CoT Reasoning

CoT: Chain-of-Thought

Overview

Chain-of-thought reasoning studies how language models break complex problems into steps, use intermediate information, and produce answers that can be checked or acted on. Approaches include prompting models to show their work, training on reasoning traces with supervised learning or reinforcement learning, and using structured methods such as code, symbolic rules, trees, or latent reasoning states. Researchers test these methods on tasks including mathematics, multi-hop question answering, coding, clinical decisions, and visual or spatial understanding, while developing verification and adaptive-compute methods to control cost. A central tension is that longer or more detailed traces do not reliably improve accuracy or explain how a model reached its answer; they can also amplify errors, bias, or unsupported claims.

Latest papers

228 papers25 papers in the last four weeks, up 56% on the four weeks before. 0.1% of all new papers.

Feb 20, 2026

VIRAASAT: Traversing Novel Paths for Indian Cultural Reasoning

Large Language Models (LLMs) have made significant progress in reasoning tasks across various domains such as mathematics and coding. However, their performance deteriorates in tasks requiring rich socio-cultural knowledge and diverse local contexts, particularly those involving Indian Culture. Existing Cultural benchmarks are (i) Manually crafted, (ii) contain single-hop questions testing factual recall, and (iii) prohibitively costly to scale, leaving this deficiency largely unmeasured. To address this, we introduce VIRAASAT, a novel, semi-automated multi-hop approach for generating cultural specific multi-hop Question-Answering dataset for Indian culture. VIRAASAT leverages a Knowledge Graph comprising more than 700 expert-curated cultural artifacts, covering 13 key attributes of Indian culture (history, festivals, etc). VIRAASAT spans all 28 states and 8 Union Territories, yielding more than 3,200 multi-hop questions that necessitate chained cultural reasoning. We evaluate current State-of-the-Art (SOTA) LLMs on VIRAASAT and identify key limitations in reasoning wherein fine-tuning on Chain-of-Thought(CoT) traces fails to ground and synthesize low-probability facts. To bridge this gap, we propose a novel framework named Symbolic Chain-of-Manipulation (SCoM). Adapting the Chain-of-Manipulation paradigm, we train the model to simulate atomic Knowledge Graph manipulations internally. SCoM teaches the model to reliably traverse the topological structure of the graph. Experiments on Supervised Fine-Tuning (SFT) demonstrate that SCoM outperforms standard CoT baselines by up to 20%. We release the VIRAASAT dataset along with our findings, laying a strong foundation towards building Culturally Aware Reasoning Models.
Feb 17, 2026

Benchmarking Zero-Shot Reasoning Approaches for Error Detection in Solidity Smart Contracts

Smart contracts play a central role in blockchain systems by encoding financial and operational logic. Still, their susceptibility to subtle security flaws poses significant risks of financial loss and erosion of trust. LLMs create new opportunities for automating vulnerability detection, yet the effectiveness of different prompting strategies and model choices in real-world contexts remains uncertain. This paper evaluates state-of-the-art LLMs on Solidity smart contract analysis using a balanced dataset of 400 contracts under two tasks: (i) Error Detection, where the model performs binary classification to decide whether a contract is vulnerable, and (ii) Error Classification, where the model must assign the predicted issue to a specific vulnerability category. Models are evaluated using zero-shot prompting strategies, including zero-shot, zero-shot Chain-of-Thought (CoT), and zero-shot Tree-of-Thought (ToT). In the Error Detection task, CoT and ToT substantially increase recall (often approaching ~ 95--99%), but typically reduce precision, indicating a more sensitive decision regime with more false positives. In the Error Classification task, Claude 3 Opus attains the best Weighted F1-score (90.8) under the ToT prompt, followed closely by its CoT.
Feb 16, 2026

