# Continuous-state reasoning

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.

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

For example: A model feeds its current hidden-state vector back as the next input. It repeats this several times before returning to text to produce an answer.

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

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

## How the methods connect and differ

**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/)

**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/)

**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/)

## Papers — oldest first

## Expediting and Elevating Large Language Model Reasoning via Hidden Chain-of-Thought Decoding

Authors: Tianqiao Liu, Zui Chen, Zitao Liu, Mi Tian, Weiqi Luo.

Trains one model to compress written reasoning into special-token representations, then trains another to answer using those representations.

First public: 2024-09-13.
ArXiv initial submission: 2024-09-13.

[Original paper](https://arxiv.org/abs/2409.08561) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2409.08561/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2409.08561/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2409.08561/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2409.08561/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.

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

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


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

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

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

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

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

### Approaches

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

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

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


## Training Large Language Models to Reason in a Continuous Latent Space

Authors: Shibo Hao, Sainbayar Sukhbaatar, DiJia Su, Xian Li, Zhiting Hu, Jason Weston, Yuandong Tian.

Feeds a model's last hidden state back as its next input, enabling recurrent reasoning in continuous space before returning to language.

First public: 2024-12-09.
ArXiv initial submission: 2024-12-09.

[Original paper](https://arxiv.org/abs/2412.06769) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2412.06769/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2412.06769/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2412.06769/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2412.06769/record.json)
[Code](https://github.com/facebookresearch/coconut)

### Method comparisons

**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/)

**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/)

**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

Training Large Language Models to Reason in a Continuous Latent Space. Shibo Hao, Sainbayar Sukhbaatar, DiJia Su, Xian Li, Zhiting Hu, Jason E Weston, Yuandong Tian. Conference on Language Modeling (COLM 2025), 2025.
[Publication](https://openreview.net/forum?id=Itxz7S4Ip3) · [BibTeX](https://latent-implicit-thinking.github.io/papers/2412.06769/publication.bib) · [CSL-JSON](https://latent-implicit-thinking.github.io/papers/2412.06769/publication.csl.json)
Metadata checked 2026-10-18 against [the publication record](https://colmweb.org/2025/AcceptedPapers.html).

### 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.

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.


## Compressed Chain of Thought: Efficient Reasoning Through Dense Representations

Authors: Jeffrey Cheng, Benjamin Van Durme.

Compresses verbose reasoning traces into shorter dense representations and evaluates the trade-off between reasoning quality and generated length.

First public: 2024-12-17.
ArXiv initial submission: 2024-12-17.

[Original paper](https://arxiv.org/abs/2412.13171) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2412.13171/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2412.13171/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2412.13171/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2412.13171/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.

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.


## Token Assorted: Mixing Latent and Text Tokens for Improved Language Model Reasoning

Authors: DiJia Su, Hanlin Zhu, Yingchen Xu, Jiantao Jiao, Yuandong Tian, Qinqing Zheng.

Interleaves latent and textual tokens so a model can combine compressed internal computation with readable reasoning steps.

First public: 2025-02-05.
ArXiv initial submission: 2025-02-05.

[Original paper](https://arxiv.org/abs/2502.03275) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2502.03275/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2502.03275/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2502.03275/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2502.03275/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.
- [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.


## LLM Pretraining with Continuous Concepts

Authors: Jihoon Tack, Jack Lanchantin, Jane Yu, Andrew Cohen, Ilia Kulikov, Janice Lan, Shibo Hao, Yuandong Tian, Jason Weston, Xian Li.

Interleaves continuous concept representations with text during pretraining so language models learn to compute over concepts as well as tokens.

First public: 2025-02-12.
ArXiv initial submission: 2025-02-12.

[Original paper](https://arxiv.org/abs/2502.08524) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2502.08524/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2502.08524/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2502.08524/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2502.08524/record.json)
[Code](https://github.com/facebookresearch/RAM/tree/main/projects/cocomix)

### 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.

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.


