# Internalized reasoning

Learn from worked solutions so that some or all of the reasoning can later happen without writing those steps. Training may use a separate teacher model or progressively remove written steps from the model being trained.

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

For example: A teacher model solves a problem in several written steps. A student model learns to produce the answer directly, using information from the teacher's intermediate reasoning during training.

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

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

## Try it

Demo: [Multiplication without written steps](https://huggingface.co/spaces/yuntian-deng/gpt2-multiplication)

Compare GPT-2 models using implicit CoT, explicit CoT, or no CoT on two numbers of up to 20 digits each.

The models can make mistakes, including on valid inputs. The implicit model writes answer digits, not intermediate steps.

[Model details](https://huggingface.co/yuntian-deng/gpt2-implicit-cot-multiplication-20-digits)

Implements: [From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step](https://latent-implicit-thinking.github.io/papers/2405.14838/).

Related method, not implemented by this demo: [Implicit Chain of Thought Reasoning via Knowledge Distillation](https://latent-implicit-thinking.github.io/papers/2311.01460/).

Demo: [Math word problems without written steps](https://huggingface.co/spaces/yuntian-deng/implicit-cot-math)

Try a Mistral-7B model trained with stepwise internalization on grade-school math word problems.

Answers can be wrong. This model is trained for grade-school math word problems, not general conversation. It still generates the answer token by token.

[Model details](https://huggingface.co/yuntian-deng/implicit-cot-math-mistral7b)

Implements: [From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step](https://latent-implicit-thinking.github.io/papers/2405.14838/).

Related method, not implemented by this demo: [Implicit Chain of Thought Reasoning via Knowledge Distillation](https://latent-implicit-thinking.github.io/papers/2311.01460/).

## How the methods connect and differ

**Distillation and stepwise internalization**

Deng et al. (2023) introduced implicit CoT as reasoning through hidden states rather than written steps; distillation is the paper's implementation of that proposal. It learns to predict a teacher's intermediate hidden states, which help a student produce the answer. Stepwise Internalization instead repeatedly shortens the written solution and fine-tunes the same model on what remains. Both use worked solutions during training; neither requires writing the removed steps at inference. Their reported experiments focus on multiplication and grade-school math, not a guarantee of general reasoning ability.

Sources: [Implicit CoT proposal, §2.3](https://arxiv.org/html/2311.01460v1#S2.SS3) · [Distillation implementation, §3](https://arxiv.org/html/2311.01460v1#S3) · [Stepwise internalization, §3](https://arxiv.org/html/2405.14838v1#S3)

Paper details: [Implicit Chain of Thought Reasoning via Knowledge Distillation](https://latent-implicit-thinking.github.io/papers/2311.01460/) · [From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step](https://latent-implicit-thinking.github.io/papers/2405.14838/)

**Hidden-state distillation: the 2023 method and CODI**

The 2023 implicit CoT paper proposes reasoning through hidden states and implements it with a teacher, a thought emulator and an answer-generating student. CODI also transfers explicit reasoning through hidden-state supervision, but uses one model for both teacher and student tasks. It aligns their states just before the answer, while the student takes successive continuous reasoning steps.

Sources: [Deng et al. (2023), §2.3](https://arxiv.org/html/2311.01460v1#S2.SS3) · [Deng et al. (2023), §3](https://arxiv.org/html/2311.01460v1#S3) · [CODI, §3](https://arxiv.org/html/2502.21074v3#S3)

Paper details: [Implicit Chain of Thought Reasoning via Knowledge Distillation](https://latent-implicit-thinking.github.io/papers/2311.01460/) · [CODI: Compressing Chain-of-Thought into Continuous Space via Self-Distillation](https://latent-implicit-thinking.github.io/papers/2502.21074/)

## Papers — oldest first

## Implicit Chain of Thought Reasoning via Knowledge Distillation

Authors: Yuntian Deng, Kiran Prasad, Roland Fernandez, Paul Smolensky, Vishrav Chaudhary, Stuart Shieber.

First proposes implicit chain-of-thought reasoning: language models carry out intermediate reasoning in continuous hidden states rather than generate it as text. Defines this setting separately from its implementation, which distills an explicit-CoT teacher's hidden states into an emulator and a student that produces the answer.

