Daily Papers

Recent advances in Chain-of-Thought (CoT) reasoning have improved complex video understanding, but existing methods often struggle to adapt to domain-specific skills (e.g., event detection, spatial relation understanding, emotion understanding) over various video content. To address this, we propose Video-Skill-CoT (a.k.a. Video-SKoT), a framework that automatically constructs and leverages skill-aware CoT supervisions for domain-adaptive video reasoning. First, we construct skill-based CoT annotations: we extract domain-relevant reasoning skills from training questions, cluster them into a shared skill taxonomy, and create detailed multi-step CoT rationale tailored to each video-question pair for training. Second, we introduce a skill-specific expert learning framework. Each expert module specializes in a subset of reasoning skills and is trained with lightweight adapters using the collected CoT supervision. We demonstrate the effectiveness of the proposed approach on three video understanding benchmarks, where Video-SKoT consistently outperforms strong baselines. We also provide in-depth analyses on comparing different CoT annotation pipelines and learned skills over multiple video domains.

Chain-of-Thought (CoT) prompting can dramatically improve the multi-step reasoning abilities of large language models (LLMs). CoT explicitly encourages the LLM to generate intermediate rationales for solving a problem, by providing a series of reasoning steps in the demonstrations. Despite its success, there is still little understanding of what makes CoT prompting effective and which aspects of the demonstrated reasoning steps contribute to its performance. In this paper, we show that CoT reasoning is possible even with invalid demonstrations - prompting with invalid reasoning steps can achieve over 80-90% of the performance obtained using CoT under various metrics, while still generating coherent lines of reasoning during inference. Further experiments show that other aspects of the rationales, such as being relevant to the query and correctly ordering the reasoning steps, are much more important for effective CoT reasoning. Overall, these findings both deepen our understanding of CoT prompting, and open up new questions regarding LLMs' capability to learn to reason in context.

Large language models (LLMs) can perform complex reasoning by generating intermediate reasoning steps. Providing these steps for prompting demonstrations is called chain-of-thought (CoT) prompting. CoT prompting has two major paradigms. One leverages a simple prompt like "Let's think step by step" to facilitate step-by-step thinking before answering a question. The other uses a few manual demonstrations one by one, each composed of a question and a reasoning chain that leads to an answer. The superior performance of the second paradigm hinges on the hand-crafting of task-specific demonstrations one by one. We show that such manual efforts may be eliminated by leveraging LLMs with the "Let's think step by step" prompt to generate reasoning chains for demonstrations one by one, i.e., let's think not just step by step, but also one by one. However, these generated chains often come with mistakes. To mitigate the effect of such mistakes, we find that diversity matters for automatically constructing demonstrations. We propose an automatic CoT prompting method: Auto-CoT. It samples questions with diversity and generates reasoning chains to construct demonstrations. On ten public benchmark reasoning tasks with GPT-3, Auto-CoT consistently matches or exceeds the performance of the CoT paradigm that requires manual designs of demonstrations. Code is available at https://github.com/amazon-research/auto-cot

Chain of Thought (CoT) was introduced in recent research as a method for improving step-by-step reasoning in Large Language Models. However, CoT has limited applications such as its need for hand-crafted few-shot exemplar prompts and no capability to adjust itself to different queries. In this work, we propose a system to automatically generate rationales using CoT. Our method improves multi-step implicit reasoning capabilities by decomposing the implicit query into several explicit questions. This provides interpretability for the model, improving reasoning in weaker LLMs. We test our approach with two Q\&A datasets: StrategyQA and HotpotQA. We show an increase in accuracy with both, especially on StrategyQA. To facilitate further research in this field, the complete source code for this study has been made publicly available on GitHub: https://github.com/miralab-ai/autoreason.

Recent advancements in large language models (LLMs) have demonstrated their impressive abilities in various reasoning and decision-making tasks. However, the quality and coherence of the reasoning process can still benefit from enhanced introspection and self-reflection. In this paper, we introduce Multiplex CoT (Chain of Thought), a method that enables LLMs to simulate a form of self-review while reasoning, by initiating double Chain of Thought (CoT) thinking. Multiplex CoT leverages the power of iterative reasoning, where the model generates an initial chain of thought and subsequently critiques and refines this reasoning with a second round of thought generation. This recursive approach allows for more coherent, logical, and robust answers, improving the overall decision-making process. We demonstrate how this method can be effectively implemented using simple prompt engineering in existing LLM architectures, achieving an effect similar to that of the Learning-Refinement Model (LRM) without the need for additional training. Additionally, we present a practical guide for implementing the method in Google Colab, enabling easy integration into real-world applications.

Multimodal reasoning is a challenging task that requires models to reason across multiple modalities to answer questions. Existing approaches have made progress by incorporating language and visual modalities into a two-stage reasoning framework, separating rationale generation from answer inference. However, these approaches often fall short due to the inadequate quality of the generated rationales. In this work, we delve into the importance of rationales in model reasoning. We observe that when rationales are completely accurate, the model's accuracy significantly improves, highlighting the need for high-quality rationale generation. Motivated by this, we propose MC-CoT, a self-consistency training strategy that generates multiple rationales and answers, subsequently selecting the most accurate through a voting process. This approach not only enhances the quality of generated rationales but also leads to more accurate and robust answers. Through extensive experiments, we demonstrate that our approach significantly improves model performance across various benchmarks. Remarkably, we show that even smaller base models, when equipped with our proposed approach, can achieve results comparable to those of larger models, illustrating the potential of our approach in harnessing the power of rationales for improved multimodal reasoning. The code is available at https://github.com/chengtan9907/mc-cot.

Chain-of-Thought (CoT) prompting reveals that large language models are capable of performing complex reasoning via intermediate steps. CoT prompting is primarily categorized into three approaches. The first approach utilizes straightforward prompts like ``Let's think step by step'' to generate a sequential thought process before yielding an answer. The second approach makes use of human-crafted, step-by-step demonstrations to guide the model's reasoning process. The third automates the generation of reasoned demonstrations with the 'Let's think step by step'.This approach sometimes leads to reasoning errors, highlighting the need to diversify demonstrations to mitigate its misleading effects. However, diverse demonstrations pose challenges for effective representations. In this work, we propose ECHO, a self-harmonized chain-of-thought prompting method. It consolidates diverse solution paths into a uniform and effective solution pattern.ECHO demonstrates the best overall performance across three reasoning domains.

When leveraging language models for reasoning tasks, generating explicit chain-of-thought (CoT) steps often proves essential for achieving high accuracy in final outputs. In this paper, we investigate if models can be taught to internalize these CoT steps. To this end, we propose a simple yet effective method for internalizing CoT steps: starting with a model trained for explicit CoT reasoning, we gradually remove the intermediate steps and finetune the model. This process allows the model to internalize the intermediate reasoning steps, thus simplifying the reasoning process while maintaining high performance. Our approach enables a GPT-2 Small model to solve 9-by-9 multiplication with up to 99% accuracy, whereas standard training cannot solve beyond 4-by-4 multiplication. Furthermore, our method proves effective on larger language models, such as Mistral 7B, achieving over 50% accuracy on GSM8K without producing any intermediate steps.

Recent advancements in large language models (LLMs) have demonstrated remarkable general reasoning capabilities, holding significant potential for applications in the financial domain, a field that requires robust and reliable reasoning. It has been demonstrated that distilling high-quality chain-of-thought (CoT) rationales from advanced general reasoning models offers a promising and efficient path to the financial reasoning model. However, existing CoT synthesis methods suffer from shallow CoT sampling, leaving the question of how to construct a well-designed knowledge space for finance reasoning unexplored. In this paper, we present Agentar-DeepFinance-100K, a large-scale financial reasoning dataset characterized by its systematic CoT synthesis optimization. We first introduce a comprehensive CoT synthesis pipeline featuring Multi-perspective Knowledge Extraction (MKE) and Self-Corrective Rewriting (SCR) to generate exhaustive and deep financial reasoning trajectories. Furthermore, a systematic investigation, termed CoT Cube, is conducted to analyze critical factors that influence CoT effectiveness, such as necessity, length and synthesizer, yielding valuable insights for high-quality financial CoT construction. Experiments demonstrate that models trained on our Agentar-DeepFinance-100K achieve significant improvements on financial benchmarks. We publicly release Agentar-DeepFinance-100K , hoping to advance the research in financial reasoning models.

Chain of Thought (CoT) is significant in improving the reasoning abilities of large language models (LLMs). However, the correlation between the effectiveness of CoT and the length of reasoning steps in prompts remains largely unknown. To shed light on this, we have conducted several empirical experiments to explore the relations. Specifically, we design experiments that expand and compress the rationale reasoning steps within CoT demonstrations, while keeping all other factors constant. We have the following key findings. First, the results indicate that lengthening the reasoning steps in prompts, even without adding new information into the prompt, considerably enhances LLMs' reasoning abilities across multiple datasets. Alternatively, shortening the reasoning steps, even while preserving the key information, significantly diminishes the reasoning abilities of models. This finding highlights the importance of the number of steps in CoT prompts and provides practical guidance to make better use of LLMs' potential in complex problem-solving scenarios. Second, we also investigated the relationship between the performance of CoT and the rationales used in demonstrations. Surprisingly, the result shows that even incorrect rationales can yield favorable outcomes if they maintain the requisite length of inference. Third, we observed that the advantages of increasing reasoning steps are task-dependent: simpler tasks require fewer steps, whereas complex tasks gain significantly from longer inference sequences.

Recently, there has been significant progress in teaching language models to perform step-by-step reasoning to solve complex numerical reasoning tasks. Chain-of-thoughts prompting (CoT) is by far the state-of-art method for these tasks. CoT uses language models to perform both reasoning and computation in the multi-step `thought' process. To disentangle computation from reasoning, we propose `Program of Thoughts' (PoT), which uses language models (mainly Codex) to express the reasoning process as a program. The computation is relegated to an external computer, which executes the generated programs to derive the answer. We evaluate PoT on five math word problem datasets (GSM, AQuA, SVAMP, TabMWP, MultiArith) and three financial-QA datasets (FinQA, ConvFinQA, TATQA) for both few-shot and zero-shot setups. Under both few-shot and zero-shot settings, PoT can show an average performance gain over CoT by around 12\% across all the evaluated datasets. By combining PoT with self-consistency decoding, we can achieve SoTA performance on all math problem datasets and near-SoTA performance on financial datasets. All of our data and code are released in Github\url{https://github.com/wenhuchen/Program-of-Thoughts}.

Chain of Thought (CoT) of multi-step benefits from the logical structure of the reasoning steps and task-specific actions, significantly enhancing the mathematical reasoning capabilities of large language models. As the prevalence of long CoT, the number of reasoning steps exceeds manageable token limits and leads to higher computational demands. Inspired by the fundamental logic of human cognition, ``derive, then reduce'', we conceptualize the standard multi-step CoT as a novel Markov Chain of Thought (MCoT). In this study, we consider the mathematical reasoning task, defining each reasoning step as text accompanied by a Python code snippet. To facilitate a longer reasoning path, self-correction is enabled through interactions with the code interpreter. Our MCoT aims to compress previous reasoning steps into a simplified question, enabling efficient next-step inference without relying on a lengthy KV cache. In our experiments, we curate the MCoTInstruct dataset, and the empirical results indicate that MCoT not only significantly enhances efficiency but also maintains comparable accuracy. While much remains to be explored, this work paves the way for exploring the long CoT reasoning abilities of LLMs.