## Seek in the Dark: Reasoning via Test-Time Instance-Level Policy Gradient in Latent Space

Authors: Hengli Li, Chenxi Li, Tong Wu, Xuekai Zhu, Yuxuan Wang, Zhaoxin Yu, Eric Hanchen Jiang, Song-Chun Zhu, Zixia Jia, Ying Nian Wu, Zilong Zheng.

Optimizes latent states for individual problems at test time using policy gradients rather than searching over written reasoning traces.

First public: 2025-05-19.
ArXiv initial submission: 2025-05-19.

[Original paper](https://arxiv.org/abs/2505.13308) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2505.13308/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2505.13308/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2505.13308/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2505.13308/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.

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.


## Text Generation Beyond Discrete Token Sampling

Authors: Yufan Zhuang, Liyuan Liu, Chandan Singh, Jingbo Shang, Jianfeng Gao.

Feeds posterior expectations back into a language model so intermediate generation can remain continuous instead of sampling discrete tokens.

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

[Original paper](https://arxiv.org/abs/2505.14827) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2505.14827/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2505.14827/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2505.14827/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2505.14827/record.json)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Alternative generation methods](https://latent-implicit-thinking.github.io/topics/alternative-reasoning-schedules/): Change how intermediate steps are generated, revised, or searched—for example, by refining several steps in parallel. These are related approaches: some still produce written chains of thought.

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.


## 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.


## Continuous Chain of Thought Enables Parallel Exploration and Reasoning

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

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

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

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

### Approaches

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

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

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


## 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.


## Machine Mental Imagery: Empower Multimodal Reasoning with Latent Visual Tokens

Authors: Zeyuan Yang, Xueyang Yu, Delin Chen, Maohao Shen, Chuang Gan.

Uses latent visual tokens as an internal imagery channel for multimodal reasoning without rendering every intermediate state.

First public: 2025-06-20.
ArXiv initial submission: 2025-06-20.

[Original paper](https://arxiv.org/abs/2506.17218) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2506.17218/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2506.17218/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2506.17218/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2506.17218/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.
- [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.


## Parallel Continuous Chain-of-Thought with Jacobi Iteration

Authors: Haoyi Wu, Zhihao Teng, Kewei Tu.

Applies Jacobi-style iteration to update continuous reasoning states in parallel rather than strictly one step at a time.

First public: 2025-06-23.
ArXiv initial submission: 2025-06-23.

[Original paper](https://arxiv.org/abs/2506.18582) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2506.18582/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2506.18582/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2506.18582/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2506.18582/record.json)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Alternative generation methods](https://latent-implicit-thinking.github.io/topics/alternative-reasoning-schedules/): Change how intermediate steps are generated, revised, or searched—for example, by refining several steps in parallel. These are related approaches: some still produce written chains of thought.

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.


## SynAdapt: Learning Adaptive Reasoning in Large Language Models via Synthetic Continuous Chain-of-Thought

Authors: Jianwei Wang, Ziming Wu, Fuming Lai, Shaobing Lian, Ziqian Zeng.

Uses synthetic continuous reasoning trajectories to train language models to allocate internal reasoning adaptively.

First public: 2025-08-01.
ArXiv initial submission: 2025-08-01.

[Original paper](https://arxiv.org/abs/2508.00574) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2508.00574/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2508.00574/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2508.00574/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2508.00574/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.

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

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


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

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

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

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

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

### Approaches

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

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

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


## 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.


## LaDiR: Latent Diffusion Enhances LLMs for Text Reasoning

Authors: Haoqiang Kang, Yizhe Zhang, Nikki Lijing Kuang, Nicklas Majamaki, Navdeep Jaitly, Yi-An Ma, Lianhui Qin.

Uses a variational autoencoder to compress textual reasoning steps into blocks of continuous states. A diffusion model repeatedly revises each block before generating the next, then produces a textual answer; diversity guidance encourages alternative reasoning trajectories.

First public: 2025-10-06.
ArXiv initial submission: 2025-10-06.

