Lu Li, Jiajun Shi, Kaijing Ma, Shanda Li, Taylor Kergan, Andrew Smith, Xingwei Qu, Mude Hui, Bohong Wu, Qiyang Min, Hongzhi Huang, Xun Zhou, Wei Ye, Jiaheng Liu, Jian Yang, Yunfeng Shi, Chenghua Lin, Enduo Zhao, Tianle Cai, Ge Zhang, Wenhao Huang, Yoshua Bengio, Jason Eshraghian.

Scales looped language models that reuse layers across recurrent depth and studies how performance changes with additional internal computation.

First public: 2025-10-29.
ArXiv initial submission: 2025-10-29.

[Original paper](https://arxiv.org/abs/2510.25741) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2510.25741/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2510.25741/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2510.25741/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2510.25741/record.json)
[Code](https://ouro-llm.github.io/)

### 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.

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.


## Teaching Pretrained Language Models to Think Deeper with Retrofitted Recurrence

Authors: Sean McLeish, Ang Li, John Kirchenbauer, Dayal Singh Kalra, Brian R. Bartoldson, Bhavya Kailkhura, Avi Schwarzschild, Jonas Geiping, Tom Goldstein, Micah Goldblum.

Adds recurrent depth to pretrained language models and trains them to use repeated internal computation without pretraining from scratch.

First public: 2025-11-10.
ArXiv initial submission: 2025-11-10.

[Original paper](https://arxiv.org/abs/2511.07384) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2511.07384/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2511.07384/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2511.07384/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2511.07384/record.json)
[Code](https://github.com/mcleish7/retrofitting-recurrence)

### 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.

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-at-Hard: Dynamic Looped Transformers for Improved Reasoning

Authors: Tianyu Fu, Yichen You, Zekai Chen, Guohao Dai, Huazhong Yang, Yu Wang.

Uses dynamic looping to vary internal depth with problem difficulty and studies the resulting reasoning and efficiency trade-offs.

First public: 2025-11-11.
ArXiv initial submission: 2025-11-11.

[Original paper](https://arxiv.org/abs/2511.08577) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2511.08577/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2511.08577/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2511.08577/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2511.08577/record.json)
[Code](https://github.com/thu-nics/TaH)

### 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.

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.


## PonderLM-3: Adaptive Token-Wise Pondering with Differentiable Masking

Authors: He Li, Feichen Song, Boyi Zeng, Shixiang Song, Zhiqin John Xu, Ziwei He, Zhouhan Lin.

Uses differentiable masks to allocate a variable number of recurrent pondering steps to different token positions.

First public: 2026-03-02.
ArXiv initial submission: 2026-03-02.

[Original paper](https://arxiv.org/abs/2603.02023) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2603.02023/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2603.02023/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2603.02023/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2603.02023/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.

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.


## Fixed-Point Reasoners: Stable and Adaptive Deep Looped Transformers

Authors: Sajad Movahedi, Vera Milovanović, Shlomo Libo Feigin, Alexander Theus, Thomas Hofmann, Valentina Boeva, T. Konstantin Rusch, Antonio Orvieto.

Stabilizes repeated transformer layers and stops looping when the hidden state converges, allowing the model to spend different amounts of computation on different problems.

First public: 2026-06-16.
ArXiv initial submission: 2026-06-16.

[Original paper](https://arxiv.org/abs/2606.18206) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2606.18206/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2606.18206/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2606.18206/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2606.18206/record.json)
[Code](https://github.com/nilskiKonjIzDunava/fprm)

### 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.

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.


## DiscoLoop: Looping Discrete Embeddings and Continuous Hidden States for Multi-hop Reasoning

Authors: Hengyu Fu, Tianyu Guo, Zixuan Wang, Hanlin Zhu, Jason D. Lee, Jiantao Jiao, Stuart Russell, Song Mei.

Feeds both token embeddings and hidden states back through repeated transformer layers to connect successive steps of multi-hop reasoning.

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

[Original paper](https://arxiv.org/abs/2607.00341) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2607.00341/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2607.00341/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2607.00341/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2607.00341/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.

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.


## T²MLR: Transformer with Temporal Middle-Layer Recurrence

Authors: Ziyang Cai, Xingyu Zhu, Yihe Dong, Yinghui He, Sanjeev Arora.