First public: 2023-11-02.
ArXiv initial submission: 2023-11-02.

[Original paper](https://arxiv.org/abs/2311.01460) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2311.01460/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2311.01460/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2311.01460/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2311.01460/record.json)
[Code](https://github.com/da03/implicit_chain_of_thought/)

Related terms: implicit CoT, latent reasoning, latent chain-of-thought, latent CoT.

### Method comparisons

**Distillation and stepwise internalization**

Deng et al. (2023) introduced implicit CoT as reasoning through hidden states rather than written steps; distillation is the paper's implementation of that proposal. It learns to predict a teacher's intermediate hidden states, which help a student produce the answer. Stepwise Internalization instead repeatedly shortens the written solution and fine-tunes the same model on what remains. Both use worked solutions during training; neither requires writing the removed steps at inference. Their reported experiments focus on multiplication and grade-school math, not a guarantee of general reasoning ability.

Sources: [Implicit CoT proposal, §2.3](https://arxiv.org/html/2311.01460v1#S2.SS3) · [Distillation implementation, §3](https://arxiv.org/html/2311.01460v1#S3) · [Stepwise internalization, §3](https://arxiv.org/html/2405.14838v1#S3)

Paper details: [Implicit Chain of Thought Reasoning via Knowledge Distillation](https://latent-implicit-thinking.github.io/papers/2311.01460/) · [From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step](https://latent-implicit-thinking.github.io/papers/2405.14838/)

**Hidden-state distillation: the 2023 method and CODI**

The 2023 implicit CoT paper proposes reasoning through hidden states and implements it with a teacher, a thought emulator and an answer-generating student. CODI also transfers explicit reasoning through hidden-state supervision, but uses one model for both teacher and student tasks. It aligns their states just before the answer, while the student takes successive continuous reasoning steps.

Sources: [Deng et al. (2023), §2.3](https://arxiv.org/html/2311.01460v1#S2.SS3) · [Deng et al. (2023), §3](https://arxiv.org/html/2311.01460v1#S3) · [CODI, §3](https://arxiv.org/html/2502.21074v3#S3)

Paper details: [Implicit Chain of Thought Reasoning via Knowledge Distillation](https://latent-implicit-thinking.github.io/papers/2311.01460/) · [CODI: Compressing Chain-of-Thought into Continuous Space via Self-Distillation](https://latent-implicit-thinking.github.io/papers/2502.21074/)

**Implicit CoT: proposal and implementation**

Deng et al. (2023) proposed implicit chain-of-thought reasoning: language models carry out intermediate reasoning in continuous hidden states rather than generate it as text. Section 2.3 defines this setting; section 3 develops a distillation method to implement it. That method transfers a teacher's reasoning into hidden states across layers. Reasoning through continuous hidden states is the broader proposal; it does not require the particular distillation procedure used in this paper. Its across-layer computation differs from the repeated hidden-state feedback used by later methods such as Coconut.

Sources: [Implicit CoT proposal, §2.3](https://arxiv.org/html/2311.01460v1#S2.SS3) · [Distillation implementation, §3](https://arxiv.org/html/2311.01460v1#S3) · [Coconut, §3](https://arxiv.org/html/2412.06769v3#S3)

Paper details: [Implicit Chain of Thought Reasoning via Knowledge Distillation](https://latent-implicit-thinking.github.io/papers/2311.01460/) · [Training Large Language Models to Reason in a Continuous Latent Space](https://latent-implicit-thinking.github.io/papers/2412.06769/)


### Demos

Related-method demo: [Multiplication without written steps](https://huggingface.co/spaces/yuntian-deng/gpt2-multiplication)

Compare GPT-2 models using implicit CoT, explicit CoT, or no CoT on two numbers of up to 20 digits each.

The models can make mistakes, including on valid inputs. The implicit model writes answer digits, not intermediate steps.

[Model details](https://huggingface.co/yuntian-deng/gpt2-implicit-cot-multiplication-20-digits)

Implements: [From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step](https://latent-implicit-thinking.github.io/papers/2405.14838/).

Related method, not implemented by this demo: [Implicit Chain of Thought Reasoning via Knowledge Distillation](https://latent-implicit-thinking.github.io/papers/2311.01460/).