[Original paper](https://arxiv.org/abs/2510.04573) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2510.04573/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2510.04573/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2510.04573/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2510.04573/record.json)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Alternative generation methods](https://latent-implicit-thinking.github.io/topics/alternative-reasoning-schedules/): Change how intermediate steps are generated, revised, or searched—for example, by refining several steps in parallel. These are related approaches: some still produce written chains of thought.

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.


## LLM Latent Reasoning as Chain of Superposition

Authors: Jingcheng Deng, Liang Pang, Zihao Wei, Shicheng Xu, Zenghao Duan, Kun Xu, Yang Song, Huawei Shen, Xueqi Cheng.

Models latent reasoning as a sequence of superposed token distributions and trains the process with supervised fine-tuning.

First public: 2025-10-17.
ArXiv initial submission: 2025-10-17.

[Original paper](https://arxiv.org/abs/2510.15522) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2510.15522/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2510.15522/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2510.15522/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2510.15522/record.json)
[Code](https://github.com/DJC-GO-SOLO/Latent-SFT)

### 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.

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.


## Learning When to Stop: Adaptive Latent Reasoning via Reinforcement Learning

Authors: Alex Ning, Yen-Ling Kuo, Gabe Gomes.

Learns a stopping policy for continuous latent reasoning so the model can allocate a variable number of internal steps.

First public: 2025-11-26.
ArXiv initial submission: 2025-11-26.

[Original paper](https://arxiv.org/abs/2511.21581) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2511.21581/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2511.21581/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2511.21581/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2511.21581/record.json)
[Code](https://github.com/apning/adaptive-latent-reasoning)

### 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.

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

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


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

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

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

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

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

### Approaches

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

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

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


## Latent Chain-of-Thought as Planning: Decoupling Reasoning from Verbalization

Authors: Jiecong Wang, Hao Peng, Zhanyi Wang, Chunyang Liu, Guanlin Wu.

Separates an internal planning process from verbalization and studies whether the latent plan supports effective downstream reasoning.

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

[Original paper](https://arxiv.org/abs/2601.21358) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2601.21358/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2601.21358/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2601.21358/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2601.21358/record.json)
[Code](https://github.com/yunsaijc/PLaT)

### 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.

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 Imitation: Reinforcement Learning for Active Latent Planning

Authors: Zhi Zheng, Wee Sun Lee.

Uses reinforcement learning to train an active latent-planning process rather than only imitating supervised reasoning traces.

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

[Original paper](https://arxiv.org/abs/2601.21598) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2601.21598/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2601.21598/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2601.21598/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2601.21598/record.json)
[Code](https://github.com/zz1358m/ATP-Latent-master)

### 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.

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

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


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

Authors: Jia Liang, Liangming Pan.

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

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

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

### Approaches

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

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

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


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

Authors: Jiaxuan Zou, Yaozhong Xiong, Yong Liu.

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

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

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

### Approaches

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

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

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


## Latent Reasoning with Supervised Thinking States

Authors: Ido Amos, Avi Caciularu, Mor Geva, Amir Globerson, Jonathan Herzig, Lior Shani, Idan Szpektor.

Supervises intermediate thinking states that bridge textual reasoning traces and latent computation.

First public: 2026-02-09.
ArXiv initial submission: 2026-02-09.

[Original paper](https://arxiv.org/abs/2602.08332) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2602.08332/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2602.08332/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2602.08332/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2602.08332/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.
- [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.


## ThinkRouter: Efficient Reasoning via Routing Thinking between Latent and Discrete Spaces

Authors: Xin Xu, Tong Yu, Xiang Chen, Haoliang Wang, Julian McAuley, Saayan Mitra.

Routes intermediate computation between latent and discrete representations to trade off reasoning quality, readability, and token cost.

First public: 2026-02-12.
ArXiv initial submission: 2026-02-12.

[Original paper](https://arxiv.org/abs/2602.11683) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2602.11683/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2602.11683/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2602.11683/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2602.11683/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.
- [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.