Carries a cached middle-layer state from one token position into an earlier layer at the next position, providing localized temporal recurrence that can also be retrofitted into pretrained transformers.

First public: 2026-07-16.
ArXiv initial submission: 2026-07-16.

[Original paper](https://arxiv.org/abs/2607.15178) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2607.15178/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2607.15178/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2607.15178/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2607.15178/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.

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.


## LoopMTP: A looped transformer guided by latent multi-token prediction

Authors: Behzad Shomali, Markus Frey, David Berghaus, Joachim Koehler, Mehdi Ali.

Trains each transformer loop to anticipate a different future token, using token embeddings to guide its hidden state.

First public: 2026-08-04.
ArXiv initial submission: 2026-08-04.

[Original paper](https://arxiv.org/abs/2608.03624) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2608.03624/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2608.03624/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2608.03624/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2608.03624/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.

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.


## 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.


## Latent Recurrent Thoughts: Recurrent Refinement of Proposed Latents for Reasoning with Frozen LLMs

Authors: Zhaoliang Chen, Jie Fu.

Uses a task-specific proposer and small recurrent auxiliary network to iteratively refine continuous thoughts that a frozen language model then decodes.

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

[Original paper](https://arxiv.org/abs/2609.01117) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.01117/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.01117/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.01117/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.01117/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.

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.


## Diffusion as a Training Curriculum for Timestep-Free Iterative Reasoning

Authors: Mariia Drozdova, Aidan Sirbu, Pietro Miotti, Robert Obryk, Mayalen Etcheverry, Eyvind Niklasson, Blake Richards.

Turns a diffusion denoiser into a recurrent puzzle solver by adding a persistent hidden state and removing timestep conditioning. Separates the role of denoising during training from the role of repeated updates and noise at inference.

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

[Original paper](https://arxiv.org/abs/2609.01449) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.01449/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.01449/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.01449/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.01449/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.
- [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.

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.


## RecurTrace: Adaptive Latent Reasoning with Loop-Time Memory

Authors: Yuxiang Wang, Kunyu Feng, Yingda Shen, Haoning Xu, Junyu Wang, Zhizheng Wu.

Lets looped layers attend to their own earlier iteration states and learns a halting head that allocates recurrent depth per input.

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

[Original paper](https://arxiv.org/abs/2609.03379) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.03379/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.03379/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.03379/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.03379/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.

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.


## DART: Distributional Adversarial Recurrent Training for Algorithm Learning

Authors: Hieu Tran Bao, Phung Thanh Dang, Pham Quang Nhat Minh, Hoang Thanh Tung.

Trains recurrent reasoners against a distribution of targets near each correct solution, using an adversarial objective instead of a single point target. Evaluates generalization and stability on maze, chess, and Sudoku tasks.

First public: 2026-09-05.
ArXiv initial submission: 2026-09-05.

[Original paper](https://arxiv.org/abs/2609.05988) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.05988/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.05988/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.05988/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.05988/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.

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.


## T-LoopFormer: Token-Level Elastic-Depth Looped Transformers with Dynamic Routing

Authors: Mingqian Yu, Wenpeng Zhang, Shaobo Cui, Peilin Zhao.

Learns a router that chooses how many recurrent passes each token receives, and keeps separate key/value caches for each pass.

First public: 2026-09-14.
ArXiv initial submission: 2026-09-14.

[Original paper](https://arxiv.org/abs/2609.15160) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.15160/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.15160/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.15160/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.15160/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.

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.


## LoopSpec: Pipelined Self-Speculative Decoding for Looped Transformers

Authors: SangLyul Cho, Langqing Cui, Sehoon Kim, Dongsu Han, Insu Han.

Drafts future tokens from early loops while later loops verify current tokens, overlapping the work without training an extra model. Final verification preserves the full model's decoding behavior.

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

[Original paper](https://arxiv.org/abs/2609.17184) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.17184/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.17184/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.17184/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.17184/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.
- [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.

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.


## Trading Depth for Time in Recurrent Transformers

Authors: Zeyi Huang, Xuehai He, Yelong Shen, Yong Jae Lee.

Inserts a hidden-state refinement step between consecutive text tokens in a recurrent transformer. Compares this extra thinking time with adding physical layers or transformer loops under matched computation budgets.

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

[Original paper](https://arxiv.org/abs/2609.21605) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.21605/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.21605/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.21605/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.21605/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.
- [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.