The Potential of CoT for Reasoning: A Closer Look at Trace Dynamics

Chain-of-thought (CoT) prompting is a de-facto standard technique to elicit reasoning-like responses from large language models (LLMs), allowing them to spell out individual steps before giving a final answer. While the resemblance to human-like reasoning is undeniable, the driving forces underpinning the success of CoT reasoning still remain largely unclear. In this work, we perform an in-depth analysis of CoT traces originating from competition-level mathematics questions, with the aim of better understanding how, and which parts of CoT actually contribute to the final answer. To this end, we introduce the notion of a potential, quantifying how much a given part of CoT increases the likelihood of a correct completion. Upon examination of reasoning traces through the lens of the potential, we identify surprising patterns including (1) its often strong non-monotonicity (due to reasoning tangents), (2) very sharp but sometimes tough to interpret spikes (reasoning insights and jumps) as well as (3) at times lucky guesses, where the model arrives at the correct answer without providing any relevant justifications before. While some of the behaviours of the potential are readily interpretable and align with human intuition (such as insights and tangents), others remain difficult to understand from a human perspective. To further quantify the reliance of LLMs on reasoning insights, we investigate the notion of CoT transferability, where we measure the potential of a weaker model under the partial CoT from another, stronger model. Indeed aligning with our previous results, we find that as little as 20% of partial CoT can ``unlock'' the performance of the weaker model on problems that were previously unsolvable for it, highlighting that a large part of the mechanics underpinning CoT are transferable.
Feb 16, 2026

Beyond the Prompt in Large Language Models: Comprehension, In-Context Learning, and Chain-of-Thought

Large Language Models (LLMs) have demonstrated remarkable proficiency across diverse tasks, exhibiting emergent properties such as semantic prompt comprehension, In-Context Learning (ICL), and Chain-of-Thought (CoT) reasoning. Despite their empirical success, the theoretical mechanisms driving these phenomena remain poorly understood. This study dives into the foundations of these observations by addressing three critical questions: (1) How do LLMs accurately decode prompt semantics despite being trained solely on a next-token prediction objective? (2) Through what mechanism does ICL facilitate performance gains without explicit parameter updates? and (3) Why do intermediate reasoning steps in CoT prompting effectively unlock capabilities for complex, multi-step problems? Our results demonstrate that, through the autoregressive process, LLMs are capable of exactly inferring the transition probabilities between tokens across distinct tasks using provided prompts. We show that ICL enhances performance by reducing prompt ambiguity and facilitating posterior concentration on the intended task. Furthermore, we find that CoT prompting activates the model's capacity for task decomposition, breaking complex problems into a sequence of simpler sub-tasks that the model has mastered during the pretraining phase. By comparing their individual error bounds, we provide novel theoretical insights into the statistical superiority of advanced prompt engineering techniques.
Feb 16, 2026

Measuring and Mitigating Post-hoc Rationalization in Reverse Chain-of-Thought Generation

Reverse Chain-of-Thought Generation (RCG) synthesizes reasoning traces from query-answer pairs, but answer-visible generation can justify a pre-committed answer rather than derive it. This post-hoc rationalization creates a train-inference mismatch because student models are trained on answer-conditioned traces but must reason without answer access at inference time. We quantify this mismatch through lexical, trajectory, and probabilistic anchoring, measuring surface overlap, answer-conditioned generation dynamics, and answer recoverability from the trace, respectively. We find that semantic suppression, a seemingly intuitive mitigation, reduces lexical overlap but increases trajectory anchoring: avoiding the answer requires continually tracking it, thereby strengthening its influence on generation. We therefore propose Structural Skeleton-guided Reasoning (SSR), which replaces suppression with structural decoupling by first generating an abstract functional skeleton and then using it to guide the full reasoning trace. Anchoring analyses show that SSR reduces all three forms of answer dependence. Across in-domain and out-of-distribution benchmarks, its distilled variant, SSR-D, improves performance by up to 10 points over suppression baselines and better preserves out-of-distribution performance. Code is available at https://github.com/viniferagy/SSR.
Feb 16, 2026

Broken Chains: The Cost of Incomplete Reasoning in LLMs

Reasoning-specialized models like OpenAI's 5.1 and DeepSeek-V3.2 allocate substantial inference compute to extended chain-of-thought (CoT) traces, yet reasoning tokens incur significant costs. How do different reasoning modalities of code, natural language, hybrid, or none do perform under token constraints? We introduce a framework that constrains models to reason exclusively through code, comments, both, or neither, then systematically ablates token budgets to 10%, 30%, 50%, and 70% of optimal. We evaluate four frontier models (GPT-5.1, Gemini 3 Flash, DeepSeek-V3.2, Grok 4.1) across mathematical benchmarks (AIME, GSM8K, HMMT). Our findings reveal: (1) truncated reasoning can hurt as DeepSeek-V3.2 achieves 53% with no reasoning but only 17% with truncated CoT at 50% budget; (2) code degrades gracefully as Gemini's comments collapse to 0% while code maintains 43-47%; (3) hybrid reasoning underperforms single modalities; (4) robustness is model-dependent as Grok maintains 80-90% at 30% budget where OpenAI and DeepSeek collapse to 7-27%. These results suggest incomplete reasoning chains actively mislead models, with implications for deploying reasoning-specialized systems under resource constraints.
Jan 30, 2026