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

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

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

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

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

### Approaches

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

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

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


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

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

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

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

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

### Approaches

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

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

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


## Demystifying Hidden-State Recurrence: Switchable Latent Reasoning with On-Policy Reinforcement Learning

Authors: Jiayu Yang, Chao Chen, Shengen Wu, Yinhong Liu, Yuxuan Fan, Lujundong Li, Songning Lai, Chengwei Qin, Zhijiang Guo.

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

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

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

### Approaches

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

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

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


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

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

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

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

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

### Approaches

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

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

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


## 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.


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

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

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

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

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

### Approaches

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

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

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


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

Authors: Hengyu Jin, Shu Yang, Di Wang.

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

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

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

### Approaches

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

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

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


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

Authors: Varun Yerram, He He, Eunsol Choi.

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

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

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

### Approaches

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

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

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


## GradCuit: Credit-Assigned Gradient Flow Enables Robust and Interpretable Test-Time Latent Reasoning

Authors: Zhaoxin Yu, Qi Shen, Hengli Li, Zhaowei Zhang, Song-Chun Zhu, Chi Zhang, Zilong Zheng.

At test time, adjusts extra hidden states inside the transformer using feedback on generated answers, while keeping the model’s weights fixed.

First public: 2026-08-03.
ArXiv initial submission: 2026-08-03.

[Original paper](https://arxiv.org/abs/2608.02585) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2608.02585/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2608.02585/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2608.02585/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2608.02585/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.

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

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


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

Authors: Pedro Ferreira, Wilker Aziz, Ivan Titov.

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

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

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

### Approaches

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

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

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


## 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.


## Structural Process Supervision for Latent Chain-of-Thought Reasoning

Authors: Yiqi Li, Xu Chen, Chen Ju, Jiangchao Yao, Zhaoyang Li, Jinsong Lan, Xiaoyong Zhu, Yu Wang.

Aligns continuous thoughts with written reasoning through shared, learnable prototypes, allowing several text steps to supervise several latent states. A positional alignment constraint is gradually relaxed during training.

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

[Original paper](https://arxiv.org/abs/2609.09928) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.09928/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.09928/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.09928/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.09928/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.

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.


## Register Tokens for Bounded-State Reasoning in Diffusion Language Models

Authors: Albert Ge, Chandan Singh, Yufan Zhuang, Xiaodong Liu, Jianfeng Gao, Frederic Sala.

Trains a diffusion language model to carry a fixed number of continuous register states between generated chunks. The model still writes text within each chunk, but clears earlier text and continues from the prompt and retained registers.

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

[Original paper](https://arxiv.org/abs/2609.16372) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.16372/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.16372/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.16372/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.16372/record.json)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Alternative generation methods](https://latent-implicit-thinking.github.io/topics/alternative-reasoning-schedules/): Change how intermediate steps are generated, revised, or searched—for example, by refining several steps in parallel. These are related approaches: some still produce written chains of thought.

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.


## Learn Your Own Thoughts: Abstract Token Curriculum

Authors: Khashayar Gatmiry, Avrajit Ghosh, Parsa Mirtaheri, Jason D. Lee, Nika Haghtalab, Emmanuel Abbe, Peter Bartlett.

Trains on progressively harder problems so that a model learns continuous intermediate thoughts without explicit reasoning-step supervision. Analyzes parity learning theoretically and tests graph reachability and arithmetic.

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

[Original paper](https://arxiv.org/abs/2609.19717) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.19717/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.19717/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.19717/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.19717/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.

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.


## Uni-LaDiR: Latent Diffusion Unifies Multimodal Reasoning

Authors: Haoqiang Kang, Yizhe Zhang, Nikki Lijing Kuang, Jiatao Gu, Yian Ma, Lianhui Qin.

Encodes teacher reasoning steps from text, images, point clouds, and robot states into a shared continuous representation. A jointly trained diffusion reasoner generates these states at inference, evaluated on visual question answering and robotic manipulation.