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.


## WaveFront Decoding: Parallelized Self-Speculative Decoding for Looped Language Models

Authors: Hyeongju Ha, Jae-Joon Kim.

Uses intermediate loop depths to propose tokens that later loops verify. Arranges speculation across recurrent depths so that more of the draft and verification work can run together.

First public: 2026-09-19.
ArXiv initial submission: 2026-09-19.

[Original paper](https://arxiv.org/abs/2609.23033) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.23033/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.23033/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.23033/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.23033/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.
- [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.

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.


## LoopCD: Loop-wise Contrastive Decoding for Improving Reasoning in Looped Language Models

Authors: Byeongho Yu, Junhyuk So, Eunhyeok Park.

Uses differences between early- and late-loop predictions to adjust token sampling at inference time, without retraining the model.

First public: 2026-09-21.
ArXiv initial submission: 2026-09-21.

[Original paper](https://arxiv.org/abs/2609.24196) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.24196/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.24196/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.24196/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.24196/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.

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.


## 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.


## Structured Sparse Memory for Recurrent Reasoning

Authors: Zixuan Zhao, Samuel Wheeler, Neil Getty, Xiaotian Duan, Rick Stevens, Fangfang Xia.

Combines a recurrent reasoner with sparse, compositional task embeddings for ARC puzzles. Studies how task-memory size, recurrent depth, and training horizon affect performance.

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

[Original paper](https://arxiv.org/abs/2609.33270) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.33270/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.33270/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.33270/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.33270/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.

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.


## Loop Dropout: Regularizing Shared Updates in Looped Language Models

Authors: Zirui Zhu, Hailun Xu, Xuanlei Zhao, Yong Liu, Yingxuan Ren, Kanchan Sarkar, Kun Xu, Yang You.

Regularizes fine-tuning of looped language models by randomly masking adapter updates at selected loops. The shared backbone still runs at every loop; the method targets adapter updates that otherwise become concentrated at particular depths.

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

[Original paper](https://arxiv.org/abs/2609.34218) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.34218/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.34218/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.34218/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.34218/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.

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.


## FlexLoop: Depth-Elastic Looped Policies for Adaptive Test-Time Computation in Deep RL

Authors: Xun Wang, Ruishuo Chen, Yu Chen, Zhuoran Li, Longbo Huang.

Post-trains a looped reinforcement-learning policy to make useful decisions at several recurrent depths. Combines its original objective with distillation between neighboring depths, then uses agreement across depths to decide when to stop.

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

[Original paper](https://arxiv.org/abs/2609.34488) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.34488/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.34488/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.34488/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.34488/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.

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.


## Shallow Queries, Mature Values: Depth-Asynchronous Self-Speculation for Looped Transformers

Authors: Guanghao Li, Zihan Su, Hao Yu, Jinyang Jiang, Tao Ren, Zehao Li, Feng Lu, Ming Tang, Chun Yuan.

Uses shallower-loop queries with values from deeper loops to improve draft-token predictions in a looped language model. Studies the different rates at which queries, keys, and values develop, and uses that difference for self-speculative decoding.

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

[Original paper](https://arxiv.org/abs/2609.34538) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.34538/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.34538/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.34538/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.34538/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.
- [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.

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.


## Improving Test-Time Scaling with Adaptive Looped Transformers

Authors: Yichen You, Tianyu Fu, Aosong Feng, Xingtai Lv, Xuefei Ning, Ning Ding, Yu Wang.

Trains an iteration controller to give extra transformer loops only to tokens whose predictions benefit from them. Compares reasoning accuracy as both output length and internal computation increase.

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

[Original paper](https://arxiv.org/abs/2609.35748) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.35748/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.35748/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.35748/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.35748/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.

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 to Loop MoE: Flatten the Experts, Untie the Attention

Authors: Shouren Wang, Chuang Ma, Mohsen Hariri, Debargha Ganguly, Wang Yang, Xiaoqing Tong, Qianying Liu, Xiaotian Han, Vipin Chaudhary.

Builds a looped mixture-of-experts model by pooling experts across layers and revisiting them. Shares experts and routing across passes while giving each pass its own attention parameters.

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

[Original paper](https://arxiv.org/abs/2609.35751) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.35751/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.35751/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.35751/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.35751/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.

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.