Divide-and-Conquer CoT: RL for Reducing Latency via Parallel Reasoning

Long chain-of-thought reasoning (Long CoT) is now fundamental to state-of-the-art LLMs, especially in mathematical reasoning. However, LLM generation is highly sequential, and long CoTs lead to a high latency. We propose to train Divide-and-Conquer CoT (DC-CoT) to reduce the latency. With DC-CoT, the model can act as a director that identifies distinct subtasks that can be performed in parallel in its reasoning process, and then spawns workers to execute the subtasks. Our goal is to achieve high accuracy, with a low longest path length, which is a theoretical measure of the latency needed for the response. We start with a long CoT base model (DeepScaleR-1.5B-Preview), and first use SFT with a small curated demonstration set to initialize its ability to spawn workers in a certain format. Because SFT degrades the accuracy significantly, we design a multi-stage RL algorithm, with various data filtering strategies, to recover the accuracy while decreasing the longest path length. Across several benchmarks including AIME 2024 and HMMT 2025, DC-CoT achieves similar accuracy as DeepScaleR-1.5B-Preview while decreasing longest path length by 35-40%. Our code, SFT dataset and models are publicly available at https://github.com/amahankali10/DC_CoT_RL_for_Low_Latency_CoT_with_Parallel_Reasoning.
Jan 12, 2026

Triggering Chain-of-Thought via Latent Feature Interventions in Large Language Models

Chain-of-Thought (CoT) prompting often improves the reasoning performance of large language models (LLMs), but the internal signal that triggers this behavior remains poorly understood. Leveraging the sparse features captured by Sparse Autoencoders (SAEs), we propose a systematic framework to analyze and intervene on the internal representations of LLMs, identifying a small set of latent features that are linked to reasoning behavior and can be causally tested through targeted intervention. Across multiple model families and reasoning benchmarks, we show that steering one or a small number of reasoning-related latent features can substantially induce reasoning behavior without explicit CoT prompting, achieving accuracy comparable to CoT. We further show that the identified features are not tied to particular wording patterns or verbosity, and confirm their causal role in reasoning through suppression experiments that impair performance even under CoT prompting. These results suggest that CoT prompting activates specific latent features to trigger reasoning, and that targeted intervention on these features offers an alternative pathway to elicit efficient reasoning behavior without explicit CoT prompting. Code is available at https://github.com/Zhenghao-He/LatentCoT.
Dec 17, 2025

Stepwise Think-Critique: Interleaved Reasoning and Self-Critique in a Single LLM

Human beings solve complex problems through critical thinking, where reasoning and evaluation are intertwined to converge toward correct solutions. However, most existing large language models (LLMs) treat the reasoning and verification as separate processes: they either generate reasoning without explicit self-checking or rely on external verifiers to detect errors post hoc. The former lacks immediate feedback, while the latter increases system complexity and hinders synchronized learning. Motivated by human critical thinking, we propose Stepwise Think-Critique (STC), an end-to-end trainable framework in which a single LLM emits a structured, step-level critique inline with each reasoning step. STC is trained with reinforcement learning that complements reasoning rewards with a critique-consistency reward derived from final-answer correctness, jointly optimizing reasoning correctness and critique reliability. On five mathematical reasoning benchmarks, STC improves Pass@1 by 7.2% over the 1.5B base model and attains 67.4% step-level critique F1, surpassing seven external process reward models evaluated at their per-dataset oracle thresholds---a step toward LLMs with built-in critical thinking.
Oct 10, 2025

Deductive Logic in Language Models: Horizontal vs Vertical Reasoning

Recent language models exhibit significant logical reasoning abilities, yet the mechanisms supporting deductive inference remain poorly understood. This paper studies small transformer-based language models trained from scratch on multi-step deductive tasks, focusing on the distinction between horizontal reasoning, where intermediate steps are generated autoregressively, and vertical reasoning, where inference unfolds implicitly across layers before the first output token is produced. We analyze two synthetic tasks: logical consequence over chains of symbolic implications and root-to-leaf navigation in binary trees. Mechanistic interpretability reveals that Chain-of-Thought supervision enables models to learn rule-based inference rather than statistical shortcuts. In the horizontal setting, a shallow attention-only model develops interpretable circuits for rule completion, rule chaining, and final decision making, largely implemented through induction-head-like mechanisms. We further introduce a truncated pseudoinverse method to decode the information carried by queries, keys, and values. For vertical reasoning, Chain-of-Thought appears to act less as explicit step-by-step guidance and more as a form of curriculum learning, helping the model acquire increasingly complex reasoning patterns. Without Chain-of-Thought, models tend to memorize or exploit dataset biases. These results provide a low-level account of how transformers can implement deductive reasoning and suggest how Chain-of-Thought may serve different functions in horizontal and vertical reasoning.
Jun 25, 2025