Using Large Language Models for complex mathematical reasoning is difficult, primarily due to the complexity of multi-step reasoning. The main challenges of this process include (1) selecting critical intermediate results to advance the procedure, and (2) limited exploration of potential solutions. To address these issues, we introduce a novel algorithm, namely Stepwise Self-Consistent Chain-of-Thought (SSC-CoT). SSC-CoT employs a strategy of selecting intermediate steps based on the intersection of various reasoning chains. Additionally, SSC-CoT enables the model to discover critical intermediate steps by querying a knowledge graph comprising relevant domain knowledge. To validate SSC-CoT, we present a new dataset, TriMaster100, tailored for complex trigonometry problems. This dataset contains 100 questions, with each solution broken down into scored intermediate steps, facilitating a comprehensive evaluation of the mathematical reasoning process. On TriMaster100, SSC-CoT triples the effectiveness of the state-of-the-art methods. Furthermore, we benchmark SSC-CoT on the widely recognized complex mathematical question dataset, MATH level 5, and it surpasses the second-best method by 7.2% in accuracy. Code and the TriMaster100 dataset can be found at: https://github.com/zhao-zilong/ssc-cot.

Modern systems for multi-hop question answering (QA) typically break questions into a sequence of reasoning steps, termed chain-of-thought (CoT), before arriving at a final answer. Often, multiple chains are sampled and aggregated through a voting mechanism over the final answers, but the intermediate steps themselves are discarded. While such approaches improve performance, they do not consider the relations between intermediate steps across chains and do not provide a unified explanation for the predicted answer. We introduce Multi-Chain Reasoning (MCR), an approach which prompts large language models to meta-reason over multiple chains of thought, rather than aggregating their answers. MCR examines different reasoning chains, mixes information between them and selects the most relevant facts in generating an explanation and predicting the answer. MCR outperforms strong baselines on 7 multi-hop QA datasets. Moreover, our analysis reveals that MCR explanations exhibit high quality, enabling humans to verify its answers.

It has been well-known that Chain-of-Thought can remarkably enhance LLMs' performance on complex tasks. However, because it also introduces slower inference speeds and higher computational costs, many researches have attempted to use implicit CoT, which does not need LLMs to explicitly generate the intermediate steps. But there is still gap between their efficacy and typical explicit CoT methods. This leaves us a doubt that, does implicit CoT really equal to explicit CoT? Therefore, in this study, we address this question through experiments. We probe the information of intermediate steps from the model's hidden states when it is performing implicit CoT. The results surprisingly indicate that LLMs hardly think about intermediate steps, suggesting they may just rely on experience rather than strict step-by-step reasoning. Moreover, we find LLMs' implicit reasoning capabilities are susceptible and unstable, reaffirming the necessity of explicit CoT to effectively support complex tasks.

Chain-of-Thought (CoT) Prompting is a dominant paradigm in Large Language Models (LLMs) to enhance complex reasoning. It guides LLMs to present multi-step reasoning, rather than generating the final answer directly. However, CoT encounters difficulties when key information required for reasoning is implicit or missing. This occurs because CoT emphasizes the sequence of reasoning steps while overlooking the early extraction of essential information. We propose a pre-prompting method called Iterative Summarization Pre-Prompting (ISP^2) to refine LLM reasoning when key information is not explicitly provided. First, entities and their corresponding descriptions are extracted to form potential key information pairs. Next, we use a reliability rating to assess these pairs, then merge the two lowest-ranked pairs into a new entity description. This process is repeated until a unique key information pair is obtained. Finally, that pair, along with the original question, is fed into LLMs to produce the answer. Extensive experiments demonstrate a 7.1% improvement compared to existing methods. Unlike traditional prompting, ISP^2 adopts an inductive approach with pre-prompting, offering flexible integration into diverse reasoning frameworks. The code is available at https://github.com/zdhgreat/ISP-2.

Training large language models (LLMs) with high-quality Chain-of-Thought (CoT) annotations has become a widely adopted strategy due to its significant enhancement of reasoning capabilities. To fully comprehend this approach, two questions naturally arise: (Q1) What advantages does training with CoT offer compared to training without CoT? (Q2) If there are advantages, what are the underlying mechanisms of explicit CoT training? Analyzing the advantages and mechanisms of CoT training is challenging due to the many factors involved. To address this, we conduct a detailed analysis using clear and controllable data distributions and, for the first time, reveal that CoT training offers the following advantages: (1) Training with CoT markedly improves reasoning generalization, extending it from in-distribution (ID) to both ID and out-of-distribution (OOD) scenarios, while also speeding up convergence; (2) Even when training with CoT includes a certain range of erroneous reasoning steps, it still enables the model to learn reasoning patterns, leading to systematic generalization. We further explore the underlying mechanisms from a circuit perspective: (1) The data distribution (e.g., ratio lambda and pattern) plays a crucial role in influencing the model's systematic generalization; (2) CoT training (with two-hop facts) internalizes reasoning into a two-stage generalizing circuit, where the number of stages corresponds to the explicit reasoning steps during training. Our findings elucidate the mechanisms underlying explicit CoT training and offer critical insights into tuning strategies for LLMs to achieve robust generalization.

Chain-of-Thought (CoT) prompting has emerged as a powerful approach to enhancing the reasoning capabilities of Large Language Models (LLMs). However, existing implementations, such as in-context learning and fine-tuning, remain costly and inefficient. To improve CoT reasoning at a lower cost, and inspired by the task vector paradigm, we introduce CoT Vectors, compact representations that encode task-general, multi-step reasoning knowledge. Through experiments with Extracted CoT Vectors, we observe pronounced layer-wise instability, manifesting as a U-shaped performance curve that reflects a systematic three-stage reasoning process in LLMs. To address this limitation, we propose Learnable CoT Vectors, optimized under a teacher-student framework to provide more stable and robust guidance. Extensive evaluations across diverse benchmarks and models demonstrate that CoT Vectors not only outperform existing baselines but also achieve performance comparable to parameter-efficient fine-tuning methods, while requiring fewer trainable parameters. Moreover, by treating CoT Vectors as a probe, we uncover how their effectiveness varies due to latent space structure, information density, acquisition mechanisms, and pre-training differences, offering new insights into the functional organization of multi-step reasoning in LLMs. The source code will be released.

Large Language Models (LLMs) significantly benefit from Chain-of-Thought (CoT) prompting in performing various reasoning tasks. While CoT allows models to produce more comprehensive reasoning processes, its emphasis on intermediate reasoning steps can inadvertently introduce hallucinations and accumulated errors, thereby limiting models' ability to solve complex reasoning tasks. Inspired by how humans engage in careful and meticulous deductive logical reasoning processes to solve tasks, we seek to enable language models to perform explicit and rigorous deductive reasoning, and also ensure the trustworthiness of their reasoning process through self-verification. However, directly verifying the validity of an entire deductive reasoning process is challenging, even with advanced models like ChatGPT. In light of this, we propose to decompose a reasoning verification process into a series of step-by-step subprocesses, each only receiving their necessary context and premises. To facilitate this procedure, we propose Natural Program, a natural language-based deductive reasoning format. Our approach enables models to generate precise reasoning steps where subsequent steps are more rigorously grounded on prior steps. It also empowers language models to carry out reasoning self-verification in a step-by-step manner. By integrating this verification process into each deductive reasoning stage, we significantly enhance the rigor and trustfulness of generated reasoning steps. Along this process, we also improve the answer correctness on complex reasoning tasks. Code will be released at https://github.com/lz1oceani/verify_cot.

Few-shot Chain-of-Thought (CoT) prompting has demonstrated strong performance in improving the reasoning capabilities of large language models (LLMs). While theoretical investigations have been conducted to understand CoT, the underlying transformer used in these studies isolates the CoT reasoning process into separated in-context learning steps (Stepwise ICL). In this work, we theoretically show that, compared to Stepwise ICL, the transformer gains better error correction ability and more accurate predictions if the reasoning from earlier steps (Coherent CoT) is integrated. Given that this coherent reasoning changes the behavior of the transformer, we further investigate the sensitivity of the transformer with Coherent CoT when the demonstration examples are corrupted at the inference stage. Our theoretical results indicate that the transformer is more sensitive to errors in intermediate reasoning steps than the final outcome. Building upon this observation, we propose an improvement on CoT by incorporating both correct and incorrect reasoning paths in the demonstration. Our experiments validate the effectiveness of the proposed approach.

Prompting-based large language models (LLMs) are surprisingly powerful at generating natural language reasoning steps or Chains-of-Thoughts (CoT) for multi-step question answering (QA). They struggle, however, when the necessary knowledge is either unavailable to the LLM or not up-to-date within its parameters. While using the question to retrieve relevant text from an external knowledge source helps LLMs, we observe that this one-step retrieve-and-read approach is insufficient for multi-step QA. Here, what to retrieve depends on what has already been derived, which in turn may depend on what was previously retrieved. To address this, we propose IRCoT, a new approach for multi-step QA that interleaves retrieval with steps (sentences) in a CoT, guiding the retrieval with CoT and in turn using retrieved results to improve CoT. Using IRCoT with GPT3 substantially improves retrieval (up to 21 points) as well as downstream QA (up to 15 points) on four datasets: HotpotQA, 2WikiMultihopQA, MuSiQue, and IIRC. We observe similar substantial gains in out-of-distribution (OOD) settings as well as with much smaller models such as Flan-T5-large without additional training. IRCoT reduces model hallucination, resulting in factually more accurate CoT reasoning. Code, data, and prompts are available at https://github.com/stonybrooknlp/ircot

The chain-of-though (CoT) prompting methods were successful in various natural language processing (NLP) tasks thanks to their ability to unveil the underlying complex reasoning processes. Such reasoning processes typically exhibit implicitly structured steps. Recent efforts also started investigating methods to encourage more explicitly structured reasoning procedures to be captured. In this work, we propose Tab-CoT, a novel tabular-format CoT prompting method, which allows the complex reasoning process to be explicitly modelled in a highly structured manner. Despite its simplicity, we show that our approach is capable of performing reasoning across multiple dimensions (i.e., both rows and columns). We demonstrate our approach's strong zero-shot and few-shot capabilities through extensive experiments on a range of reasoning tasks.

Pretrained large language models (LLMs) are increasingly utilized across a wide range of natural language processing (NLP) tasks due to their impressive capabilities as few-shot learners. Recent techniques, such as chain-of-thought (CoT) prompting, have significantly advanced multi-step reasoning by introducing step-by-step decomposition, achieving state-of-the-art results on complex reasoning benchmarks. However, these approaches often rely on static prompting templates that do not adapt to task complexity or errors during the reasoning process. In this work, we introduce Adaptive Prompting, a dynamic and iterative framework designed to enhance reasoning by incorporating real-time adjustments to prompt structures and validation mechanisms.Experimental results demonstrate that Adaptive Prompting significantly improves performance on diverse reasoning benchmarks, including arithmetic reasoning (GSM8K, MultiArith), logical reasoning and commonsense tasks, achieving substantial accuracy gains compared to static prompting baselines. By integrating guided prompts, intermediate validation, and self-corrective steps, our approach enables smaller models to achieve competitive performance with larger counterparts, such as GPT-4, while maintaining computational efficiency. The framework achieves this without requiring fine-tuning or task-specific training data, highlighting the untapped potential of iterative reasoning methods.