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

[Original paper](https://arxiv.org/abs/2609.19878) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.19878/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.19878/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.19878/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.19878/record.json)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Alternative generation methods](https://latent-implicit-thinking.github.io/topics/alternative-reasoning-schedules/): Change how intermediate steps are generated, revised, or searched—for example, by refining several steps in parallel. These are related approaches: some still produce written chains of thought.

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.


## Schema-Anchored Latent Reasoning for Semantic Parsing-Based Knowledge Base Question Answering

Authors: Guangze Gao, Zixuan Li, Sikui Zhang, Chunfeng Yuan, Wenjuan Li, Bing Li, Xiaolong Jin, Weiming Hu.

Aligns continuous thoughts with a codebook of knowledge-base relations and classes, using schema traces derived from correct logical forms. Feeds the aligned codes into later reasoning steps before generating an executable query.

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

[Original paper](https://arxiv.org/abs/2609.20398) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.20398/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.20398/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.20398/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.20398/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.

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.


## CaLR: Causal Latent Revision for Robust Diffusion Reasoning

Authors: Wei Cai, Jian Zhao, Yuchen Yuan, Xuelong Li.

Uses an expert-derived causal dependency matrix to guide gradient-based revision of diffusion reasoning states. The aim is to preserve logical dependencies while revising several intermediate positions during parallel generation.

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

[Original paper](https://arxiv.org/abs/2609.20981) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.20981/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.20981/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.20981/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.20981/record.json)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Alternative generation methods](https://latent-implicit-thinking.github.io/topics/alternative-reasoning-schedules/): Change how intermediate steps are generated, revised, or searched—for example, by refining several steps in parallel. These are related approaches: some still produce written chains of thought.

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

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


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

Authors: Gaoxiang Huang, Lei Qi.

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

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

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

### Approaches

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

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

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


## ELF-REG: Scaling Continuous Diffusion Language Models to Reasoning Tasks

Authors: Zeyu Michael Li, William Xingxu Chen, Bingshuo Qian, Jiayin Liu, Xiang Cheng.

Adapts continuous diffusion to mathematics and code using intermediate-feature supervision and a global representation from a frozen autoregressive teacher. It denoises continuous response representations and decodes all response tokens only at the end.

First public: 2026-09-24.
ArXiv initial submission: 2026-09-24.

[Original paper](https://arxiv.org/abs/2609.29102) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.29102/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.29102/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.29102/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.29102/record.json)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Alternative generation methods](https://latent-implicit-thinking.github.io/topics/alternative-reasoning-schedules/): Change how intermediate steps are generated, revised, or searched—for example, by refining several steps in parallel. These are related approaches: some still produce written chains of thought.

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.


## Task-Oriented Key-Layer KV Communication for Efficient Latent Multi-Agent Collaboration

Authors: Dongsen Zhang, Peipei Li, Zekun Li, Wenjun Xu.

Lets agents perform hidden-state reasoning and pass working memory through the key-value cache of one selected transformer layer. Reuses that layer as the entry point for subsequent reasoning updates, avoiding earlier layers and decoding only the final agent's response into text.

First public: 2026-09-24.
ArXiv initial submission: 2026-09-24.

[Original paper](https://arxiv.org/abs/2610.08820) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.08820/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.08820/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.08820/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.08820/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.

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.


## Next Thoughts Are Distributions: Generative Autoregressive Reasoning in the Latent Space

Authors: Yang Li, Yi Wang, Shiyuan Huang, Yang Liu, Hao Wang, Chengzhi Mao.

Adds a diffusion head that samples the next continuous thought from a distribution rather than predicting one fixed vector. Feeds each sampled thought back into an autoregressive reasoner, supporting variable-length latent traces and multiple reasoning paths.

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

[Original paper](https://arxiv.org/abs/2609.33271) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.33271/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.33271/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.33271/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.33271/record.json)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Alternative generation methods](https://latent-implicit-thinking.github.io/topics/alternative-reasoning-schedules/): Change how intermediate steps are generated, revised, or searched—for example, by refining several steps in parallel. These are related approaches: some still produce written chains of thought.