ππ-CoT: Prolog-Initialized Chain-of-Thought Prompting for Multi-Hop Question-Answering

Chain-of-Thought (CoT) prompting significantly enhances large language models' (LLMs) problem-solving capabilities, but still struggles with complex multi-hop questions, often falling into circular reasoning patterns or deviating from the logical path entirely. This limitation is particularly acute in retrieval-augmented generation (RAG) settings, where obtaining the right context is critical. We introduce Prolog-Initialized Chain-of-Thought (ππ-CoT), a novel prompting strategy that combines logic programming's structural rigor with language models' flexibility. ππ-CoT reformulates multi-hop questions into Prolog queries decomposed as single-hop sub-queries. These are resolved sequentially, producing intermediate artifacts, with which we initialize the subsequent CoT reasoning procedure. Extensive experiments demonstrate that ππ-CoT matches or outperforms standard RAG and in-context CoT on multi-hop question-answering benchmarks, with the largest gains on questions for which retrieval surfaces the necessary evidence.
May 28, 2025

Learning Composable Chains-of-Thought

A common approach for teaching large language models (LLMs) to reason is to train on chain-of-thought (CoT) traces of in-distribution reasoning problems, but such annotated data is costly to obtain for every problem of interest. We want reasoning models to generalize beyond their training distribution, and ideally to generalize compositionally: combine atomic reasoning skills to solve harder, unseen reasoning tasks. We take a step towards compositional generalization of reasoning skills when addressing a target compositional task that has no labeled CoT data. We find that simply training models on CoT data of atomic tasks leads to limited generalization, but minimally modifying CoT formats of constituent atomic tasks to be composable can lead to improvements. We can train "atomic CoT" models on the atomic tasks with Composable CoT data and combine them with multitask learning or model merging for better zero-shot performance on the target compositional task. Such a combined model can be further bootstrapped on a small amount of compositional data using rejection sampling fine-tuning (RFT). Results on string operations and natural language skill compositions show that training LLMs on Composable CoT outperforms multitask learning and continued fine-tuning baselines within a given training data budget.
May 22, 2025

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

Large Language Models (LLMs) have shown impressive performance on complex tasks through Chain-of-Thought (CoT) reasoning. However, conventional CoT relies on explicitly verbalized intermediate steps, which constrains its broader applicability, particularly in abstract reasoning tasks beyond language. To address this, there has been growing research interest in latent CoT reasoning, where the reasoning process is embedded within latent spaces. By decoupling reasoning from explicit language generation, latent CoT offers the promise of richer cognitive representations and facilitates more flexible, faster inference. This paper aims to present a comprehensive overview of this emerging paradigm and establish a systematic taxonomy. We analyze recent advances in methods, categorizing them from token-wise horizontal approaches to layer-wise vertical strategies. We then provide in-depth discussions of these methods, highlighting their design principles, applications, and remaining challenges. We hope that our survey provides a structured foundation for advancing this promising direction in LLM reasoning. The relevant papers will be regularly updated at https://github.com/EIT-NLP/Awesome-Latent-CoT.
Mar 3, 2025

HoT: Highlighted Chain of Thought for Referencing Supporting Facts from Inputs

An Achilles heel of Large Language Models (LLMs) is their tendency to hallucinate non-factual statements. A response mixed of factual and non-factual statements poses a challenge for humans to verify and accurately base their decisions on. To combat this problem, we propose Highlighted Chain-of-Thought Prompting (HoT), a technique for prompting LLMs to generate responses with XML tags that ground facts to those provided in the question. That is, given an input question, LLMs would first re-format the question to add XML tags highlighting key facts, and then, generate a response with highlights over the facts referenced from the input. Compared to vanilla chain of thought prompting (CoT), HoT reduces the rate of hallucination and separately improves LLM accuracy consistently on over 22 tasks from arithmetic, reading comprehension, to logical reasoning. When asking humans to verify LLM responses, highlights help time-limited participants to more accurately and efficiently recognize when LLMs are correct. Yet, surprisingly, when LLMs are wrong, HoTs tend to fool users into believing that an answer is correct.
Feb 21, 2025