Related-method demo: [Math word problems without written steps](https://huggingface.co/spaces/yuntian-deng/implicit-cot-math)

Try a Mistral-7B model trained with stepwise internalization on grade-school math word problems.

Answers can be wrong. This model is trained for grade-school math word problems, not general conversation. It still generates the answer token by token.

[Model details](https://huggingface.co/yuntian-deng/implicit-cot-math-mistral7b)

Implements: [From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step](https://latent-implicit-thinking.github.io/papers/2405.14838/).

Related method, not implemented by this demo: [Implicit Chain of Thought Reasoning via Knowledge Distillation](https://latent-implicit-thinking.github.io/papers/2311.01460/).


### Approaches

- [Internalized reasoning](https://latent-implicit-thinking.github.io/topics/internalized-reasoning/): Learn from worked solutions so that some or all of the reasoning can later happen without writing those steps. Training may use a separate teacher model or progressively remove written steps from the model being trained.

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.


## From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step

Authors: Yuntian Deng, Yejin Choi, Stuart Shieber.

Uses a curriculum that progressively removes intermediate reasoning steps during fine-tuning, teaching a model to internalize an explicit chain of thought.

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

[Original paper](https://arxiv.org/abs/2405.14838) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2405.14838/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2405.14838/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2405.14838/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2405.14838/record.json)
[Code](https://github.com/da03/Internalize_CoT_Step_by_Step)

Related terms: implicit CoT, latent reasoning, latent chain-of-thought, latent CoT.

### Method comparisons

**Distillation and stepwise internalization**

Deng et al. (2023) introduced implicit CoT as reasoning through hidden states rather than written steps; distillation is the paper's implementation of that proposal. It learns to predict a teacher's intermediate hidden states, which help a student produce the answer. Stepwise Internalization instead repeatedly shortens the written solution and fine-tunes the same model on what remains. Both use worked solutions during training; neither requires writing the removed steps at inference. Their reported experiments focus on multiplication and grade-school math, not a guarantee of general reasoning ability.

Sources: [Implicit CoT proposal, §2.3](https://arxiv.org/html/2311.01460v1#S2.SS3) · [Distillation implementation, §3](https://arxiv.org/html/2311.01460v1#S3) · [Stepwise internalization, §3](https://arxiv.org/html/2405.14838v1#S3)

Paper details: [Implicit Chain of Thought Reasoning via Knowledge Distillation](https://latent-implicit-thinking.github.io/papers/2311.01460/) · [From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step](https://latent-implicit-thinking.github.io/papers/2405.14838/)

**From stepwise internalization to Coconut**

Coconut explicitly credits Deng et al. (2024) as the inspiration for its multistage training curriculum. Stepwise internalization gradually removes written CoT tokens until the model answers directly. Coconut instead replaces removed steps with continuous hidden-state inputs, retaining a sequence of internal reasoning steps before the answer. It also follows the earlier work in resetting the optimizer between training stages.

Sources: [Deng et al. (2024), §3](https://arxiv.org/html/2405.14838v1#S3) · [Coconut, §3](https://arxiv.org/html/2412.06769v3#S3)

Paper details: [From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step](https://latent-implicit-thinking.github.io/papers/2405.14838/) · [Training Large Language Models to Reason in a Continuous Latent Space](https://latent-implicit-thinking.github.io/papers/2412.06769/)

**Changing generation order or removing written steps**

Diffusion of Thought changes how a chain of thought is generated: it refines the solution through denoising rather than committing to words strictly from left to right. This changes the generation schedule, not necessarily the visibility of the reasoning. The resulting chain can still be text, unlike methods that only emit the final answer.

Sources: [Diffusion of Thought](https://proceedings.neurips.cc/paper_files/paper/2024/hash/be30024e7fa2c29cac7a6dafcbb8571f-Abstract-Conference.html) · [Deng et al. (2024), §3](https://arxiv.org/html/2405.14838v1#S3)

Paper details: [Diffusion of Thoughts: Chain-of-Thought Reasoning in Diffusion Language Models](https://latent-implicit-thinking.github.io/papers/2402.07754/) · [From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step](https://latent-implicit-thinking.github.io/papers/2405.14838/)


### Demos

Demo: [Multiplication without written steps](https://huggingface.co/spaces/yuntian-deng/gpt2-multiplication)

Compare GPT-2 models using implicit CoT, explicit CoT, or no CoT on two numbers of up to 20 digits each.