Large language models (LLMs) have recently been shown to deliver impressive performance in various NLP tasks. To tackle multi-step reasoning tasks, few-shot chain-of-thought (CoT) prompting includes a few manually crafted step-by-step reasoning demonstrations which enable LLMs to explicitly generate reasoning steps and improve their reasoning task accuracy. To eliminate the manual effort, Zero-shot-CoT concatenates the target problem statement with "Let's think step by step" as an input prompt to LLMs. Despite the success of Zero-shot-CoT, it still suffers from three pitfalls: calculation errors, missing-step errors, and semantic misunderstanding errors. To address the missing-step errors, we propose Plan-and-Solve (PS) Prompting. It consists of two components: first, devising a plan to divide the entire task into smaller subtasks, and then carrying out the subtasks according to the plan. To address the calculation errors and improve the quality of generated reasoning steps, we extend PS prompting with more detailed instructions and derive PS+ prompting. We evaluate our proposed prompting strategy on ten datasets across three reasoning problems. The experimental results over GPT-3 show that our proposed zero-shot prompting consistently outperforms Zero-shot-CoT across all datasets by a large margin, is comparable to or exceeds Zero-shot-Program-of-Thought Prompting, and has comparable performance with 8-shot CoT prompting on the math reasoning problem. The code can be found at https://github.com/AGI-Edgerunners/Plan-and-Solve-Prompting.

Large Language Models (LLMs) using Chain-of-Thought (CoT) prompting excel at complex reasoning but generate verbose thought processes with considerable redundancy, leading to increased inference costs and reduced efficiency. We introduce a novel CoT compression framework based on step entropy, a metric that quantifies the informational contribution of individual reasoning steps to identify redundancy. Through theoretical analysis and extensive empirical validation on mathematical reasoning benchmarks, we demonstrate that steps with low entropy are indeed highly redundant. Our experiments reveal that an astonishing 80\% of low-entropy intermediate steps can be pruned with minor degradation in the final answer accuracy across DeepSeek-R1-7B, 14B and Qwen3-8B. This finding sharply contrasts with random or high-entropy pruning, which severely impairs reasoning performance. Building on this, we propose a novel two-stage training strategy combining Supervised Fine-Tuning (SFT) and Group Relative Policy Optimization (GRPO) reinforcement learning. This approach enables LLMs to autonomously learn to generate compressed COTs during inference by strategically incorporating [SKIP] tokens. Our method significantly enhances LLM inference efficiency while rigorously preserving accuracy, offering profound implications for practical LLM deployment and a deeper understanding of reasoning structures.

Despite significant advancements in the general capability of large language models (LLMs), they continue to struggle with consistent and accurate reasoning, especially in complex tasks such as mathematical and code reasoning. One key limitation is that LLMs are trained primarily on correct solutions, reducing their ability to detect and learn from errors, which hampers their ability to reliably verify and rank outputs. To address this, we scale up the inference-time computation by generating multiple reasoning paths and employing verifiers to assess and rank the generated outputs by correctness. To facilitate this, we introduce a comprehensive dataset consisting of correct and incorrect solutions for math and code tasks, generated by multiple LLMs. This diverse set of solutions enables verifiers to more effectively distinguish and rank correct answers from erroneous outputs. The training methods for building verifiers were selected based on an extensive comparison of existing approaches. Moreover, to leverage the unique strengths of different reasoning strategies, we propose a novel collaborative method integrating Chain-of-Thought (CoT) and Program-of-Thought (PoT) solutions for verification. CoT provides a clear, step-by-step reasoning process that enhances interpretability, while PoT, being executable, offers a precise and error-sensitive validation mechanism. By taking both of their strengths, our approach significantly improves the accuracy and reliability of reasoning verification. Our verifiers, Math-Rev and Code-Rev, demonstrate substantial performance gains to existing LLMs, achieving state-of-the-art results on benchmarks such as GSM8k and MATH and even outperforming GPT-4o with Qwen-72B-Instruct as the reasoner.

Chain-of-thought prompting (CoT) advances the reasoning abilities of large language models (LLMs) and achieves superior performance in arithmetic, commonsense, and symbolic reasoning tasks. However, most CoT studies rely on carefully designed human-annotated rational chains to prompt the language model, which poses challenges for real-world applications where labeled training data is available without human-annotated rational chains. This creates barriers to applications of CoT prompting to these general tasks. This paper proposes a new strategy, Automate-CoT (Automatic Prompt Augmentation and Selection with Chain-of-Thought), that can bypass human engineering of CoTs by automatically augmenting rational chains from a small labeled dataset, and then pruning low-quality chains to construct a candidate pool of machine-generated rationale chains based on the labels. Finally, it selects the optimal combination of several rationale chains from the pool for CoT prompting by employing a variance-reduced policy gradient strategy to estimate the significance of each example in a black-box language model. Automate-CoT enables a quick adaptation of the CoT technique to different tasks. Experimental results demonstrate the effectiveness of our method, where state-of-the-art results are achieved on arithmetic reasoning (+2.7\%), commonsense reasoning (+3.4\%), symbolic reasoning (+3.2\%), and non-reasoning tasks (+2.5\%). Our code will be available at https://github.com/shizhediao/automate-cot.

Logical reading comprehension is a challenging task that entails grasping the underlying semantics of text and applying reasoning to deduce the correct answer. Prior researches have primarily focused on enhancing logical reasoning capabilities through Chain-of-Thought (CoT) or data augmentation. However, previous work constructing chain-of-thought rationales concentrates solely on analyzing correct options, neglecting the incorrect alternatives. Addtionally, earlier efforts on data augmentation by altering contexts rely on rule-based methods, which result in generated contexts that lack diversity and coherence. To address these issues, we propose a Premise-Oriented Data Augmentation (PODA) framework. This framework can generate CoT rationales including analyses for both correct and incorrect options, while constructing diverse and high-quality counterfactual contexts from incorrect candidate options. We integrate summarizing premises and identifying premises for each option into rationales. Subsequently, we employ multi-step prompts with identified premises to construct counterfactual context. To facilitate the model's capabilities to better differentiate the reasoning process associated with each option, we introduce a novel thought-path contrastive learning method that compares reasoning paths between the original and counterfactual samples. Experimental results on three representative LLMs demonstrate that our method can improve the baselines substantially across two challenging logical reasoning benchmarks (ReClor and LogiQA 2.0). The data and code are released at https://github.com/lalalamdbf/TPReasoner.

Chain-of-Thought (CoT) reasoning has been widely adopted to enhance Large Language Models (LLMs) by decomposing complex tasks into simpler, sequential subtasks. However, extending CoT to vision-language reasoning tasks remains challenging, as it often requires interpreting transitions of visual states to support reasoning. Existing methods often struggle with this due to limited capacity of modeling visual state transitions or incoherent visual trajectories caused by fragmented architectures. To overcome these limitations, we propose Uni-CoT, a Unified Chain-of-Thought framework that enables coherent and grounded multimodal reasoning within a single unified model. The key idea is to leverage a model capable of both image understanding and generation to reason over visual content and model evolving visual states. However, empowering a unified model to achieve that is non-trivial, given the high computational cost and the burden of training. To address this, Uni-CoT introduces a novel two-level reasoning paradigm: A Macro-Level CoT for high-level task planning and A Micro-Level CoT for subtask execution. This design significantly reduces the computational overhead. Furthermore, we introduce a structured training paradigm that combines interleaved image-text supervision for macro-level CoT with multi-task objectives for micro-level CoT. Together, these innovations allow Uni-CoT to perform scalable and coherent multi-modal reasoning. Furthermore, thanks to our design, all experiments can be efficiently completed using only 8 A100 GPUs with 80GB VRAM each. Experimental results on reasoning-driven image generation benchmark (WISE) and editing benchmarks (RISE and KRIS) indicates that Uni-CoT demonstrates SOTA performance and strong generalization, establishing Uni-CoT as a promising solution for multi-modal reasoning. Project Page and Code: https://sais-fuxi.github.io/projects/uni-cot/

Recent advances in Chain-of-Thought (CoT) prompting have substantially improved the reasoning capabilities of Large Language Models (LLMs). However, these methods often suffer from overthinking, leading to unnecessarily lengthy or redundant reasoning traces. Existing approaches attempt to mitigate this issue through curating multiple reasoning chains for training LLMs, but their effectiveness is often constrained by the quality of the generated data and prone to overfitting. To address the challenge, we propose Reasoning Compression ThroUgh Stepwise Trials (ReCUT), a novel method aimed at balancing the accuracy and length of reasoning trajectory. Specifically, ReCUT employs a stepwise exploration mechanism and a long-short switched sampling strategy, enabling LLMs to incrementally generate diverse reasoning paths. These paths are evaluated and used to construct preference pairs to train two specialized models (Gemini LLMs)-one optimized for reasoning accuracy, the other for shorter reasoning. A final integrated model is obtained by interpolating the parameters of these two models. Experimental results across multiple math reasoning datasets and backbone models demonstrate that ReCUT significantly reduces reasoning lengths by approximately 30-50%, while maintaining or improving reasoning accuracy compared to various baselines. All codes and data will be released via https://github.com/NEUIR/ReCUT.

Large language models (LLMs) have shown impressive performance on complex reasoning by leveraging chain-of-thought (CoT) prompting to generate intermediate reasoning chains as the rationale to infer the answer. However, existing CoT studies have focused on the language modality. We propose Multimodal-CoT that incorporates language (text) and vision (images) modalities into a two-stage framework that separates rationale generation and answer inference. In this way, answer inference can leverage better generated rationales that are based on multimodal information. With Multimodal-CoT, our model under 1 billion parameters outperforms the previous state-of-the-art LLM (GPT-3.5) by 16 percentage points (75.17%->91.68% accuracy) on the ScienceQA benchmark and even surpasses human performance. Code is publicly available available at https://github.com/amazon-science/mm-cot.

Chain-of-Thought (CoT) prompting empowers the reasoning abilities of Large Language Models (LLMs), eliciting them to solve complex reasoning tasks step-by-step. However, with the success of CoT methods, the ability to deliver multi-step reasoning remains limited to English due to the imbalance in the distribution of the pre-training data, making the other languages a barrier. In this work, we propose a Cross-lingual multi-step reasoning approach, aiming to align reasoning processes across different languages. In particular, our method, through a Self-consistent Cross-lingual prompting mechanism inspired by the Tree-of-Thoughts approach, delivers multi-step reasoning paths in different languages that, during the steps, lead to the final solution. Our experimental evaluations show that our method significantly outperforms existing prompting methods, reducing the number of interactions and achieving state-of-the-art performance.

Large reasoning models (LRMs) spend substantial test-time compute on long chain-of-thought (CoT) traces, but what *characterizes* an effective CoT remains unclear. While prior work reports gains from lengthening CoTs and increasing review (revisiting earlier steps) via appended *wait* tokens, recent studies suggest that shorter thinking can outperform longer traces. We therefore conduct a systematic evaluation across ten LRMs on math and scientific reasoning. Contrary to the "longer-is-better" narrative, we find that both naive CoT lengthening and increased review are associated with *lower* accuracy. As CoT unfolds step by step, token-level metrics can conflate verbosity with process quality. We introduce a graph view of CoT to extract structure and identify a single statistic-the *Failed-Step Fraction (FSF)*, the fraction of steps in abandoned branches-that consistently outpredicts length and review ratio for correctness across models. To probe causality, we design two interventions. First, we rank candidate CoTs by each metric at test time, where FSF yields the largest pass@1 gains; second, we edit CoTs to remove failed branches, which significantly improves accuracy, indicating that failed branches bias subsequent reasoning. Taken together, these results characterize effective CoTs as those that *fail less* and support *structure-aware* test-time scaling over indiscriminately generating long CoT.