The relationship between reasoning and performance in large language models--o3 (mini) thinks harder, not longer

Large language models have demonstrated remarkable progress in mathematical reasoning, leveraging chain-of-thought and reinforcement learning. However, many open questions remain regarding the interplay between reasoning token usage and accuracy gains. In particular, when comparing models across generations, it is unclear whether improved performance results from longer reasoning chains or more efficient reasoning. We systematically analyze reasoning chain length across o1-mini and o3-mini variants on the Omni-MATH benchmark, finding that o3-mini (m) achieves superior accuracy without requiring longer reasoning chains than o1-mini. Moreover, we show that accuracy generally declines as reasoning chains grow across all models and compute settings, even when controlling for difficulty of the questions. This accuracy drop is significantly smaller in more proficient models, suggesting that new generations of reasoning models use test-time compute more effectively. Finally, we highlight that while o3-mini (h) achieves a marginal accuracy gain over o3-mini (m), it does so by allocating substantially more reasoning tokens across all problems, even the ones that o3-mini (m) can already solve. These findings provide new insights into the relationship between model capability and reasoning length, with implications for efficiency, scaling, and evaluation methodologies.
Jul 18, 2024

Thought-Like-Pro: Enhancing Reasoning of Large Language Models through Self-Bootstrapped Prolog-based Chain-of-Thought

Large language models have demonstrated remarkable capabilities as general-purpose assistants, excelling in a wide range of reasoning tasks and supporting various aspects of daily web usage. This achievement represents a significant step toward achieving artificial general intelligence. Despite these advancements, the effectiveness of large language models often hinges on the specific prompting strategies employed, and there remains a lack of a robust framework to facilitate learning and generalization across diverse reasoning tasks. To address these challenges, we introduce a novel learning framework, Thought-Like-Pro. In this framework, we utilize imitation learning to imitate the Chain-of-Thought process which is verified and translated from reasoning trajectories generated by a symbolic Prolog logic engine. This framework proceeds in a prompt-guided but self-bootstrapped manner, that enables large language models to formulate rules and statements from given instructions and leverage the symbolic Prolog engine to derive results. Subsequently, large language models convert Prolog-derived successive reasoning trajectories into natural language chain-of-thought for imitation learning. The empirical findings indicate that our proposed approach greatly improves the reasoning capacity of large language models. By employing model averaging techniques, our method exhibits only a marginal decline in performance for distributional extrapolation tasks, showing robust generalization capabilities. We present a technical approach that integrates symbolic reasoning with language modeling, with the potential to support the development of large language models as cognitively inspired systems. The part of the dataset we used has been open-sourced.
Mar 7, 2024

Few shot chain-of-thought driven reasoning to prompt LLMs for open ended medical question answering

In this paper, we propose a modified version of the MedQA-USMLE dataset, named MEDQA-OPEN, which contains open-ended medical questions without options to mimic clinical scenarios, along with clinician-approved reasoned answers. Additionally, we implement a prompt driven by Chain of Thought (CoT) reasoning, CLINICR, to mirror the prospective process of incremental reasoning, reaching a correct response to medical questions. We empirically demonstrate how CLINICR outperforms the state-of-the-art 5-shot CoT-based prompt (Liévin et al., 2022). We also present an approach that mirrors real-life clinical practice by first exploring multiple differential diagnoses through MCQ-CLINICR and subsequently narrowing down to a final diagnosis using MCQ-ELIMINATIVE. Finally, emphasizing the importance of response verification in medical settings, we utilize a reward model mechanism, replacing the elimination process performed by MCQ-ELIMINATIVE.
Oct 6, 2023

Amortizing intractable inference in large language models

Autoregressive large language models (LLMs) compress knowledge from their training data through next-token conditional distributions. This limits tractable querying of this knowledge to start-to-end autoregressive sampling. However, many tasks of interest -- including sequence continuation, infilling, and other forms of constrained generation -- involve sampling from intractable posterior distributions. We address this limitation by using amortized Bayesian inference to sample from these intractable posteriors. Such amortization is algorithmically achieved by fine-tuning LLMs via diversity-seeking reinforcement learning algorithms: generative flow networks (GFlowNets). We empirically demonstrate that this distribution-matching paradigm of LLM fine-tuning can serve as an effective alternative to maximum-likelihood training and reward-maximizing policy optimization. As an important application, we interpret chain-of-thought reasoning as a latent variable modeling problem and demonstrate that our approach enables data-efficient adaptation of LLMs to tasks that require multi-step rationalization and tool use.