## Port-Hamiltonian Latent Deliberation: Mitigating the Deliberation Drift Cliff in Test-Time Compute Scaling

Authors: Zeyu Jia.

Separates hidden-state updates into attracting and rotating components to reduce errors from running a recurrent reasoner for more steps. Tests a tensor-based implementation on logical and multi-hop reasoning tasks.

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

[Original paper](https://arxiv.org/abs/2609.37351) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.37351/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.37351/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.37351/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.37351/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.

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.


## Looped Actor: Depth-Recurrent Reasoning Models for Reinforcement Learning

Authors: T. Konstantin Rusch, Tim Seyde, Jared Boyer, Zach J. Patterson, Daniela Rus.

Uses a shared transformer block to refine a reinforcement-learning policy's internal state before choosing an action. Learns to vary the number of loops with the current state, and studies adaptive computation in puzzles and robotic-control tasks.

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

[Original paper](https://arxiv.org/abs/2609.37432) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.37432/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.37432/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.37432/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.37432/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.

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.


## LoopVL: Recurrent Visual Intelligence

Authors: Zhe Qian, Ziyang Gong, Zhongxing Xu, Hehan Li, Zhonghua Wang, Hanmeng Liu, Liwei Qian, Xin Pei, Peizhi Xu, Fei Luo, Mingxuan Wang, Xue Yang, Shiwei Liu, Yanbiao Ma, Junchi Yan, Jungong Han.

Extends shared-module and whole-model looping to vision-language models, repeatedly updating a joint visual-language state. Trains from scratch through language and multimodal stages and evaluates visual understanding and reasoning.

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

[Original paper](https://arxiv.org/abs/2609.38426) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.38426/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.38426/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.38426/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.38426/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.

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.


## LatentHarness: Learning Latent Actions for Memory and Reasoning via Counterfactual Policy Distillation

Authors: Xiaoqiang Wang, Suyuchen Wang, Bang Liu.

Learns when to perform another internal reasoning step, recall stored evidence or intermediate states, or emit a token. Trains these choices by branching over alternative actions and measuring their effects on the next emitted token.

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

[Original paper](https://arxiv.org/abs/2609.39740) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.39740/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.39740/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.39740/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.39740/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.

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.


## Closing the Loop: Practical Training Recipes for Looped Language Models

Authors: Andrei Marchenko, Viacheslav Bezrukov, Oleg Kashurin, Inessa Fedorova, Dmitry Bocharov, Yuliana Shakhvalieva, Maria Tikhonova, Valerii Ternovskii.

Gives training recipes for looped language models both from scratch and by converting pretrained models. Uses controlled data and compute comparisons to separate the benefit of recurrence from the training setup.

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

[Original paper](https://arxiv.org/abs/2610.00673) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.00673/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.00673/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.00673/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.00673/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.

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.


## Rotate the Loop: Blockwise Conformality for Looped Transformers

Authors: Alexey Zemtsov, Albina Klepach, Vadim Lomshakov, Andrei Polubarov, Nikita Lyubaykin, Alexander Derevyagin, Vladislav Kurenkov, Alexander Nikulin.

Splits the recurrent residual into groups and rotates each group separately, aiming to preserve information across repeated transformer loops. Evaluates state tracking and language modeling.

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

[Original paper](https://arxiv.org/abs/2610.14030) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.14030/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.14030/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.14030/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.14030/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.

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.


## Looping Beyond Twice: A Scalable Recipe for Looped Mixture-of-Experts

Authors: Di He, Pengxiang Li, Da Chang, Qingyan Meng, Lu Yin, Shiwei Liu.

Studies how to train mixture-of-experts transformers with more than two recurrent passes. Combines stabilized residual updates, reintroduced input information, and loop-specific routing to support deeper reuse of the shared model.

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

[Original paper](https://arxiv.org/abs/2610.01153) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.01153/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.01153/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.01153/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.01153/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.

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.


## Decoding Looped Transformers Better for (Almost) Free

Authors: Weihao Liu, Huangjie Zheng, Tianrong Chen, Rohit Dilip, Richard He Bai, Yizhu Jiao, Yuyang Wang, Ruixiang Zhang.

Compares a looped model's final prediction with predictions from earlier loops to improve decoding without additional training. Tests contrastive variants using either output logits or hidden states on mathematical reasoning and code generation.