The models can make mistakes, including on valid inputs. The implicit model writes answer digits, not intermediate steps.

[Model details](https://huggingface.co/yuntian-deng/gpt2-implicit-cot-multiplication-20-digits)

Implements: [From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step](https://latent-implicit-thinking.github.io/papers/2405.14838/).

Related method, not implemented by this demo: [Implicit Chain of Thought Reasoning via Knowledge Distillation](https://latent-implicit-thinking.github.io/papers/2311.01460/).

Demo: [Math word problems without written steps](https://huggingface.co/spaces/yuntian-deng/implicit-cot-math)

Try a Mistral-7B model trained with stepwise internalization on grade-school math word problems.

Answers can be wrong. This model is trained for grade-school math word problems, not general conversation. It still generates the answer token by token.

[Model details](https://huggingface.co/yuntian-deng/implicit-cot-math-mistral7b)

Implements: [From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step](https://latent-implicit-thinking.github.io/papers/2405.14838/).

Related method, not implemented by this demo: [Implicit Chain of Thought Reasoning via Knowledge Distillation](https://latent-implicit-thinking.github.io/papers/2311.01460/).


### Approaches

- [Internalized reasoning](https://latent-implicit-thinking.github.io/topics/internalized-reasoning/): Learn from worked solutions so that some or all of the reasoning can later happen without writing those steps. Training may use a separate teacher model or progressively remove written steps from the model being trained.

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.


## Distilling System 2 into System 1

Authors: Ping Yu, Jing Xu, Jason Weston, Ilia Kulikov.

Uses outputs from a slower deliberative process as training data for a faster model, studying when System-2-like behavior can be compressed into direct prediction.

First public: 2024-07-08.
ArXiv initial submission: 2024-07-08.

[Original paper](https://arxiv.org/abs/2407.06023) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2407.06023/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2407.06023/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2407.06023/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2407.06023/record.json)

### Approaches

- [Internalized reasoning](https://latent-implicit-thinking.github.io/topics/internalized-reasoning/): Learn from worked solutions so that some or all of the reasoning can later happen without writing those steps. Training may use a separate teacher model or progressively remove written steps from the model being trained.

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.


## Dualformer: Controllable Fast and Slow Thinking by Learning with Randomized Reasoning Traces

Authors: DiJia Su, Sainbayar Sukhbaatar, Michael Rabbat, Yuandong Tian, Qinqing Zheng.

Randomizes which reasoning steps remain visible during training so one model can interpolate between direct and explicit reasoning.

First public: 2024-10-13.
ArXiv initial submission: 2024-10-13.

[Original paper](https://arxiv.org/abs/2410.09918) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2410.09918/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2410.09918/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2410.09918/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2410.09918/record.json)

### Approaches

- [Internalized reasoning](https://latent-implicit-thinking.github.io/topics/internalized-reasoning/): Learn from worked solutions so that some or all of the reasoning can later happen without writing those steps. Training may use a separate teacher model or progressively remove written steps from the model being trained.

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

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


## Efficient Reasoning with Hidden Thinking

Authors: Xuan Shen, Yizhou Wang, Yufa Zhou, Xiangxi Shi, Pu Zhao, Yanzhi Wang, Jiuxiang Gu.

Compresses visible reasoning into hidden thinking states to reduce generated reasoning length while preserving task performance.

First public: 2025-01-31.
ArXiv initial submission: 2025-01-31.

[Original paper](https://arxiv.org/abs/2501.19201) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2501.19201/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2501.19201/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2501.19201/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2501.19201/record.json)

### Approaches

- [Internalized reasoning](https://latent-implicit-thinking.github.io/topics/internalized-reasoning/): Learn from worked solutions so that some or all of the reasoning can later happen without writing those steps. Training may use a separate teacher model or progressively remove written steps from the model being trained.
- [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.

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.