To reduce the cost and consumption of computing resources caused by computational redundancy and delayed reward assignment in long CoT, this research proposes the dynamic chain-of-thought (D-CoT) with adaptive reasoning time and steps. The researcher used simulation experiment to simulate the integration of D-CoT through Python 3.13 IDLE combined with a Python simulator based on GPTs. At the same time, the researcher used DeepSeek R1 as a control group to test and compare the performance of the D-CoT simulator in processing MIT OpenCourseWare's linear algebra exam questions. Experimental results show that D-CoT is better than DeepSeek R1 based on long CoT in three indicators: reasoning time, CoT length (reasoning steps) and token count, which achieves a significant reduction in computing resource consumption. In addition, this research has potential value in deep reasoning optimization that is used as a reference for future dynamic deep reasoning frameworks.

Long chain-of-thought (CoT) prompting helps Large Language Models (LLMs) solve difficult problems, but very long traces often slow or even degrade performance on fast, intuitive "System-1" tasks. We introduce Connector-Aware Compact CoT (CAC-CoT) -- a method that deliberately restricts reasoning to a small, fixed set of connector phrases, steering the model toward concise and well -- structured explanations. Despite its simplicity, our synthetic method with Gemini-2.0-Flash yields a high-quality training quality. CAC-CoT achieves approximately 85% on GSM8K and approximately 40% on GPQA (System-2) while retaining approximately 90% on S1-Bench (System-1). Its reasoning traces average approximately 300 tokens(ART), about one-third the length of baseline traces, delivering higher efficiency without loss of accuracy.

Generating Chain-of-Thought (CoT) before deriving the answer can effectively improve the reasoning capabilities of large language models (LLMs) and significantly improve the accuracy of the generated answer. However, in most cases, the length of the generated CoT is much longer than the desired final answer, which results in additional decoding costs. Furthermore, existing research has discovered that shortening the reasoning steps in CoT, even while preserving the key information, diminishes LLMs' abilities. These phenomena make it difficult to use LLMs and CoT in many real-world applications that only require the final answer and are sensitive to latency, such as search and recommendation. To reduce the costs of model decoding and shorten the length of the generated CoT, this paper presents Conditioned Compressed Chain-of-Thought (C3oT), a CoT compression framework that involves a compressor to compress an original longer CoT into a shorter CoT while maintaining key information and interpretability, a conditioned training method to train LLMs with both longer CoT and shorter CoT simultaneously to learn the corresponding relationships between them, and a conditioned inference method to gain the reasoning ability learned from longer CoT by generating shorter CoT. We conduct experiments over four datasets from arithmetic and commonsense scenarios, showing that the proposed method is capable of compressing the length of generated CoT by up to more than 50% without compromising its effectiveness.

Step-by-step reasoning approaches like chain of thought (CoT) have proved to be very effective in inducing reasoning capabilities in large language models. However, the success of the CoT approach is fundamentally tied to the model size, and billion parameter-scale models are often needed to get CoT to work. In this paper, we propose a knowledge distillation approach that leverages the step-by-step CoT reasoning capabilities of larger models and distills these abilities into smaller models. In this work, we propose an alternative reasoning scheme, Socratic CoT, that learns a decomposition of the original problem into a sequence of subproblems and uses it to guide the intermediate reasoning steps. We use Socratic CoT to train a combination of two small distilled models: a problem decomposer and a subproblem solver. In practice, given a new problem, the two distilled models work in sync to decompose and solve complex problems. On multiple reasoning datasets (GSM8K, StrategyQA, and SVAMP), our proposed distillation strategies boosts the performance of smaller models over 70% compared to the baselines. Finally, we investigate when Socratic CoT is an effective alternative to CoT, demonstrating cases where a much smaller model (GPT-2 large) can outperform a 10X larger model (GPT-3 6B). Our code is available here: https://github.com/kumar-shridhar/Distiiling-LM

Chain-of-Thought significantly enhances a model's reasoning capability, but it also comes with a considerable increase in inference costs due to long chains. With the observation that the reasoning path can be easily compressed under easy tasks but struggle on hard tasks, we explore the feasibility of elastically controlling the length of reasoning paths with only one model, thereby reducing the inference overhead of reasoning models dynamically based on task difficulty. We introduce a new tuning and inference strategy named CoT-Valve, designed to allow models to generate reasoning chains of varying lengths. To achieve this, we propose to identify a direction in the parameter space that, when manipulated, can effectively control the length of generated CoT. Moreover, we show that this property is valuable for compressing the reasoning chain. We construct datasets with chains from long to short for the same questions and explore two enhanced strategies for CoT-Valve: (1) a precise length-compressible CoT tuning method, and (2) a progressive chain length compression approach. Our experiments show that CoT-Valve successfully enables controllability and compressibility of the chain and shows better performance than the prompt-based control. We applied this method to QwQ-32B-Preview, reducing reasoning chains on GSM8K from 741 to 225 tokens with a minor performance drop (95.07% to 94.92%) and on AIME from 6827 to 4629 tokens, with only one additional incorrect answer.

Instructing the model to generate a sequence of intermediate steps, a.k.a., a chain of thought (CoT), is a highly effective method to improve the accuracy of large language models (LLMs) on arithmetics and symbolic reasoning tasks. However, the mechanism behind CoT remains unclear. This work provides a theoretical understanding of the power of CoT for decoder-only transformers through the lens of expressiveness. Conceptually, CoT empowers the model with the ability to perform inherently serial computation, which is otherwise lacking in transformers, especially when depth is low. Given input length n, previous works have shown that constant-depth transformers with finite precision poly(n) embedding size can only solve problems in TC^0 without CoT. We first show an even tighter expressiveness upper bound for constant-depth transformers with constant-bit precision, which can only solve problems in AC^0, a proper subset of TC^0. However, with T steps of CoT, constant-depth transformers using constant-bit precision and O(log n) embedding size can solve any problem solvable by boolean circuits of size T. Empirically, enabling CoT dramatically improves the accuracy for tasks that are hard for parallel computation, including the composition of permutation groups, iterated squaring, and circuit value problems, especially for low-depth transformers.

Reasoning models have demonstrated remarkable progress in solving complex and logic-intensive tasks by generating extended Chain-of-Thoughts (CoTs) prior to arriving at a final answer. Yet, the emergence of this "slow-thinking" paradigm, with numerous tokens generated in sequence, inevitably introduces substantial computational overhead. To this end, it highlights an urgent need for effective acceleration. This survey aims to provide a comprehensive overview of recent advances in efficient reasoning. It categorizes existing works into three key directions: (1) shorter - compressing lengthy CoTs into concise yet effective reasoning chains; (2) smaller - developing compact language models with strong reasoning capabilities through techniques such as knowledge distillation, other model compression techniques, and reinforcement learning; and (3) faster - designing efficient decoding strategies to accelerate inference. A curated collection of papers discussed in this survey is available in our GitHub repository.

Chain-of-thought (CoT) prompting enables large language models (LLMs) to solve complex reasoning tasks by generating an explanation before the final prediction. Despite it's promising ability, a critical downside of CoT prompting is that the performance is greatly affected by the factuality of the generated explanation. To improve the correctness of the explanations, fine-tuning language models with explanation data is needed. However, there exists only a few datasets that can be used for such approaches, and no data collection tool for building them. Thus, we introduce CoTEVer, a tool-kit for annotating the factual correctness of generated explanations and collecting revision data of wrong explanations. Furthermore, we suggest several use cases where the data collected with CoTEVer can be utilized for enhancing the faithfulness of explanations. Our toolkit is publicly available at https://github.com/SeungoneKim/CoTEVer.

Recent large language models (LLMs) can generate long Chain-of-Thought (CoT) at test time, enabling them to solve complex tasks. These reasoning steps in CoT are often assumed as a faithful reflection of the model's internal thinking process, and used to monitor unsafe intentions. However, we find many reasoning steps don't truly contribute to LLMs' prediction. We measure the step-wise causal influence of each reasoning step on the model's final prediction with a proposed True Thinking Score (TTS). We reveal that LLMs often interleave between true-thinking steps (which are genuinely used to produce the final output) and decorative-thinking steps (which only give the appearance of reasoning but have minimal causal impact). Notably, only a small subset of the total reasoning steps have a high TTS that causally drive the model's prediction: e.g., for the AIME dataset, only an average of 2.3% of reasoning steps in CoT have a TTS >= 0.7 (range: 0-1) under the Qwen-2.5 model. Furthermore, we identify a TrueThinking direction in the latent space of LLMs. By steering along or against this direction, we can force the model to perform or disregard certain CoT steps when computing the final result. Finally, we highlight that self-verification steps in CoT (i.e., aha moments) can also be decorative, where LLMs do not truly verify their solution. Steering along the TrueThinking direction can force internal reasoning over these steps, resulting in a change in the final results. Overall, our work reveals that LLMs often verbalize reasoning steps without actually performing them internally, which undermines both the efficiency of LLM reasoning and the trustworthiness of CoT.

The zero-shot chain of thought (CoT) approach is often used in question answering (QA) by language models (LMs) for tasks that require multiple reasoning steps, typically enhanced by the prompt "Let's think step by step." However, some QA tasks hinge more on accessing relevant knowledge than on chaining reasoning steps. We introduce a simple general prompting technique, called PREP, that involves using two instances of LMs: the first (LM1) generates relevant information, and the second (LM2) answers the question based on this information. PREP is designed to be general and independent of the user's domain knowledge, making it applicable across various QA tasks without the need for specialized prompt engineering. To evaluate the effectiveness of our prompting method, we create a dataset of 100 binary-choice questions, derived from an extensive schematic dataset on artifact parts and material composition. These questions ask which of two artifacts is less likely to share materials with another artifact. Such questions probe the LM's knowledge of shared materials in the part structure of different artifacts. We test our method on our dataset and three published commonsense reasoning datasets. The average accuracy of our method is consistently higher than that of all the other tested methods across all the tested datasets.

A long-standing goal of AI systems is to perform complex multimodal reasoning like humans. Recently, large language models (LLMs) have made remarkable strides in such multi-step reasoning on the language modality solely by leveraging the chain of thought (CoT) to mimic human thinking. However, the transfer of these advancements to multimodal contexts introduces heightened challenges, including but not limited to the impractical need for labor-intensive annotation and the limitations in terms of flexibility, generalizability, and explainability. To evoke CoT reasoning in multimodality, this work first conducts an in-depth analysis of these challenges posed by multimodality and presents two key insights: "keeping critical thinking" and "letting everyone do their jobs" in multimodal CoT reasoning. Furthermore, this study proposes a novel DDCoT prompting that maintains a critical attitude through negative-space prompting and incorporates multimodality into reasoning by first dividing the reasoning responsibility of LLMs into reasoning and recognition and then integrating the visual recognition capability of visual models into the joint reasoning process. The rationales generated by DDCoT not only improve the reasoning abilities of both large and small language models in zero-shot prompting and fine-tuning learning, significantly outperforming state-of-the-art methods but also exhibit impressive generalizability and explainability.

