AgentFlareScholar · chain-of-thought reasoning language models
Chain-of-thought research shifts from prompting tricks to long and latent reasoning
Foundational work showed that step-by-step prompts elicit reasoning in large models. Recent preprints probe what those chains encode, how to verify and distill them, and how to compress them into latent states.
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Prompting elicits step-by-step reasoning
The anchor result is chain-of-thought prompting (R6), where a few exemplars of intermediate reasoning steps improve arithmetic, commonsense and symbolic tasks. A 540B-parameter model prompted with eight exemplars reached state-of-the-art accuracy on GSM8K. Follow-ups reduce manual effort or fix failure modes. Automatic CoT prompting (R2) targets exemplar construction, and Active-Prompt (R8) uses uncertainty-based active learning to pick which questions to annotate. Plan-and-Solve (R4) addresses missing-step errors in Zero-shot-CoT by planning subtasks first. R10 adds logic to zero-shot CoT. Together these papers treat the prompt as the main lever on reasoning quality.
Sampling, structure and modality beyond a single chain
Several works move past one linear text chain. Self-consistency (R3) improves CoT reasoning by aggregating over sampled reasoning, graph-of-thought (R7) gives reasoning a graph structure, and multimodal CoT (R1) extends the idea beyond text. This line continues in recent work on voting. Length-Conditioned Majority Voting (A7) builds on the observation that longer CoTs tend to be associated with a lower probability of correctness. It adapts a length-based prior at test time using only unlabeled testing data, to weight each sampled answer. The shared theme is spending extra inference computation to make CoT answers more reliable.
Long chains and latent reasoning
The survey on long chain-of-thought (R5) frames reasoning models such as OpenAI-o1 and DeepSeek-R1 around deep reasoning, extensive exploration and feasible reflection, and distinguishes Long CoT from Short CoT. Recent preprints ask what such chains actually do. A1 measures information density across CoT steps and tests whether it predicts correctness. A2 examines whether latent chains of continuous hidden states carry real computation. A8 distills multiple textual rationales into a distribution over fixed-length latent sequences. Together they question how much of the written or latent chain drives the answer.
Verification, distillation and uncertainty for reasoning traces
As chains become training data and decision aids, work focuses on trusting them. CoTranslator (A3) turns cheaper reverse CoT responses into forward-style data for reasoning distillation. MolLean (A4) targets hallucinated claims in chemical CoT with a process-verifiable language and a Lean-based kernel. Argument Graph Uncertainty (A5) estimates confidence from the logical structure of a single reasoning trace. On the interface side, Interactive Reasoning (R9) visualizes and controls chains in a prototype for AI-assisted decision making. The common concern is checking, calibrating or steering the reasoning steps themselves.
What’s new on arXiv
Monthly submissions were 289 in Oct 2025, peaked at 307 in May 2026, and stood at 178 in Sep 2026.
A1 studies information density across CoT steps, using LP variance and a compression ratio, and tests whether it predicts correctness and can be steered. A2 uses chain deletion, content replacement and probes across twenty-one configurations to test whether latent chains affect answers.
CoTranslator (A3) learns to translate reverse CoT responses toward the distribution of verified forward responses for distillation. A7 weights majority votes with a length-conditioned prior adapted at test time. A8 distills multiple rationales into a flow over latent sequences.
MolLean (A4) grounds chemical reasoning in an explicit molecular state checked by a Lean-based kernel, with a stateful tool interface giving feedback during generation. A5 builds argument graphs from a single CoT trace to produce calibrated uncertainty for multiple choice tasks.
FACES (A6) applies structured CoT anchors for token-level credit assignment in multimodal emotional support conversation. It combines multi-source rewards with a non-compensatory gated fusion mechanism to reduce cross-dimension reward offset.