## LightThinker: Thinking Step-by-Step Compression

Authors: Jintian Zhang, Yuqi Zhu, Mengshu Sun, Yujie Luo, Shuofei Qiao, Lun Du, Da Zheng, Huajun Chen, Ningyu Zhang.

Compresses segments of a generated reasoning chain into dense states while retaining a stepwise inference process.

First public: 2025-02-21.
ArXiv initial submission: 2025-02-21.

[Original paper](https://arxiv.org/abs/2502.15589) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2502.15589/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2502.15589/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2502.15589/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2502.15589/record.json)

### Approaches

- [Internalized reasoning](https://latent-implicit-thinking.github.io/topics/internalized-reasoning/): Learn from worked solutions so that some or all of the reasoning can later happen without writing those steps. Training may use a separate teacher model or progressively remove written steps from the model being trained.
- [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.

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.


## CODI: Compressing Chain-of-Thought into Continuous Space via Self-Distillation

Authors: Zhenyi Shen, Hanqi Yan, Linhai Zhang, Zhanghao Hu, Yali Du, Yulan He.

Uses self-distillation to align continuous internal reasoning states with explicit chain-of-thought behavior while reducing visible reasoning tokens.

First public: 2025-02-28.
ArXiv initial submission: 2025-02-28.

[Original paper](https://arxiv.org/abs/2502.21074) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2502.21074/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2502.21074/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2502.21074/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2502.21074/record.json)

### Method comparisons

**Hidden-state distillation: the 2023 method and CODI**

The 2023 implicit CoT paper proposes reasoning through hidden states and implements it with a teacher, a thought emulator and an answer-generating student. CODI also transfers explicit reasoning through hidden-state supervision, but uses one model for both teacher and student tasks. It aligns their states just before the answer, while the student takes successive continuous reasoning steps.

Sources: [Deng et al. (2023), §2.3](https://arxiv.org/html/2311.01460v1#S2.SS3) · [Deng et al. (2023), §3](https://arxiv.org/html/2311.01460v1#S3) · [CODI, §3](https://arxiv.org/html/2502.21074v3#S3)

Paper details: [Implicit Chain of Thought Reasoning via Knowledge Distillation](https://latent-implicit-thinking.github.io/papers/2311.01460/) · [CODI: Compressing Chain-of-Thought into Continuous Space via Self-Distillation](https://latent-implicit-thinking.github.io/papers/2502.21074/)

**Coconut and CODI: similar computation, different training**

Coconut and CODI both pass continuous states between reasoning steps, but supervise them differently. Coconut gradually replaces written steps with hidden-state inputs and trains on the remaining text. CODI jointly trains explicit and implicit reasoning tasks, matching their hidden states at a selected position before the answer. These models avoid decoding a word at every intermediate step; they still perform successive model passes, so fewer written tokens does not mean no reasoning-time computation.

Sources: [Coconut, §3](https://arxiv.org/html/2412.06769v3#S3) · [CODI, §3](https://arxiv.org/html/2502.21074v3#S3)

Paper details: [Training Large Language Models to Reason in a Continuous Latent Space](https://latent-implicit-thinking.github.io/papers/2412.06769/) · [CODI: Compressing Chain-of-Thought into Continuous Space via Self-Distillation](https://latent-implicit-thinking.github.io/papers/2502.21074/)


### Published version

CODI: Compressing Chain-of-Thought into Continuous Space via Self-Distillation. Zhenyi Shen, Hanqi Yan, Linhai Zhang, Zhanghao Hu, Yali Du, Yulan He. Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing, 2025.
[Publication](https://aclanthology.org/2025.emnlp-main.36/) · [BibTeX](https://latent-implicit-thinking.github.io/papers/2502.21074/publication.bib) · [CSL-JSON](https://latent-implicit-thinking.github.io/papers/2502.21074/publication.csl.json)
Metadata checked 2026-10-18 against [the publication record](https://aclanthology.org/2025.emnlp-main.36/).

### Approaches

- [Internalized reasoning](https://latent-implicit-thinking.github.io/topics/internalized-reasoning/): Learn from worked solutions so that some or all of the reasoning can later happen without writing those steps. Training may use a separate teacher model or progressively remove written steps from the model being trained.
- [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.