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.


## VaME: Exploring Variational Latent Reasoning for Multimodal Embeddings

Authors: Peixi Wu, Mingzhou Jiang, Feipeng Ma, Biao Yang, Yunhao Zhou, Wei Yuan, Bosong Chai, Huizu Lin, Jie Chen, Zhangchi Hu, Fan Yang, Wenwu Ou, Hebei Li, Xiaoyan Sun.

Learns a distribution over continuous reasoning trajectories before producing a retrieval embedding. A lightweight decoder provides reconstruction supervision and a semantic reward for reinforcement learning, evaluated on image, video, and visual-document retrieval.

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

[Original paper](https://arxiv.org/abs/2609.33402) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.33402/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.33402/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.33402/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.33402/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.

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 Continuous Latent Diffusion

Authors: Xiang Cheng.

CEDR learns compact representations from several teacher layers, denoises them at different rates, and trains a smaller prompt encoder to replace the teacher at inference. It generates complete mathematical and coding solutions through continuous refinement before text decoding.

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

[Original paper](https://arxiv.org/abs/2609.35694) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.35694/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.35694/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.35694/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.35694/record.json)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Alternative generation methods](https://latent-implicit-thinking.github.io/topics/alternative-reasoning-schedules/): Change how intermediate steps are generated, revised, or searched—for example, by refining several steps in parallel. These are related approaches: some still produce written chains of thought.

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.


## 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.


## Hierarchical Continuous Diffusion Language Models

Authors: Hui Ren, Zihan Li, Chang Liu, Huidong Liu, Alexander Schwing.

Keeps a continuous state throughout denoising while reading out tokens at each step and feeding them back into the next state update. Tests whether this coupling preserves dependencies during parallel generation on Sudoku, Countdown, and language modeling.

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

[Original paper](https://arxiv.org/abs/2610.02193) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.02193/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.02193/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.02193/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.02193/record.json)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Alternative generation methods](https://latent-implicit-thinking.github.io/topics/alternative-reasoning-schedules/): Change how intermediate steps are generated, revised, or searched—for example, by refining several steps in parallel. These are related approaches: some still produce written chains of thought.

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 Language Continuous Diffusion Models

Authors: Zhihan Yang, Wei Guo, Jean-Marie Lemercier, Simon Welker, Yonggan Fu, Mohammad Mahdi Kamani, Sajad Norouzi, Julius Berner, Tomas Geffner, Karsten Kreis, Yongxin Chen, Molei Tao, John Thickstun, Pavlo Molchanov, Ante Jukić, Arash Vahdat, Morteza Mardani.

Sigma denoises learned continuous token embeddings in blocks, starting from autoregressive pretrained weights. Studies how guidance and temperature affect mathematical reasoning, coding, output diversity, and performance when fewer refinement steps are used.

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

[Original paper](https://arxiv.org/abs/2610.02665) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.02665/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.02665/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.02665/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.02665/record.json)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Alternative generation methods](https://latent-implicit-thinking.github.io/topics/alternative-reasoning-schedules/): Change how intermediate steps are generated, revised, or searched—for example, by refining several steps in parallel. These are related approaches: some still produce written chains of thought.

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.


## What Matters for Latent Reasoning with Flow Matching

Authors: Yassine Ouali, Adrian Bulat, Georgios Tzimiropoulos.

Compresses symbolic reasoning into latent codes and trains a flow model to refine a block of noise into a thought before decoding the answer. Studies training choices, self-training on verified thoughts, and tests of whether the answer actually uses those thoughts.

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

[Original paper](https://arxiv.org/abs/2610.06666) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.06666/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.06666/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.06666/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.06666/record.json)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Alternative generation methods](https://latent-implicit-thinking.github.io/topics/alternative-reasoning-schedules/): Change how intermediate steps are generated, revised, or searched—for example, by refining several steps in parallel. These are related approaches: some still produce written chains of thought.