The Density of Thought: Predicting and Steering Reasoning in Large Language Models
Tanush Kalhan, Anupam Chattopadhyay, Sriram Ranga, Amritendu Mukherjee
We investigate whether variation in information density across chain-of-thought (CoT) reasoning steps predicts answer correctness and can serve as a controllable inference-time target. We prompt frozen pretrained models to solve problems via CoT and measure the density of each reasoning step with two independent metrics: LP variance (how unevenly information is distributed across steps, computed as the variance in mean per-token negative log-likelihood) and the Caveman compression ratio. We then test whether density correlates with, and can be steered to improve, answer correctness. Experiments across six model scales, two training paradigms, and 60 GSM8K problems yield four main findings. First, lower LP variance predicts correctness in supervised fine-tuned (SFT) models, but this relationship weakens with scale and reverses in reinforcement-learning (RL) distilled models. Training paradigm therefore appears more influential than model size in determining density behaviour. Second, synthetic experiments reveal an intrinsic complexity preference: models trained on uniformly distributed data learn complexity-favouring distributions 2.0 to 2.6 times more accurately than simplicity-favouring ones. Third, direct inference-time density steering reduces accuracy from 60.0% to 8.3%, indicating that natural density patterns are functionally important to reasoning. Fourth, pre-generation nudging combining hint injection with contrastive KV-cache steering improves accuracy by 13.3 percentage points, consistent across both metrics. Finally, we introduce Entropy-Gated Density Routing (EGDR), a self-supervised method using token-level Shannon entropy to gate proportional KVcache adjustments during generation, improving accuracy by 10.0 percentage points without any external guidance.
Does Latent Chain-of-Thought Actually Reason? A Single, Unifying Taxonomy for Latent Reasoning
Jingjie Qiu, Sheldon Yu, Xunyi Jiang, Jiajin Liu, Zihan Huang, Zhendong Chu, Tong Yu, Julian McAuley, Junda Wu
Latent chain-of-thought replaces written reasoning steps with continuous hidden states, giving models additional steps to compute before answering. It remains unclear what computation these steps actually perform. High task accuracy and decodable intermediate answers do not establish that a model uses its latent chain to reach an answer. We study this question across twenty-one model-task configurations covering three training recipes, three reasoning tasks, and two backbones. We combine chain deletion and content replacement with probes and trajectory analysis to test whether the chain affects the answer, what it encodes, and how its states change. On logical tasks, COCONUT often carries an answer that is already readable before the chain begins. Its states settle early, and deleting the chain leaves predictions almost unchanged. Per-step supervision produces an ordered layout of reasoning steps and can make the model depend on the chain. Yet even an ordered chain can act as a placeholder, with deletion hurting performance while content replacement leaves answers unchanged. On arithmetic tasks, all tested recipes show dependence on chain content. These results show why readable latent states alone are insufficient evidence of reasoning. We introduce a taxonomy that separates what a chain represents from how the model uses it. Seen this way, earlier reports no longer compete: placeholder tokens, collapsed superposition and step-dependent causal roles are each consistent with a different kind of chain, each obtained on a different task, training recipe or measurement. Once a study says which property it tested, whether the model uses the chain, what the chain holds, or how its state moves, claims about latent reasoning can be compared.
CoTranslator: Reverse to Forward Chain-of-Thought Translator for Reasoning Distillation
Zinan Tang, Zhuoshi Pan, Kairui Chen, Ze Yan, Shaomian Zheng, Yukun Zhang, Gang Wang, Biqing Huang
Reasoning distillation requires chain-of-thought (CoT) data with correct answers, but obtaining such data efficiently remains challenging. Forward CoT generation (FCG) followed by rejection sampling (RS) produces verified, question-only responses, yet may require many teacher calls for difficult problems. Reverse CoT generation (RCG) is cheaper because it conditions on the known answer, but access to this answer can lead to post-hoc rationalization and a mismatch with the student's answer-free inference setting. We propose CoTranslator, which learns to translate reverse CoT responses toward the distribution of verified forward responses. Trained on a small set of paired reverse and rejection-sampled forward responses, it supports large-scale generation and verification of student training data. Across six student models evaluated on six mathematics benchmarks, CoTranslator improves average accuracy over semantic suppression by up to 5.82 percentage points. For two 4B students, it retains 95.0\% of rejection sampling's average accuracy while using 35.9\% of its estimated compute. Without retraining, the same translator transfers to a new mathematics dataset, a different teacher, and STEM problems, improving average STEM accuracy by 4.88 and 4.31 percentage points for 4B and 8B students, respectively. These results show that CoTranslator offers an efficient and transferable approach to reasoning distillation.