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 Silently, Think Fast: Dynamic Latent Compression of LLM Reasoning Chains

Authors: Wenhui Tan, Jiaze Li, Jianzhong Ju, Zhenbo Luo, Ruihua Song, Jian Luan.

Dynamically compresses portions of a reasoning chain into latent states according to the problem and intermediate context.

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

[Original paper](https://arxiv.org/abs/2505.16552) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2505.16552/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2505.16552/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2505.16552/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2505.16552/record.json)

### Approaches

- [Internalized reasoning](https://latent-implicit-thinking.github.io/topics/internalized-reasoning/): Learn from worked solutions so that some or all of the reasoning can later happen without writing those steps. Training may use a separate teacher model or progressively remove written steps from the model being trained.
- [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.

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.


## Hybrid Latent Reasoning via Reinforcement Learning

Authors: Zhenrui Yue, Bowen Jin, Huimin Zeng, Honglei Zhuang, Zhen Qin, Jinsung Yoon, Lanyu Shang, Jiawei Han, Dong Wang.

Uses reinforcement learning to choose and train a mixture of latent and written reasoning steps.

First public: 2025-05-24.
ArXiv initial submission: 2025-05-24.

[Original paper](https://arxiv.org/abs/2505.18454) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2505.18454/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2505.18454/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2505.18454/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2505.18454/record.json)

### Approaches

- [Internalized reasoning](https://latent-implicit-thinking.github.io/topics/internalized-reasoning/): Learn from worked solutions so that some or all of the reasoning can later happen without writing those steps. Training may use a separate teacher model or progressively remove written steps from the model being trained.
- [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.

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.


## System-1.5 Reasoning: Traversal in Language and Latent Spaces with Dynamic Shortcuts

Authors: Xiaoqiang Wang, Suyuchen Wang, Yun Zhu, Bang Liu.

Learns dynamic shortcuts between language and latent states to skip portions of an otherwise explicit reasoning trajectory.

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

[Original paper](https://arxiv.org/abs/2505.18962) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2505.18962/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2505.18962/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2505.18962/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2505.18962/record.json)

### Approaches

- [Internalized reasoning](https://latent-implicit-thinking.github.io/topics/internalized-reasoning/): Learn from worked solutions so that some or all of the reasoning can later happen without writing those steps. Training may use a separate teacher model or progressively remove written steps from the model being trained.
- [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.

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: Distilling Autoregressive Reasoning to Silent Thought

Authors: Nan Jiang, Ziming Wu, De-Chuan Zhan, Fuming Lai, Shaobing Lian.

Distills an autoregressive textual reasoner into a model that carries the intermediate process through silent internal states.

First public: 2025-06-13.
ArXiv initial submission: 2025-06-13.

[Original paper](https://arxiv.org/abs/2506.11752) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2506.11752/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2506.11752/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2506.11752/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2506.11752/record.json)

### Approaches

- [Internalized reasoning](https://latent-implicit-thinking.github.io/topics/internalized-reasoning/): Learn from worked solutions so that some or all of the reasoning can later happen without writing those steps. Training may use a separate teacher model or progressively remove written steps from the model being trained.
- [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.

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.


## SIM-CoT: Supervised Implicit Chain-of-Thought

Authors: Xilin Wei, Xiaoran Liu, Yuhang Zang, Xiaoyi Dong, Yuhang Cao, Jiaqi Wang, Xipeng Qiu, Dahua Lin.

Trains continuous intermediate states with explicit supervision so reasoning can proceed without emitting a full textual trace.

First public: 2025-09-24.
ArXiv initial submission: 2025-09-24.

[Original paper](https://arxiv.org/abs/2509.20317) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2509.20317/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2509.20317/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2509.20317/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2509.20317/record.json)
[Code](https://github.com/InternLM/SIM-CoT)

### Approaches

- [Internalized reasoning](https://latent-implicit-thinking.github.io/topics/internalized-reasoning/): Learn from worked solutions so that some or all of the reasoning can later happen without writing those steps. Training may use a separate teacher model or progressively remove written steps from the model being trained.
- [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.

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.


## SemCoT: Accelerating Chain-of-Thought Reasoning through Semantically-Aligned Implicit Tokens

Authors: Yinhan He, Wendy Zheng, Yaochen Zhu, Zaiyi Zheng, Lin Su, Sriram Vasudevan, Qi Guo, Liangjie Hong, Jundong Li.