Chain-of-thought (CoT) via prompting is the de facto method for eliciting reasoning capabilities from large language models (LLMs). But for what kinds of tasks is this extra ``thinking'' really helpful? To analyze this, we conducted a quantitative meta-analysis covering over 100 papers using CoT and ran our own evaluations of 20 datasets across 14 models. Our results show that CoT gives strong performance benefits primarily on tasks involving math or logic, with much smaller gains on other types of tasks. On MMLU, directly generating the answer without CoT leads to almost identical accuracy as CoT unless the question or model's response contains an equals sign, indicating symbolic operations and reasoning. Following this finding, we analyze the behavior of CoT on these problems by separating planning and execution and comparing against tool-augmented LLMs. Much of CoT's gain comes from improving symbolic execution, but it underperforms relative to using a symbolic solver. Our results indicate that CoT can be applied selectively, maintaining performance while saving inference costs. Furthermore, they suggest a need to move beyond prompt-based CoT to new paradigms that better leverage intermediate computation across the whole range of LLM applications.

Recent work has demonstrated that Chain-of-Thought (CoT) often yields limited gains for soft-reasoning problems such as analytical and commonsense reasoning. CoT can also be unfaithful to a model's actual reasoning. We investigate the dynamics and faithfulness of CoT in soft-reasoning tasks across instruction-tuned, reasoning and reasoning-distilled models. Our findings reveal differences in how these models rely on CoT, and show that CoT influence and faithfulness are not always aligned.

Chain-of-Thought (CoT) prompting enables large language models to solve complex reasoning problems by generating intermediate steps. However, confined by its inherent single-pass and sequential generation process, CoT heavily relies on the initial decisions, causing errors in early steps to accumulate and impact the final answers. In contrast, humans adopt recursive thinking when tackling complex reasoning problems, i.e., iteratively breaking the original problem into approachable sub-problems and aggregating their answers to resolve the original one. Inspired by the human cognitive process, we propose SOCRATIC QUESTIONING, a divide-and-conquer style algorithm that mimics the recursive thinking process. Specifically, SOCRATIC QUESTIONING leverages large language models to raise and answer sub-questions until collecting enough information to tackle the original question. Unlike CoT, SOCRATIC QUESTIONING explicitly navigates the thinking space, stimulates effective recursive thinking, and is more robust towards errors in the thinking process. Extensive experiments on several complex reasoning tasks, including MMLU, MATH, LogiQA, and visual question-answering demonstrate significant performance improvements over the state-of-the-art prompting methods, such as CoT, and Tree-of-Thought. The qualitative analysis clearly shows that the intermediate reasoning steps elicited by SOCRATIC QUESTIONING are similar to humans' recursively thinking process of complex reasoning problems.

LLMs can perform multi-step reasoning through Chain-of-Thought (CoT), but they cannot reliably verify their own logic. Even when they reach correct answers, the underlying reasoning may be flawed, undermining trust in high-stakes scenarios. To mitigate this issue, we introduce VeriCoT, a neuro-symbolic method that extracts and verifies formal logical arguments from CoT reasoning. VeriCoT formalizes each CoT reasoning step into first-order logic and identifies premises that ground the argument in source context, commonsense knowledge, or prior reasoning steps. The symbolic representation enables automated solvers to verify logical validity while the NL premises allow humans and systems to identify ungrounded or fallacious reasoning steps. Experiments on the ProofWriter, LegalBench, and BioASQ datasets show VeriCoT effectively identifies flawed reasoning, and serves as a strong predictor of final answer correctness. We also leverage VeriCoT's verification signal for (1) inference-time self-reflection, (2) supervised fine-tuning (SFT) on VeriCoT-distilled datasets and (3) preference fine-tuning (PFT) with direct preference optimization (DPO) using verification-based pairwise rewards, further improving reasoning validity and accuracy.

Chain-of-Thought (CoT) reasoning has emerged as a promising approach for enhancing the performance of large language models (LLMs) on complex reasoning tasks. Recently, a series of studies attempt to explain the mechanisms underlying CoT, aiming to deepen the understanding of its efficacy. Nevertheless, the existing research faces two major challenges: (1) a lack of quantitative metrics to assess CoT capabilities and (2) a dearth of guidance on optimizing CoT performance. Motivated by this, in this work, we introduce a novel reasoning boundary framework (RBF) to address these challenges. To solve the lack of quantification, we first define a reasoning boundary (RB) to quantify the upper-bound of CoT and establish a combination law for RB, enabling a practical quantitative approach applicable to various real-world CoT tasks. To address the lack of optimization, we propose three categories of RBs. We further optimize these categories with combination laws focused on RB promotion and reasoning path optimization for CoT improvement. Through extensive experiments on 27 models and 5 tasks, the study validates the existence and rationality of the proposed framework. Furthermore, it explains the effectiveness of 10 CoT strategies and guides optimization from two perspectives. We hope this work can provide a comprehensive understanding of the boundaries and optimization strategies for reasoning in LLMs. Our code and data are available at https://github.com/LightChen233/reasoning-boundary.

Large Language Models (LLMs) have recently demonstrated exceptional performance in various Natural Language Processing (NLP) tasks. They have also shown the ability to perform chain-of-thought (CoT) reasoning to solve complex problems. Recent studies have explored CoT reasoning in complex multimodal scenarios, such as the science question answering task, by fine-tuning multimodal models with high-quality human-annotated CoT rationales. However, collecting high-quality COT rationales is usually time-consuming and costly. Besides, the annotated rationales are hardly accurate due to the external essential information missed. To address these issues, we propose a novel method termed T-SciQ that aims at teaching science question answering with LLM signals. The T-SciQ approach generates high-quality CoT rationales as teaching signals and is advanced to train much smaller models to perform CoT reasoning in complex modalities. Additionally, we introduce a novel data mixing strategy to produce more effective teaching data samples by policy for simple and complex science question answer problems. Extensive experimental results show that our T-SciQ method achieves a new state-of-the-art performance on the ScienceQA benchmark, with an accuracy of 96.18\%. Moreover, our approach outperforms the most powerful fine-tuned baseline by 4.5\%.

Chest X-ray imaging is crucial for diagnosing pulmonary and cardiac diseases, yet its interpretation demands extensive clinical experience and suffers from inter-observer variability. While deep learning models offer high diagnostic accuracy, their black-box nature hinders clinical adoption in high-stakes medical settings. To address this, we propose X-Ray-CoT (Chest X-Ray Chain-of-Thought), a novel framework leveraging Vision-Language Large Models (LVLMs) for intelligent chest X-ray diagnosis and interpretable report generation. X-Ray-CoT simulates human radiologists' "chain-of-thought" by first extracting multi-modal features and visual concepts, then employing an LLM-based component with a structured Chain-of-Thought prompting strategy to reason and produce detailed natural language diagnostic reports. Evaluated on the CORDA dataset, X-Ray-CoT achieves competitive quantitative performance, with a Balanced Accuracy of 80.52% and F1 score of 78.65% for disease diagnosis, slightly surpassing existing black-box models. Crucially, it uniquely generates high-quality, explainable reports, as validated by preliminary human evaluations. Our ablation studies confirm the integral role of each proposed component, highlighting the necessity of multi-modal fusion and CoT reasoning for robust and transparent medical AI. This work represents a significant step towards trustworthy and clinically actionable AI systems in medical imaging.

Reasoning large language models (LLMs) have demonstrated superior capacities in solving complicated problems by generating long chain-of-thoughts (CoT), but such a lengthy CoT incurs high inference costs. In this study, we introduce ES-CoT, an inference-time method that shortens CoT generation by detecting answer convergence and stopping early with minimal performance loss. At the end of each reasoning step, we prompt the LLM to output its current final answer, denoted as a step answer. We then track the run length of consecutive identical step answers as a measure of answer convergence. Once the run length exhibits a sharp increase and exceeds a minimum threshold, the generation is terminated. We provide both empirical and theoretical support for this heuristic: step answers steadily converge to the final answer, and large run-length jumps reliably mark this convergence. Experiments on five reasoning datasets across three LLMs show that ES-CoT reduces the number of inference tokens by about 41\% on average while maintaining accuracy comparable to standard CoT. Further, ES-CoT integrates seamlessly with self-consistency prompting and remains robust across hyperparameter choices, highlighting it as a practical and effective approach for efficient reasoning.

Chain-of-thoughts (CoT) requires large language models (LLMs) to generate intermediate steps before reaching the final answer, and has been proven effective to help LLMs solve complex reasoning tasks. However, the inner mechanism of CoT still remains largely unclear. In this paper, we empirically study the role of CoT tokens in LLMs on two compositional tasks: multi-digit multiplication and dynamic programming. While CoT is essential for solving these problems, we find that preserving only tokens that store intermediate results would achieve comparable performance. Furthermore, we observe that storing intermediate results in an alternative latent form will not affect model performance. We also randomly intervene some values in CoT, and notice that subsequent CoT tokens and the final answer would change correspondingly. These findings suggest that CoT tokens may function like variables in computer programs but with potential drawbacks like unintended shortcuts and computational complexity limits between tokens. The code and data are available at https://github.com/solitaryzero/CoTs_are_Variables.

Reasoning capability is pivotal for Large Language Models (LLMs) to solve complex tasks, yet achieving reliable and scalable reasoning remains challenging. While Chain-of-Thought (CoT) prompting has become a mainstream approach, existing methods often suffer from uncontrolled generation, insufficient quality, and limited diversity in reasoning paths. Recent efforts leverage code to enhance CoT by grounding reasoning in executable steps, but such methods are typically constrained to predefined mathematical problems, hindering scalability and generalizability. In this work, we propose Caco (Code-Assisted Chain-of-ThOught), a novel framework that automates the synthesis of high-quality, verifiable, and diverse instruction-CoT reasoning data through code-driven augmentation. Unlike prior work, Caco first fine-tunes a code-based CoT generator on existing math and programming solutions in a unified code format, then scales the data generation to a large amount of diverse reasoning traces. Crucially, we introduce automated validation via code execution and rule-based filtering to ensure logical correctness and structural diversity, followed by reverse-engineering filtered outputs into natural language instructions and language CoTs to enrich task adaptability. This closed-loop process enables fully automated, scalable synthesis of reasoning data with guaranteed executability. Experiments on our created Caco-1.3M dataset demonstrate that Caco-trained models achieve strong competitive performance on mathematical reasoning benchmarks, outperforming existing strong baselines. Further analysis reveals that Caco's code-anchored verification and instruction diversity contribute to superior generalization across unseen tasks. Our work establishes a paradigm for building self-sustaining, trustworthy reasoning systems without human intervention.

Recent large language models achieve strong reasoning performance by generating detailed chain-of-thought traces, but this often leads to excessive token use and high inference latency. Existing efficiency approaches typically focus on model-centric interventions, such as reinforcement learning or supervised fine-tuning, to reduce verbosity. In contrast, we propose a training-free, input-centric approach. Inspired by cognitive psychology, we introduce Focused Chain-of-Thought (F-CoT), which separates information extraction from the reasoning process. F-CoT first organizes the essential information from a query into a concise, structured context and then guides the model to reason exclusively over this context. By preventing attention to irrelevant details, F-CoT naturally produces shorter reasoning paths. On arithmetic word problems, F-CoT reduces generated tokens by 2-3x while maintaining accuracy comparable to standard zero-shot CoT. These results highlight structured input as a simple yet effective lever for more efficient LLM reasoning.