MolLean: A Process-Verifiable Language for Chemical Reasoning
Jiatong Li, Yatao Bian
Chemical chain-of-thought can contain hallucinated structural and property claims. We thereby introduce MolLean, a process-verifiable language that grounds chemical reasoning in an explicit molecular state. A layered Lean-based kernel checks state transitions and assertions over molecular readouts, from primitive graph edits to compound transformations. Meanwhile, a typed witness protocol separates native structural checks from externally supplied measurements. We further introduce MolLean-MCP, a stateful tool interface that exposes these transitions, checks, and readouts during generation: the model receives feedback to decide its next action, and rejected actions leave the state unchanged. MolLean supports one-pass trace execution, whole-trace refinement, and interactive reasoning through MolLean-MCP. We evaluate these three modes with direct chain-of-thought on 8,800 matched examples across 12 tasks spanning molecular generation, editing, optimization, and reactions. With Qwen3.6-27B, whole-trace refinement outperforms direct chain-of-thought on all 12 tasks. MolLean-MCP complements whole-trace refinement with stepwise verification feedback, reaching better performance in reaction tasks. Together, these results highlight an executable foundation for chemical reasoning, in which explicit chemical commitments can be checked and revised rather than remaining solely in free-form explanations.
Argument Graph Uncertainty: Quantifying Uncertainty from the Logical Structure of Reasoning Chains
Simon Baur, Sumire Honda, Wojciech Samek, Jackie Ma
Reliable uncertainty estimation is essential for deploying large language models in high-stakes reasoning tasks, yet most existing approaches rely on expensive sampling strategies or shallow token-level signals that ignore the internal logical structure of model outputs. We introduce Argument Graph Uncertainty, a post-hoc framework for multiple choice question tasks, that estimates model confidence directly from the logical structure of a single chain-of-thought reasoning trace. Our method uses either a lightweight instruction-tuned model or a simple deterministic rule to segment the reasoning chain into propositional units, then applies a NLI model to infer relational edges and construct two complementary argument graphs over these segments. The resulting edge scores are aggregated into a Dirichlet posterior over answer options, whose concentration yields calibrated uncertainty estimates reflecting both local step-to-step coherence and global logical consistency across the reasoning trace. Evaluated on GPQA, MMLU-Pro and TruthfulQA, our method consistently surpasses token-based and consistency-based uncertainty baselines across multiple reasoning models. We further demonstrate through extensive combination analyses that argument graph uncertainty captures an orthogonal signal to existing approaches, making it a complementary component in uncertainty ensembles. Crucially, our framework requires no additional calls to the evaluated model and relies entirely on small, efficient auxiliary models, producing fully interpretable, per-node uncertainty attributions at low computational cost.
FACES: Fine-grained Gated Semantic Alignment for Multimodal Emotional Support Conversation
Hang Ren, Peidong Wang, Yichen Gao, Wen Zhang, Jiayang Yu, Xiaocui Yang, Shi Feng
In recent years, with advances in multimodal interaction technologies and the growing demand for intelligent emotional support, Multimodal Emotional Support Conversation (MESC) has emerged as an important task. However, existing systems still suffer from shallow responses and inappropriate support strategies due to weak semantic feedback, cross-dimension reward compensation, and coarse reasoning supervision. To address these challenges, we propose FACES, a fine-grained gated semantic alignment framework for MESC. Specifically, FACES integrates multi-source rewards to construct multidimensional semantic and functional alignment signals, employs a non-compensatory gated fusion mechanism to reduce cross-dimension reward offset, and leverages structured Chain-of-Thought (CoT) anchors to perform token-level credit assignment. Under a controlled response-length protocol, FACES improves the average MLLM-based evaluation score from 3.61 to 4.04 and achieves an 80.22% pairwise win rate over SOTA. Human evaluation under the same protocol yields a 75.3% preference rate. Results on three external datasets further support transferability. The code and dataset are available at https://github.com/OCT-ARR/arr.