Compresses textual reasoning into semantically aligned implicit tokens intended to preserve useful intermediate computation with fewer generated steps.

First public: 2025-10-28.
ArXiv initial submission: 2025-10-28.

[Original paper](https://arxiv.org/abs/2510.24940) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2510.24940/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2510.24940/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2510.24940/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2510.24940/record.json)
[Code](https://github.com/YinhanHe123/SemCoT)

### Approaches

- [Internalized reasoning](https://latent-implicit-thinking.github.io/topics/internalized-reasoning/): Learn from worked solutions so that some or all of the reasoning can later happen without writing those steps. Training may use a separate teacher model or progressively remove written steps from the model being trained.
- [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.

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

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


## Chain Of Thought Compression: A Theoretical Analysis

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

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

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

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

### Approaches

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

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

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


## Internalized Reasoning for Long-Context Visual Document Understanding

Authors: Austin Veselka.

Trains on synthetic traces that rank document pages and extract relevant evidence, then uses low-strength model merging to internalize the trained reasoning behavior. Compares answering with and without written reasoning on long visual documents.

First public: 2026-03-31.
ArXiv initial submission: 2026-03-31.

[Original paper](https://arxiv.org/abs/2604.02371) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2604.02371/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2604.02371/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2604.02371/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2604.02371/record.json)

### Approaches

- [Internalized reasoning](https://latent-implicit-thinking.github.io/topics/internalized-reasoning/): Learn from worked solutions so that some or all of the reasoning can later happen without writing those steps. Training may use a separate teacher model or progressively remove written steps from the model being trained.

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 Agents: A Post-Training Procedure for Internalized Multi-Agent Debate

Authors: John Seon Keun Yi, Aaron Mueller, Dokyun Lee.

Post-trains a single model to internalize the computation of a multi-agent debate rather than emitting the debate as text.

First public: 2026-04-27.
ArXiv initial submission: 2026-04-27.

[Original paper](https://arxiv.org/abs/2604.24881) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2604.24881/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2604.24881/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2604.24881/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2604.24881/record.json)
[Code](https://github.com/johnsk95/latent_agents)

### Approaches

- [Internalized reasoning](https://latent-implicit-thinking.github.io/topics/internalized-reasoning/): Learn from worked solutions so that some or all of the reasoning can later happen without writing those steps. Training may use a separate teacher model or progressively remove written steps from the model being trained.

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

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


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

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

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

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

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

### Approaches

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

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

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


## Distilling Visual Reasoning into Text Space

Authors: Wenhan Yang, Nilay Naharas, Ali Payani, Baharan Mirzasoleiman.

Distills a teacher's interleaved visual and textual reasoning into a student that no longer generates intermediate visual representations. The student still writes a textual chain of thought; what is internalized is the visual portion of the reasoning.

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

[Original paper](https://arxiv.org/abs/2609.34408) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.34408/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.34408/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.34408/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.34408/record.json)

### Approaches

- [Internalized reasoning](https://latent-implicit-thinking.github.io/topics/internalized-reasoning/): Learn from worked solutions so that some or all of the reasoning can later happen without writing those steps. Training may use a separate teacher model or progressively remove written steps from the model being trained.

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.


## Large Decision Models: Repurposing Large Language Models as Single-Pass Decision Makers

Authors: Ziyi Chen, Yan Zhang, Jianhui Wei, Jianing Yin, Daoan Zhang.

Trains a language model to score labels supplied at inference in one forward pass, without generating a reasoning trace. Distills label distributions from repeated teacher reasoning and studies routing uncertain decisions back to explicit reasoning.

First public: 2026-10-11.
ArXiv initial submission: 2026-10-11.

[Original paper](https://arxiv.org/abs/2610.15501) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.15501/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.15501/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.15501/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.15501/record.json)

### Approaches

- [Internalized reasoning](https://latent-implicit-thinking.github.io/topics/internalized-reasoning/): Learn from worked solutions so that some or all of the reasoning can later happen without writing those steps. Training may use a separate teacher model or progressively remove written steps from the model being trained.

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.