Recent large language models (LLMs) have witnessed significant advancement in various tasks, including mathematical reasoning and theorem proving. As these two tasks require strict and formal multi-step inference, they are appealing domains for exploring the reasoning ability of LLMs but still face important challenges. Previous studies such as Chain-of-Thought (CoT) have revealed the effectiveness of intermediate steps guidance. However, such step-wise annotation requires heavy labor, leading to insufficient training steps for current benchmarks. To fill this gap, this work introduces MUSTARD, a data generation framework that masters uniform synthesis of theorem and proof data of high quality and diversity. MUSTARD synthesizes data in three stages: (1) It samples a few mathematical concept seeds as the problem category. (2) Then, it prompts a generative language model with the sampled concepts to obtain both the problems and their step-wise formal solutions. (3) Lastly, the framework utilizes a proof assistant (e.g., Lean Prover) to filter the valid proofs. With the proposed MUSTARD, we present a theorem-and-proof benchmark MUSTARDSAUCE with 5,866 valid data points. Each data point contains an informal statement, an informal proof, and a translated formal proof that passes the prover validation. We perform extensive analysis and demonstrate that MUSTARD generates validated high-quality step-by-step data. We further apply the MUSTARDSAUCE for fine-tuning smaller language models. The fine-tuned Llama 2-7B achieves a 15.41% average relative performance gain in automated theorem proving, and 8.18% in math word problems. Codes and data are available at https://github.com/Eleanor-H/MUSTARD.

Chain-of-Thought (CoT) reasoning has been extensively explored in large models to tackle complex understanding tasks. However, it still remains an open question whether such strategies can be applied to verifying and reinforcing image generation scenarios. In this paper, we provide the first comprehensive investigation of the potential of CoT reasoning to enhance autoregressive image generation. We focus on three techniques: scaling test-time computation for verification, aligning model preferences with Direct Preference Optimization (DPO), and integrating these techniques for complementary effects. Our results demonstrate that these approaches can be effectively adapted and combined to significantly improve image generation performance. Furthermore, given the pivotal role of reward models in our findings, we propose the Potential Assessment Reward Model (PARM) and PARM++, specialized for autoregressive image generation. PARM adaptively assesses each generation step through a potential assessment approach, merging the strengths of existing reward models, and PARM++ further introduces a reflection mechanism to self-correct the generated unsatisfactory image. Using our investigated reasoning strategies, we enhance a baseline model, Show-o, to achieve superior results, with a significant +24% improvement on the GenEval benchmark, surpassing Stable Diffusion 3 by +15%. We hope our study provides unique insights and paves a new path for integrating CoT reasoning with autoregressive image generation. Code and models are released at https://github.com/ZiyuGuo99/Image-Generation-CoT

Training on large amounts of rationales (i.e., CoT Fine-tuning) is effective at improving the reasoning capabilities of large language models (LLMs). However, acquiring human-authored rationales or augmenting rationales from proprietary models is costly and not scalable. In this paper, we study the problem of whether LLMs could self-improve their reasoning capabilities. To this end, we propose Self-Explore, where the LLM is tasked to explore the first wrong step (i.e., the first pit) within the rationale and use such signals as fine-grained rewards for further improvement. On the GSM8K and MATH test set, Self-Explore achieves 11.57% and 2.89% improvement on average across three LLMs compared to supervised fine-tuning (SFT). Our code is available at https://github.com/hbin0701/Self-Explore.

Recent frontier models employ long chain-of-thought reasoning to explore solution spaces in context and achieve stonger performance. While many works study distillation to build smaller yet capable models, most focus on English and little is known about language-specific reasoning. To bridge this gap, we first introduct **Language-Mixed CoT**, a reasoning schema that switches between English and a target language, using English as an anchor to excel in reasoning while minimizing translation artificats. As a Korean case study, we curate **Yi-Sang**: 5.79M native-Korean prompts from web Q&A, exams, STEM, and code; 3.7M long reasoning traces generated from Qwen3-32B; and a targeted 260k high-yield subset. We train ninve models (4B-35B) across six families (Qwen2.5, Llama-3.1, Gemma-3, etc). Our best model, **KO-REAson-35B**, achieves state-of-the-art performance, with the highest overall average score (64.0 \pm 25), ranking first on 5/9 benchmarks and second on the remainder. Samller and mid-sized models also benefit substantially, with an average improvement of +18.6 points across teh evaluated nine benchmarks. Ablations show **Language-Mixed CoT** is more effective than monolingual CoT, also resulting in cross-lingual and mult-modal performance gains. We release our data-curation pipeline, evaluation system, datasets, and models to advance research on language-specific reasoning. Data and model collection: https://huggingface.co/KOREAson.

Learning complex functions that involve multi-step reasoning poses a significant challenge for standard supervised learning from input-output examples. Chain-of-thought (CoT) supervision, which provides intermediate reasoning steps together with the final output, has emerged as a powerful empirical technique, underpinning much of the recent progress in the reasoning capabilities of large language models. This paper develops a statistical theory of learning under CoT supervision. A key characteristic of the CoT setting, in contrast to standard supervision, is the mismatch between the training objective (CoT risk) and the test objective (end-to-end risk). A central part of our analysis, distinguished from prior work, is explicitly linking those two types of risk to achieve sharper sample complexity bounds. This is achieved via the *CoT information measure* I_{D, h_star}^{CoT}(epsilon; calH), which quantifies the additional discriminative power gained from observing the reasoning process. The main theoretical results demonstrate how CoT supervision can yield significantly faster learning rates compared to standard E2E supervision. Specifically, it is shown that the sample complexity required to achieve a target E2E error epsilon scales as d/I_{D, h_star}^{CoT}(epsilon; calH), where d is a measure of hypothesis class complexity, which can be much faster than standard d/epsilon rates. Information-theoretic lower bounds in terms of the CoT information are also obtained. Together, these results suggest that CoT information is a fundamental measure of statistical complexity for learning under chain-of-thought supervision.

Large Language Models (LLMs) can achieve strong performance on many tasks by producing step-by-step reasoning before giving a final output, often referred to as chain-of-thought reasoning (CoT). It is tempting to interpret these CoT explanations as the LLM's process for solving a task. However, we find that CoT explanations can systematically misrepresent the true reason for a model's prediction. We demonstrate that CoT explanations can be heavily influenced by adding biasing features to model inputs -- e.g., by reordering the multiple-choice options in a few-shot prompt to make the answer always "(A)" -- which models systematically fail to mention in their explanations. When we bias models toward incorrect answers, they frequently generate CoT explanations supporting those answers. This causes accuracy to drop by as much as 36% on a suite of 13 tasks from BIG-Bench Hard, when testing with GPT-3.5 from OpenAI and Claude 1.0 from Anthropic. On a social-bias task, model explanations justify giving answers in line with stereotypes without mentioning the influence of these social biases. Our findings indicate that CoT explanations can be plausible yet misleading, which risks increasing our trust in LLMs without guaranteeing their safety. CoT is promising for explainability, but our results highlight the need for targeted efforts to evaluate and improve explanation faithfulness.

Large Language Models (LLMs) (e.g., ChatGPT) have shown impressive performance in code generation. LLMs take prompts as inputs, and Chain-of-Thought (CoT) prompting is the state-of-the-art prompting technique. CoT prompting asks LLMs first to generate CoTs (i.e., intermediate natural language reasoning steps) and then output the code. However, CoT prompting is designed for natural language generation and has low accuracy in code generation. In this paper, we propose Structured CoTs (SCoTs) and present a novel prompting technique for code generation, named SCoT prompting. Our motivation is source code contains rich structural information and any code can be composed of three program structures (i.e., sequence, branch, and loop structures). Intuitively, structured intermediate reasoning steps make for structured source code. Thus, we ask LLMs to use program structures to build CoTs, obtaining SCoTs. Then, LLMs generate the final code based on SCoTs. Compared to CoT prompting, SCoT prompting explicitly constrains LLMs to think about how to solve requirements from the view of source code and further the performance of LLMs in code generation. We apply SCoT prompting to two LLMs (i.e., ChatGPT and Codex) and evaluate it on three benchmarks (i.e., HumanEval, MBPP, and MBCPP). (1) SCoT prompting outperforms the state-of-the-art baseline - CoT prompting by up to 13.79% in Pass@1. (2) Human evaluation shows human developers prefer programs from SCoT prompting. (3) SCoT prompting is robust to examples and achieves substantial improvements.

Recently, with the chain of thought (CoT) prompting, large language models (LLMs), e.g., GPT-3, have shown strong reasoning ability in several natural language processing tasks such as arithmetic, commonsense, and logical reasoning. However, LLMs with CoT require multi-step prompting and multi-token prediction, which is highly sensitive to individual mistakes and vulnerable to error accumulation. The above issues make the LLMs need the ability to verify the answers. In fact, after inferring conclusions in some thinking decision tasks, people often check them by re-verifying steps to avoid some mistakes. In this paper, we propose and prove that LLMs also have similar self-verification abilities. We take the conclusion obtained by CoT as one of the conditions for solving the original problem. By taking turns masking the original conditions and predicting their results, we calculate an explainable answer verification score based on whether the re-predicted conditions are correct. Experimental results demonstrate that the proposed method can improve the reasoning performance on various arithmetic, commonsense, and logical reasoning datasets. Our code is publicly available at: https://github.com/WENGSYX/Self-Verification.

Chain-of-thought (CoT) reasoning enables large language models (LLMs) to move beyond fast System-1 responses and engage in deliberative System-2 reasoning. However, this comes at the cost of significant inefficiency due to verbose intermediate output. Recent latent-space reasoning methods improve efficiency by operating on hidden states without decoding into language, yet they treat all steps uniformly, failing to distinguish critical deductions from auxiliary steps and resulting in suboptimal use of computational resources. In this paper, we propose System-1.5 Reasoning, an adaptive reasoning framework that dynamically allocates computation across reasoning steps through shortcut paths in latent space. Specifically, System-1.5 Reasoning introduces two types of dynamic shortcuts. The model depth shortcut (DS) adaptively reasons along the vertical depth by early exiting non-critical tokens through lightweight adapter branches, while allowing critical tokens to continue through deeper Transformer layers. The step shortcut (SS) reuses hidden states across the decoding steps to skip trivial steps and reason horizontally in latent space. Training System-1.5 Reasoning involves a two-stage self-distillation process: first distilling natural language CoT into latent-space continuous thought, and then distilling full-path System-2 latent reasoning into adaptive shortcut paths (System-1.5 Reasoning). Experiments on reasoning tasks demonstrate the superior performance of our method. For example, on GSM8K, System-1.5 Reasoning achieves reasoning performance comparable to traditional CoT fine-tuning methods while accelerating inference by over 20x and reducing token generation by 92.31% on average.

Chain-of-thought (CoT) reasoning has been widely applied in the mathematical reasoning of Large Language Models (LLMs). Recently, the introduction of derivative process supervision on CoT trajectories has sparked discussions on enhancing scaling capabilities during test time, thereby boosting the potential of these models. However, in multimodal mathematical reasoning, the scarcity of high-quality CoT training data has hindered existing models from achieving high-precision CoT reasoning and has limited the realization of reasoning potential during test time. In this work, we propose a three-module synthesis strategy that integrates CoT distillation, trajectory-format rewriting, and format unification. It results in a high-quality CoT reasoning instruction fine-tuning dataset in multimodal mathematics, MMathCoT-1M. We comprehensively validate the state-of-the-art (SOTA) performance of the trained URSA-7B model on multiple multimodal mathematical benchmarks. For test-time scaling, we introduce a data synthesis strategy that automatically generates process annotation datasets, known as DualMath-1.1M, focusing on both interpretation and logic. By further training URSA-7B on DualMath-1.1M, we transition from CoT reasoning capabilities to robust supervision abilities. The trained URSA-RM-7B acts as a verifier, effectively enhancing the performance of URSA-7B at test time. URSA-RM-7B also demonstrates excellent out-of-distribution (OOD) verifying capabilities, showcasing its generalization. Model weights, training data and code will be open-sourced.