Frustratingly Easy Majority Voting Using Length Conditioning
Fiorenzo Parascandolo, Enver Sangineto, Xiaoyi Yu, Wenhui Tan, Jipei He, Ruihua Song, Rita Cucchiara
Majority Voting (MV) is a simple and widely used strategy which improves the reasoning accuracy of Large Language Models (LLMs) by allocating additional inference-time computation. Specifically, in MV multiple Chain-of-Thoughts (CoTs) are independently sampled and the most frequent final answer is selected. In this work, we propose Length-Conditioned Majority Voting (LCMV), a Test-Time Training approach which improves MV leveraging an empirical observation that has recently been established in several studies: longer CoTs tend to be associated with a lower probability of correctness. We formulate this inductive bias as a length-conditioned prior probability, which is modeled by a simple logistic function. Moreover, we adapt this prior at test time using only unlabeled testing data and without fine-tuning the LLM. Finally, the adapted prior is used to weight the vote of each sampled answer. Extensive experiments across multiple LLMs and reasoning benchmarks show that LCMV consistently improves over both standard MV and existing length-based and confidence-based aggregation strategies, while retaining the simplicity and model-agnostic nature of MV. Our code is available at: https://github.com/aimagelab/LCMV.
Rationale Distribution Distillation via Flow Matching for Distributional Continuous Latent Reasoning
Mingyeong Kim, Gyusang Cho, Juho Lee, Giung Nam
Sampling multiple chain-of-thought rationales from a language model can uncover correct solutions missed by a single attempt. However, these rationales are typically lengthy, making repeated autoregressive generation costly. Continuous latent reasoning offers a compact alternative, but point-valued methods condition repeated answer sampling on a single rationale, which can limit exploration of diverse paths and answer coverage. We thus propose rationale distribution distillation (RDD), training a conditional flow over fixed-length latent sequences by distilling from multiple textual reasoning paths. Furthermore, we expand the distillation targets through within-query mixup, interpolating between complete latent rationales for the same query. The flow nonautoregressively generates the entire latent sequence, and a frozen language model autoregressively decodes answers from sampled rationale contexts. Empirically, the resulting distributional reasoner achieves higher answer coverage than the evaluated point-valued latent reasoning baselines, particularly on advanced mathematical tasks.
Foundational papers
- 2022
- 2022
- 2022
- 2023Multimodal chain-of-thought reasoning in language models1,354 citations
- 2023
- 2023
- 2024
- 2024
- 2026-10
Multimodal chain-of-thought reasoning in language models
Z Zhang, A Zhang, M Li, H Zhao, G Karypis et al.
… Large language models (LLMs) have shown impressive performance on complex reasoning by leveraging chain-of-thought (CoT) prompting to generate intermediate reasoning chains …
Automatic chain of thought prompting in large language models
Z Zhang, A Zhang, M Li, A Smola
… This section reviews two lines of research that form the basis of this work: chain-of-thought (CoT) prompting for multi-step reasoning and in-context learning for inducing LLMs to learn …
Self-consistency improves chain of thought reasoning in language models
X Wang, J Wei, D Schuurmans, Q Le, E Chi et al.
… language model with chain-of-thought prompting, then instead of greedily decoding the optimal reasoning … first sample from the language model’s decoder to generate a diverse set of …
Plan-and-solve prompting: Improving zero-shot chain-of-thought reasoning by large language models
L Wang, W Xu, Y Lan, Z Hu, Y Lan et al.
Contribution. Proposes Plan-and-Solve prompting, which first devises a plan dividing the task into subtasks and then executes them, targeting missing-step errors in Zero-shot-CoT; it is extended to address calculation errors.
Towards reasoning era: A survey of long chain-of-thought for reasoning large language models
Q Chen, L Qin, J Liu, D Peng, J Guan, P Wang et al.
Contribution. Surveys long chain-of-thought for reasoning LLMs, separating it from Short CoT with a new taxonomy and covering deep reasoning, extensive exploration, reflection, overthinking and inference-time scaling.
Chain-of-thought prompting elicits reasoning in large language models
J Wei, X Wang, D Schuurmans et al.
Contribution. Shows that chain-of-thought prompting with a few exemplars elicits reasoning in large models; a 540B-parameter model with eight exemplars reached state-of-the-art accuracy on GSM8K.