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

[Original paper](https://arxiv.org/abs/2610.02185) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.02185/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.02185/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.02185/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.02185/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.

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.


## The Surprising Effectiveness of Shared Memory in Looped Transformers

Authors: Giovanni Monea, Keshav Ramji, Yousef El-Kurdi, Luis A. Lastras, Yoav Artzi, Nathan Godey, Ramón Fernandez Astudillo.

Shares a long-context KV memory written by the first loop across later loops, which also keep a short local memory. Studies this architecture during pretraining and examines how shared memory changes representations and gradient flow.

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

[Original paper](https://arxiv.org/abs/2610.02383) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.02383/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.02383/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.02383/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.02383/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.

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.


## AdaLoop: Adaptive-Depth Latent Reasoning for Audio Language Models

Authors: Lee Seung-woo, Bowen Qi.

Adds a shared recurrent block between an audio encoder and language model. A question-conditioned halting mechanism chooses how many refinement passes to apply, with deeper computation learned for tasks requiring finer acoustic distinctions.

First public: 2026-10-03.
ArXiv initial submission: 2026-10-03.

[Original paper](https://arxiv.org/abs/2610.06949) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.06949/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.06949/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.06949/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.06949/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.

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.


## Enhancing Long-Video VLM Embeddings with Query-Aware Streaming Latent Reasoning

Authors: Haozhe Chi, Song Jin, Yang Jin, Yadong Mu.

Processes selected video clips sequentially while persistent think tokens accumulate evidence for a fixed-size retrieval embedding. Intermediate retrieval supervision and self-distillation train partial-video readouts; the output is an embedding rather than a generated reasoning trace.

First public: 2026-10-04.
ArXiv initial submission: 2026-10-04.

[Original paper](https://arxiv.org/abs/2610.04864) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.04864/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.04864/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.04864/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.04864/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.

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 Looped Models Done Right, Part II: Rethinking at Fixed Points

Authors: Benhao Huang, Chufan Shi, Junlin Chen, Shicheng Wen, Zhengzhong Liu, Eric Xing, Xuezhe Ma.

Uses near-fixed-point recurrent states to reduce the cost of training, key/value caching, and prefill. Learns how to sample loop depths and changes how the input is reintroduced on each loop.

First public: 2026-10-05.
ArXiv initial submission: 2026-10-05.

[Original paper](https://arxiv.org/abs/2610.06833) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.06833/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.06833/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.06833/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.06833/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.

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.


## Recurrent Looped Transformer

Authors: Yifan Zhang, Jichen Feng, Shihan Qin, Sun-Yuan Kung, Mengdi Wang.

Passes each token's final decoder state to the next token, alongside a causal encoder representation. Tests whether this growing computation path supports state tracking on sequences longer than those seen during training.

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

[Original paper](https://arxiv.org/abs/2610.07591) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.07591/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.07591/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.07591/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.07591/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.

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.


## SanSi: A Looped Typed Decision Model for System 1.5 Thinking

Authors: Shuyu Gan, Young-Jun Lee, Dongyeop Kang.

Refines an internal state across loops to choose among typed answer options without generating a written reasoning trace. Supervises decisions at multiple depths and evaluates how prediction quality changes with the available computation budget.

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

[Original paper](https://arxiv.org/abs/2610.07730) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.07730/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.07730/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.07730/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.07730/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.

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 Memory Machines

Authors: Ciaran Regan, Kai Arulkumaran, Luke Darlow, Stefania Druga, Sebastian Risi, Llion Jones.

Keeps separate short- and long-term matrix memories and lets a transformer update both through bidirectional reads and writes. Tests this recurrent architecture on algorithmic, in-context learning, and reasoning tasks.

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

[Original paper](https://arxiv.org/abs/2610.07907) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.07907/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.07907/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.07907/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.07907/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.

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 Before You Paint: Recursive Latent Reasoning for Diffusion Models

Authors: Paweł Skierś, Małgorzata Grzanka, Wojciech Masarczyk, Jan-Willem van de Meent, Kamil Deja.

PaTh uses a small recursive network to refine learned image-state tokens inside each denoising step and steer a frozen diffusion model through adapters. It learns visual puzzles from reconstruction targets without symbolic solutions or an external verifier.

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

[Original paper](https://arxiv.org/abs/2610.09876) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.09876/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.09876/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.09876/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.09876/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.
- [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.

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.