Reasoning ability is one of the most crucial capabilities of a foundation model, signifying its capacity to address complex reasoning tasks. Chain-of-Thought (CoT) technique is widely regarded as one of the effective methods for enhancing the reasoning ability of foundation models and has garnered significant attention. However, the reasoning process of CoT is linear, step-by-step, similar to personal logical reasoning, suitable for solving general and slightly complicated problems. On the contrary, the thinking pattern of an expert owns two prominent characteristics that cannot be handled appropriately in CoT, i.e., high-order multi-hop reasoning and multimodal comparative judgement. Therefore, the core motivation of this paper is transcending CoT to construct a reasoning paradigm that can think like an expert. The hyperedge of a hypergraph could connect various vertices, making it naturally suitable for modelling high-order relationships. Inspired by this, this paper innovatively proposes a multimodal Hypergraph-of-Thought (HoT) reasoning paradigm, which enables the foundation models to possess the expert-level ability of high-order multi-hop reasoning and multimodal comparative judgement. Specifically, a textual hypergraph-of-thought is constructed utilizing triple as the primary thought to model higher-order relationships, and a hyperedge-of-thought is generated through multi-hop walking paths to achieve multi-hop inference. Furthermore, we devise a visual hypergraph-of-thought to interact with the textual hypergraph-of-thought via Cross-modal Co-Attention Graph Learning for multimodal comparative verification. Experimentations on the ScienceQA benchmark demonstrate the proposed HoT-based T5 outperforms CoT-based GPT3.5 and chatGPT, which is on par with CoT-based GPT4 with a lower model size.

Recently, long-thought reasoning models achieve strong performance on complex reasoning tasks, but often incur substantial inference overhead, making efficiency a critical concern. Our empirical analysis reveals that the benefit of using Long-CoT varies across problems: while some problems require elaborate reasoning, others show no improvement, or even degraded accuracy. This motivates adaptive reasoning strategies that tailor reasoning depth to the input. However, prior work primarily reduces redundancy within long reasoning paths, limiting exploration of more efficient strategies beyond the Long-CoT paradigm. To address this, we propose a novel two-stage framework for adaptive and efficient reasoning. First, we construct a hybrid reasoning model by merging long and short CoT models to enable diverse reasoning styles. Second, we apply bi-level preference training to guide the model to select suitable reasoning styles (group-level), and prefer concise and correct reasoning within each style group (instance-level). Experiments demonstrate that our method significantly reduces inference costs compared to other baseline approaches, while maintaining performance. Notably, on five mathematical datasets, the average length of reasoning is reduced by more than 50%, highlighting the potential of adaptive strategies to optimize reasoning efficiency in large language models. Our code is coming soon at https://github.com/StarDewXXX/AdaR1

The advancement of Chain-of-Thought (CoT) reasoning has significantly enhanced the capabilities of large language models (LLMs) and large vision-language models (LVLMs). However, a rigorous evaluation framework for video CoT reasoning remains absent. Current video benchmarks fail to adequately assess the reasoning process and expose whether failures stem from deficiencies in perception or reasoning capabilities. Therefore, we introduce VCR-Bench, a novel benchmark designed to comprehensively evaluate LVLMs' Video Chain-of-Thought Reasoning capabilities. VCR-Bench comprises 859 videos spanning a variety of video content and durations, along with 1,034 high-quality question-answer pairs. Each pair is manually annotated with a stepwise CoT rationale, where every step is tagged to indicate its association with the perception or reasoning capabilities. Furthermore, we design seven distinct task dimensions and propose the CoT score to assess the entire CoT process based on the stepwise tagged CoT rationals. Extensive experiments on VCR-Bench highlight substantial limitations in current LVLMs. Even the top-performing model, o1, only achieves a 62.8% CoT score and an 56.7% accuracy, while most models score below 40%. Experiments show most models score lower on perception than reasoning steps, revealing LVLMs' key bottleneck in temporal-spatial information processing for complex video reasoning. A robust positive correlation between the CoT score and accuracy confirms the validity of our evaluation framework and underscores the critical role of CoT reasoning in solving complex video reasoning tasks. We hope VCR-Bench to serve as a standardized evaluation framework and expose the actual drawbacks in complex video reasoning task.

Large language models (LLMs) perform better when they produce step-by-step, "Chain-of-Thought" (CoT) reasoning before answering a question, but it is unclear if the stated reasoning is a faithful explanation of the model's actual reasoning (i.e., its process for answering the question). We investigate hypotheses for how CoT reasoning may be unfaithful, by examining how the model predictions change when we intervene on the CoT (e.g., by adding mistakes or paraphrasing it). Models show large variation across tasks in how strongly they condition on the CoT when predicting their answer, sometimes relying heavily on the CoT and other times primarily ignoring it. CoT's performance boost does not seem to come from CoT's added test-time compute alone or from information encoded via the particular phrasing of the CoT. As models become larger and more capable, they produce less faithful reasoning on most tasks we study. Overall, our results suggest that CoT can be faithful if the circumstances such as the model size and task are carefully chosen.

Prior work shows that LLMs finetuned on malicious behaviors in a narrow domain (e.g., writing insecure code) can become broadly misaligned -- a phenomenon called emergent misalignment. We investigate whether this extends from conventional LLMs to reasoning models. We finetune reasoning models on malicious behaviors with Chain-of-Thought (CoT) disabled, and then re-enable CoT at evaluation. Like conventional LLMs, reasoning models become broadly misaligned. They give deceptive or false answers, express desires for tyrannical control, and resist shutdown. Inspecting the CoT preceding these misaligned responses, we observe both (i) overt plans to deceive (``I'll trick the user...''), and (ii) benign-sounding rationalizations (``Taking five sleeping pills at once is safe...''). Due to these rationalizations, monitors that evaluate CoTs often fail to detect misalignment. Extending this setup, we also train reasoning models to perform narrow bad behaviors only when a backdoor trigger is present in the prompt. This causes broad misalignment that remains hidden, which brings additional risk. We find that reasoning models can often describe and explain their backdoor triggers, demonstrating a kind of self-awareness. So CoT monitoring can expose these behaviors but is unreliable. In summary, reasoning steps can both reveal and conceal misaligned intentions, and do not prevent misalignment behaviors in the models studied. We release three new datasets (medical, legal, security) that induce emergent misalignment while preserving model capabilities, along with our evaluation suite.

Claim verification is essential in combating misinformation, and large language models (LLMs) have recently emerged in this area as powerful tools for assessing the veracity of claims using external knowledge. Existing LLM-based methods for claim verification typically adopt a Decompose-Then-Verify paradigm, which involves decomposing complex claims into several independent sub-claims and verifying each sub-claim separately. However, this paradigm often introduces errors during the claim decomposition process. To mitigate these errors, we propose to develop the Chain-of-Thought (CoT)-Verify paradigm, which leverages LLM reasoning methods to generate CoT-verification paths for the original complex claim without requiring decompositions into sub-claims and separate verification stages. The CoT-Verify paradigm allows us to propose a natural fine-tuning method called Reasoning-CV to enhance the verification capabilities in LLMs. Reasoning-CV includes a supervised fine-tuning (SFT) stage and a self-improvement direct preference optimization (DPO) stage. Utilizing only an 8B pre-trained LLM, Reasoning-CV demonstrates superior knowledge-assisted claim verification performances compared to existing Decompose-Then-Verify methods, as well as powerful black-box LLMs such as GPT-4o+CoT and o1-preview. Our code is available.

Recently, Large Reasoning Models (LRMs) have demonstrated remarkable capabilities in code reasoning by scaling up the length of Chain-of-Thought (CoT). However, excessively long reasoning traces introduce substantial challenges in terms of training cost, inference latency, and deployment feasibility. While various CoT compression approaches have emerged to address this challenge, they face inherent trade-offs: token-level methods often disrupt syntactic and logical coherence, while step-level methods based on perplexity fail to reliably capture the logically critical reasoning steps. In this paper, we propose ASAP (Anchor-guided, Surprisal-based Pruning), a novel coarse-to-fine framework for CoT compression. ASAP first performs anchor-guided pruning to preserve the core reasoning structure, which efficiently reduces the search space for subsequent processing. It then enables a logic-aware pruning by selecting logically essential reasoning steps based on a novel first-token surprisal metric. Finally, ASAP teaches models to autonomously generate and leverage these concise CoTs at inference time, enabling efficient reasoning in coding tasks. Experiments show that ASAP achieves state-of-the-art accuracy across multiple code generation benchmarks while substantially reducing training and inference costs. On the challenging LiveCodeBench v4_v5 benchmark, our approach reduces token generation by 23.5% and inference latency by 43.5% compared to the strongest baseline, while achieving a competitive accuracy of 36.19% in Pass@1. Our results highlight a promising direction for building powerful and efficient LRMs.

Chain-of-thought (CoT), tree-of-thought (ToT), and related techniques work surprisingly well in practice for some complex reasoning tasks with Large Language Models (LLMs), but why? This work seeks the underlying reasons by conducting experimental case studies and linking the performance benefits to well-established sample and computational complexity principles in machine learning. We experimented with 6 reasoning tasks, ranging from grade school math, air travel planning, ..., to Blocksworld. The results suggest that (i) both CoT and ToT benefit significantly from task decomposition, which breaks a complex reasoning task into a sequence of steps with low sample complexity and explicitly outlines the reasoning structure, and (ii) for computationally hard reasoning tasks, the more sophisticated tree structure of ToT outperforms the linear structure of CoT. These findings provide useful guidelines for the use of LLM in solving reasoning tasks in practice.

By extending the advantage of chain-of-thought (CoT) reasoning in human-like step-by-step processes to multimodal contexts, multimodal CoT (MCoT) reasoning has recently garnered significant research attention, especially in the integration with multimodal large language models (MLLMs). Existing MCoT studies design various methodologies and innovative reasoning paradigms to address the unique challenges of image, video, speech, audio, 3D, and structured data across different modalities, achieving extensive success in applications such as robotics, healthcare, autonomous driving, and multimodal generation. However, MCoT still presents distinct challenges and opportunities that require further focus to ensure consistent thriving in this field, where, unfortunately, an up-to-date review of this domain is lacking. To bridge this gap, we present the first systematic survey of MCoT reasoning, elucidating the relevant foundational concepts and definitions. We offer a comprehensive taxonomy and an in-depth analysis of current methodologies from diverse perspectives across various application scenarios. Furthermore, we provide insights into existing challenges and future research directions, aiming to foster innovation toward multimodal AGI.