Beyond chain-of-thought, effective graph-of-thought reasoning in language models
Y Yao, Z Li, H Zhao
… , which simulates the deductive process in human reasoning. We have used T5 (Raffel et al.… 2020a) pre-trained language model as our backbone model. GoT is encoded with a graph …
Active prompting with chain-of-thought for large language models
S Diao, P Wang, Y Lin, R Pan, X Liu et al.
Contribution. Introduces Active-Prompt, which uses uncertainty-based active learning to choose which task-specific questions to annotate with CoT exemplars, instead of relying on a fixed human-annotated set.
Interactive reasoning: Visualizing and controlling chain-of-thought reasoning in large language models
RY Pang, KJK Feng, S Feng, C Li, W Shi et al.
Contribution. Introduces Interactive Reasoning, an interaction design that visualizes chain-of-thought, implemented in Hippo, a prototype for AI-assisted decision making.
Enhancing zero-shot chain-of-thought reasoning in large language models through logic
X Zhao, M Li, W Lu, C Weber, JH Lee et al.
… possess extensive knowledge, their reasoning often fails to … models sometimes show hallucinations as their reasoning … -shot chain-of-thought reasoning ability of large language …
Open problems
- Whether latent reasoning chains actually compute the answer, since accurate outputs and decodable intermediate answers do not show the chain is used.
- Information density predicts correctness in some models, but the relationship weakens with scale and reverses in RL-distilled models.
- Obtaining verified CoT training data cheaply without post-hoc rationalization from answer-conditioned generation.
- Hallucinated claims inside chains, for example in chemistry, call for reasoning steps that can be checked during generation.
FAQ
What is chain-of-thought prompting?
It is a method where a language model generates a series of intermediate reasoning steps, often guided by a few exemplars in the prompt. It improves performance on arithmetic, commonsense and symbolic reasoning tasks (R6).
How does long CoT differ from short CoT?
The long chain-of-thought survey (R5) distinguishes them and describes Long CoT by deep reasoning, extensive exploration and feasible reflection, as seen in models such as OpenAI-o1 and DeepSeek-R1.
What is latent chain-of-thought?
It replaces written reasoning steps with continuous hidden states, giving the model extra computation steps before answering. Recent work (A2) tests whether those steps actually influence the final answer.
How this page is made. Foundational papers and citation counts come from academic search via the AISA Scholar API, with abstracts read from each paper’s page; recent preprints and monthly volumes come from the public arXiv API (metadata CC0). The digest is written by a language model from those abstracts only — every theme links the papers it draws on, and figures not in the inputs are removed.
Sources & citations
- Multimodal chain-of-thought reasoning in language models 1,354 citations
- Automatic chain of thought prompting in large language models 1,975 citations
- Self-consistency improves chain of thought reasoning in language models 6,086 citations
- Plan-and-solve prompting: Improving zero-shot chain-of-thought reasoning by large language models 797 citations
- Towards reasoning era: A survey of long chain-of-thought for reasoning large language models 609 citations
- Chain-of-thought prompting elicits reasoning in large language models 40,175 citations
- Beyond chain-of-thought, effective graph-of-thought reasoning in language models 204 citations
- Active prompting with chain-of-thought for large language models 452 citations
- Interactive reasoning: Visualizing and controlling chain-of-thought reasoning in large language models 36 citations
- Enhancing zero-shot chain-of-thought reasoning in large language models through logic 113 citations
- The Density of Thought: Predicting and Steering Reasoning in Large Language Models arXiv · 2026-10-15
- Does Latent Chain-of-Thought Actually Reason? A Single, Unifying Taxonomy for Latent Reasoning arXiv · 2026-10-15
- CoTranslator: Reverse to Forward Chain-of-Thought Translator for Reasoning Distillation arXiv · 2026-10-14
- MolLean: A Process-Verifiable Language for Chemical Reasoning arXiv · 2026-10-14
- Argument Graph Uncertainty: Quantifying Uncertainty from the Logical Structure of Reasoning Chains arXiv · 2026-10-14
- FACES: Fine-grained Gated Semantic Alignment for Multimodal Emotional Support Conversation arXiv · 2026-10-14
- Frustratingly Easy Majority Voting Using Length Conditioning arXiv · 2026-10-14
- Rationale Distribution Distillation via Flow Matching for Distributional Continuous Latent Reasoning arXiv · 2026-10-14