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.


## CALR: Continuous Anchored Latent Reasoning via Render-of-Thought Compression

Authors: Zhaoyang Wei, Bowen Jiang, Yanchao Hao, Wenchao Ding, Zheng Wei, Shaocheng Wu, Zhenjun Han, Jianbin Jiao.

Compresses images of written derivations into continuous states, training both the answers they support and the reasoning that can be recovered from them. Gradually shifts from generating latent blocks in parallel to generating them in sequence.

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

[Original paper](https://arxiv.org/abs/2610.07175) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.07175/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.07175/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.07175/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.07175/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.

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.


## Noise Your Prompt: Noising Conditioning Tokens in Continuous Diffusion Language Models

Authors: Justin Jung.

Adds noise to conditioning tokens during training instead of keeping the prompt clean. Tests improvements in Sudoku and N-Queens generalization and solution diversity, while reporting that the gains do not transfer to every language-generation task.

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

[Original paper](https://arxiv.org/abs/2610.09145) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.09145/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.09145/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.09145/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.09145/record.json)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Alternative generation methods](https://latent-implicit-thinking.github.io/topics/alternative-reasoning-schedules/): Change how intermediate steps are generated, revised, or searched—for example, by refining several steps in parallel. These are related approaches: some still produce written chains of thought.

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

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


## Efficient Reasoning with Flow Language Models

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

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

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

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

### Approaches

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

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

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


## 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.


## Dynamic K-Head: Difficulty-Supervised Budget Selection for Continuous Latent Reasoning

Authors: Ying Li, Yuqi Chen, Sixuan Li, Yunfeng Cai.

Predicts from the question how many continuous reasoning updates to perform. Evaluates total cost including latent updates, special tokens, and any written continuation rather than counting latent steps alone.

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

[Original paper](https://arxiv.org/abs/2610.17679) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.17679/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.17679/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.17679/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.17679/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.

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.


## Backpropagating Verifier Rewards Through Continuous Flow Language Models

Authors: Xu Han, Jiajing Hu, Li-Ping Liu.

Trains a critic to score intermediate continuous token representations, enabling reward gradients through the denoising trajectory before final discrete decoding. Evaluates this post-training approach on four reasoning tasks.

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

[Original paper](https://arxiv.org/abs/2610.19080) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.19080/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.19080/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.19080/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.19080/record.json)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Alternative generation methods](https://latent-implicit-thinking.github.io/topics/alternative-reasoning-schedules/): Change how intermediate steps are generated, revised, or searched—for example, by refining several steps in parallel. These are related approaches: some still produce written chains of thought.

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.


## INTACT: Inducing Latent Reasoning on a Frozen Backbone

Authors: Kutay Tire, Atula Tejaswi, Haris Vikalo, Sujay Sanghavi.

Trains a small encoder to turn a frozen model's hidden states into successive blocks of continuous thoughts. After this latent prefix, the frozen model writes its remaining reasoning and answer; the encoder learns through distillation and answer-correctness rewards.

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

[Original paper](https://arxiv.org/abs/2610.19568) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.19568/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.19568/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.19568/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.19568/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.

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.


## Rationale Distribution Distillation via Flow Matching for Distributional Continuous Latent Reasoning

Authors: Mingyeong Kim, Gyusang Cho, Juho Lee, Giung Nam.

Distills multiple written reasoning paths for each question into a flow model over fixed-length latent sequences, including mixtures of complete rationales. Generates all latent slots together, then uses a frozen language model to decode answers from sampled rationale contexts.

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

[Original paper](https://arxiv.org/abs/2610.19871) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.19871/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.19871/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.19871/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.19871/record.json)

### Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Alternative generation methods](https://latent-implicit-thinking.github.io/topics/alternative-reasoning-schedules/): Change how intermediate steps are generated, revised, or searched—for example, by refining several steps in parallel. These are related approaches: some still produce written chains of thought.

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

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


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

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

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

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

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

### Approaches

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

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

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