## Recurrent Self-Improvement: Dynamic Cross-Loop On-Policy Distillation for Looped Language Models

Authors: Yi Wang, Rui Qian, Yu Li, Haoyang Yao, Wenjie Wang.

Trains an intermediate loop using a deeper loop of the same language model as its teacher on student-generated outputs. A dynamic variant refreshes the teacher during training, turning additional recurrent computation into a source of supervision.

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

[Original paper](https://arxiv.org/abs/2610.10623) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.10623/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.10623/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.10623/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.10623/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.

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.


## Invariant-Measure Reasoners: Stable Representations for Latent Reasoning

Authors: Yuto Inui, Takuya Konishi, Yoshinobu Kawahara.

Predicts by averaging over the long-run distribution of recurrent hidden states instead of reading a single final state. This lets the model use changing hidden states without requiring them to settle at one fixed point.

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

[Original paper](https://arxiv.org/abs/2610.10996) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.10996/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.10996/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.10996/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.10996/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.

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 to Tens of Thousands of Test-Time Iterations with Loop-Native Attention Residuals

Authors: Pengxiang Li, Dilxat Muhtar, Di He, Guinan Su, Lu Yin, Shiwei Liu.

Adds a learned running summary of previous recurrent states so that each update can retain useful earlier work. Uses content-based weighting and temporal decay with constant aggregation memory, and tests whether puzzle-solving improves over much longer inference runs.

First public: 2026-10-08.
ArXiv initial submission: 2026-10-08.

[Original paper](https://arxiv.org/abs/2610.11570) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.11570/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.11570/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.11570/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.11570/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.

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.


## One Model to Loop Them All: Elastic Latent Recurrence for Language Models

Authors: Faisal Ladhak, Shantanu Acharya, Santiago Akle Serano, Simeng Sun, Boris Ginsburg, Krishna C Puvvada.

Trains one language model to operate at different loop counts by mixing depths during training and conditioning each pass on its index and budget. A learned gate controls each recurrent update.

First public: 2026-10-08.
ArXiv initial submission: 2026-10-08.

[Original paper](https://arxiv.org/abs/2610.12582) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.12582/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.12582/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.12582/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.12582/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.

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.


## Adaptive-Depth Is a Finishing Stage

Authors: Andrei Piterbarg, Sean McLeish, Dhruv Pai, Benjamin Keigwin.

Trains a looped language model at a fixed depth first, then introduces varying depths only near the end of training. Compares the resulting training cost and performance across inference depths with varying depth throughout training.

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

[Original paper](https://arxiv.org/abs/2610.14252) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.14252/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.14252/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.14252/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.14252/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.

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.


## LoOPSD: On-Policy Self-Distillation with Looped Teachers

Authors: Wei Fan, Qingyue Yang, Chao-Hong Tan, Qian Chen, Wen Wang, Xiangang Li, Kejiang Chen, Weiming Zhang, Nenghai Yu.

Searches for layers to repeat to make a stronger teacher from the current model, then distills its predictions into the original student. Repeats search and distillation as the student improves.

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

[Original paper](https://arxiv.org/abs/2610.18162) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.18162/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.18162/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.18162/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.18162/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.

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.


## Input-Conditioned Search for Efficient Test-Time Scaling of Recursive Reasoners

Authors: Haochen Shi, Tianwen Fu, Qianggang Ding, Yinhan Lu, Yizhan Li, Huan Zhang, Yajie Zhao, Xingdi Yuan, Hengyang Lu, Bang Liu.

Searches over input conditions to change a recursive reasoner's update rule without retraining it. Tests whether these alternative updates can redirect a trajectory away from an incorrect solution, rather than only adding more steps or perturbing its state.

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

[Original paper](https://arxiv.org/abs/2610.18547) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.18547/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.18547/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.18547/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.18547/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.

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.


## LoopAhead: Speculating Ahead for Faster Decoding in Looped Language Models

Authors: Zixuan Liu, Nan Xue, Rui Bao, Yuhang Xu, Xiaofeng Cao, Jiangchao Yao, Zhiyong Chen.

Trains a small drafter to predict several future tokens from early-loop hidden states. Later loops decide which speculative branches to continue, and full-depth verification determines the final output.

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

[Original paper](https://arxiv.org/abs/2610.21594) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.21594/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.21594/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.21594/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.21594/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.
- [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.

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.