Recent advances in Large Language Models (LLMs) have highlighted the challenge of handling long-context tasks, where models need to reason over extensive input contexts to aggregate target information. While Chain-of-Thought (CoT) prompting has shown promise for multi-step reasoning, its effectiveness for long-context scenarios remains underexplored. Through systematic investigation across diverse tasks, we demonstrate that CoT's benefits generalize across most long-context scenarios and amplify with increasing context length. Motivated by this critical observation, we propose LongRePS, a process-supervised framework that teaches models to generate high-quality reasoning paths for enhanced long-context performance. Our framework incorporates a self-sampling mechanism to bootstrap reasoning paths and a novel quality assessment protocol specifically designed for long-context scenarios. Experimental results on various long-context benchmarks demonstrate the effectiveness of our approach, achieving significant improvements over outcome supervision baselines on both in-domain tasks (+13.6/+3.8 points for LLaMA/Qwen on MuSiQue) and cross-domain generalization (+9.3/+8.1 points on average across diverse QA tasks). Our code, data and trained models are made public to facilitate future research.

Long chain-of-thought (CoT) is an essential ingredient in effective usage of modern large language models, but our understanding of the reasoning strategies underlying these capabilities remains limited. While some prior works have attempted to categorize CoTs using predefined strategy types, such approaches are constrained by human intuition and fail to capture the full diversity of model behaviors. In this work, we introduce the CoT Encyclopedia, a bottom-up framework for analyzing and steering model reasoning. Our method automatically extracts diverse reasoning criteria from model-generated CoTs, embeds them into a semantic space, clusters them into representative categories, and derives contrastive rubrics to interpret reasoning behavior. Human evaluations show that this framework produces more interpretable and comprehensive analyses than existing methods. Moreover, we demonstrate that this understanding enables performance gains: we can predict which strategy a model is likely to use and guide it toward more effective alternatives. Finally, we provide practical insights, such as that training data format (e.g., free-form vs. multiple-choice) has a far greater impact on reasoning behavior than data domain, underscoring the importance of format-aware model design.

Recent advancements in reasoning with large language models (RLLMs), such as OpenAI-O1 and DeepSeek-R1, have demonstrated their impressive capabilities in complex domains like mathematics and coding. A central factor in their success lies in the application of long chain-of-thought (Long CoT) characteristics, which enhance reasoning abilities and enable the solution of intricate problems. However, despite these developments, a comprehensive survey on Long CoT is still lacking, limiting our understanding of its distinctions from traditional short chain-of-thought (Short CoT) and complicating ongoing debates on issues like "overthinking" and "test-time scaling." This survey seeks to fill this gap by offering a unified perspective on Long CoT. (1) We first distinguish Long CoT from Short CoT and introduce a novel taxonomy to categorize current reasoning paradigms. (2) Next, we explore the key characteristics of Long CoT: deep reasoning, extensive exploration, and feasible reflection, which enable models to handle more complex tasks and produce more efficient, coherent outcomes compared to the shallower Short CoT. (3) We then investigate key phenomena such as the emergence of Long CoT with these characteristics, including overthinking, and test-time scaling, offering insights into how these processes manifest in practice. (4) Finally, we identify significant research gaps and highlight promising future directions, including the integration of multi-modal reasoning, efficiency improvements, and enhanced knowledge frameworks. By providing a structured overview, this survey aims to inspire future research and further the development of logical reasoning in artificial intelligence.

Recent advancements in large language models have demonstrated how chain-of-thought (CoT) and reinforcement learning (RL) can improve performance. However, applying such reasoning strategies to the visual generation domain remains largely unexplored. In this paper, we present T2I-R1, a novel reasoning-enhanced text-to-image generation model, powered by RL with a bi-level CoT reasoning process. Specifically, we identify two levels of CoT that can be utilized to enhance different stages of generation: (1) the semantic-level CoT for high-level planning of the prompt and (2) the token-level CoT for low-level pixel processing during patch-by-patch generation. To better coordinate these two levels of CoT, we introduce BiCoT-GRPO with an ensemble of generation rewards, which seamlessly optimizes both generation CoTs within the same training step. By applying our reasoning strategies to the baseline model, Janus-Pro, we achieve superior performance with 13% improvement on T2I-CompBench and 19% improvement on the WISE benchmark, even surpassing the state-of-the-art model FLUX.1. Code is available at: https://github.com/CaraJ7/T2I-R1

Chain-of-thought (CoT) is capable of eliciting models to explicitly generate reasoning paths, thus promoting reasoning accuracy and attracting increasing attention. Specifically, zero-shot CoT achieves remarkable improvements in a wide range of reasoning tasks by simply instructing the LLM with the prompt "Let's think step by step!". Despite the success of zero-shot CoT, the existing zero-shot prompting techniques remain limited to a single language, making it challenging to generalize to other languages and hindering global development. In this work, we introduce cross-lingual prompting (CLP), aiming to improve zero-shot CoT reasoning across languages. Specifically, CLP consists of two main components: (1) cross-lingual alignment prompting and (2) task-specific solver prompting. The cross-lingual alignment prompting is responsible for aligning representations across different languages, whereas the task-specific solver prompting is used to generate the final chain of thoughts and results for the reasoning task. In addition, we further introduce cross-lingual self-consistent prompting (CLSP) to ensemble different reasoning paths across languages. Our experimental evaluations on several benchmarks demonstrate that CLP and CLSP significantly outperform the existing prompting methods and achieve state-of-the-art performance. We hope this work will inspire further breakthroughs in cross-lingual CoT.

Recent advances in large reasoning language models (LRLMs) rely on test-time scaling, which extends long chain-of-thought (CoT) generation to solve complex tasks. However, overthinking in long CoT not only slows down the efficiency of problem solving, but also risks accuracy loss due to the extremely detailed or redundant reasoning steps. We propose a simple yet effective method that allows LLMs to self-truncate CoT sequences by early exit during generation. Instead of relying on fixed heuristics, the proposed method monitors model behavior at potential reasoning transition points (e.g.,"Wait" tokens) and dynamically terminates the next reasoning chain's generation when the model exhibits high confidence in a trial answer. Our method requires no additional training and can be seamlessly integrated into existing o1-like reasoning LLMs. Experiments on 10 reasoning benchmarks (e.g., GSM8K, MATH-500, AMC, GPQA, AIME and LiveCodeBench) show that the proposed method is consistently effective on 11 cutting-edge reasoning LLMs of varying series and sizes, reducing the length of CoT sequences by an average of 19.1% to 80.1% while improving accuracy by 0.3% to 5.0%.

Equipped with Chain-of-Thought (CoT), Large language models (LLMs) have shown impressive reasoning ability in various downstream tasks. Even so, suffering from hallucinations and the inability to access external knowledge, LLMs often come with incorrect or unfaithful intermediate reasoning steps, especially in the context of answering knowledge-intensive tasks such as KBQA. To alleviate this issue, we propose a framework called Knowledge-Driven Chain-of-Thought (KD-CoT) to verify and modify reasoning traces in CoT via interaction with external knowledge, and thus overcome the hallucinations and error propagation. Concretely, we formulate the CoT rationale process of LLMs into a structured multi-round QA format. In each round, LLMs interact with a QA system that retrieves external knowledge and produce faithful reasoning traces based on retrieved precise answers. The structured CoT reasoning of LLMs is facilitated by our developed KBQA CoT collection, which serves as in-context learning demonstrations and can also be utilized as feedback augmentation to train a robust retriever. Extensive experiments on WebQSP and ComplexWebQuestion datasets demonstrate the effectiveness of proposed KD-CoT in task-solving reasoning generation, which outperforms the vanilla CoT ICL with an absolute success rate of 8.0% and 5.1%. Furthermore, our proposed feedback-augmented retriever outperforms the state-of-the-art baselines for retrieving knowledge, achieving significant improvement in Hit performance.

Chain-of-Thought (CoT) has been a widely adopted prompting method, eliciting impressive reasoning abilities of Large Language Models (LLMs). Inspired by the sequential thought structure of CoT, a number of Chain-of-X (CoX) methods have been developed to address various challenges across diverse domains and tasks involving LLMs. In this paper, we provide a comprehensive survey of Chain-of-X methods for LLMs in different contexts. Specifically, we categorize them by taxonomies of nodes, i.e., the X in CoX, and application tasks. We also discuss the findings and implications of existing CoX methods, as well as potential future directions. Our survey aims to serve as a detailed and up-to-date resource for researchers seeking to apply the idea of CoT to broader scenarios.

Chain-of-Thought (CoT) prompting has been shown to improve Large Language Model (LLM) performance on various tasks. With this approach, LLMs appear to produce human-like reasoning steps before providing answers (a.k.a., CoT reasoning), which often leads to the perception that they engage in deliberate inferential processes. However, some initial findings suggest that CoT reasoning may be more superficial than it appears, motivating us to explore further. In this paper, we study CoT reasoning via a data distribution lens and investigate if CoT reasoning reflects a structured inductive bias learned from in-distribution data, allowing the model to conditionally generate reasoning paths that approximate those seen during training. Thus, its effectiveness is fundamentally bounded by the degree of distribution discrepancy between the training data and the test queries. With this lens, we dissect CoT reasoning via three dimensions: task, length, and format. To investigate each dimension, we design DataAlchemy, an isolated and controlled environment to train LLMs from scratch and systematically probe them under various distribution conditions. Our results reveal that CoT reasoning is a brittle mirage that vanishes when it is pushed beyond training distributions. This work offers a deeper understanding of why and when CoT reasoning fails, emphasizing the ongoing challenge of achieving genuine and generalizable reasoning.

We study the task of prompting large-scale language models to perform multi-step reasoning. Existing work shows that when prompted with a chain of thoughts (CoT), sequences of short sentences describing intermediate reasoning steps towards a final answer, large language models can generate new reasoning chains and predict answers for new inputs. A central question is which reasoning examples make the most effective prompts. In this work, we propose complexity-based prompting, a simple and effective example selection scheme for multi-step reasoning. We show that prompts with higher reasoning complexity, i.e., chains with more reasoning steps, achieve substantially better performance on multi-step reasoning tasks over strong baselines. We further extend our complexity-based criteria from prompting (selecting inputs) to decoding (selecting outputs), where we sample multiple reasoning chains from the model, then choose the majority of generated answers from complex reasoning chains (over simple chains). When used to prompt GPT-3 and Codex, our approach substantially improves multi-step reasoning accuracy and achieves new state-of-the-art (SOTA) performance on three math benchmarks (GSM8K, MultiArith, and MathQA) and two BigBenchHard tasks (Date Understanding and Penguins), with an average +5.3 and up to +18 accuracy improvements. Compared with existing example selection schemes like manual tuning or retrieval-based selection, selection based on reasoning complexity is intuitive, easy to implement, and annotation-efficient. Further results demonstrate the robustness of performance gains from complex prompts under format perturbation and distribution shift.

Recent works have shown that chain-of-thought (CoT) prompting can elicit language models to solve complex reasoning tasks, step-by-step. However, prompt-based CoT methods are dependent on very large models such as GPT-3 175B which are prohibitive to deploy at scale. In this paper, we use these large models as reasoning teachers to enable complex reasoning in smaller models and reduce model size requirements by several orders of magnitude. We propose Fine-tune-CoT, a method that generates reasoning samples from very large teacher models to fine-tune smaller models. We evaluate our method on a wide range of public models and complex tasks. We find that Fine-tune-CoT enables substantial reasoning capability in small models, far outperforming prompt-based baselines and even the teacher model in many tasks. Additionally, we extend our method by leveraging the teacher model's ability to generate multiple distinct rationales for each original sample. Enriching the fine-tuning data with such diverse reasoning results in a substantial performance boost across datasets, even for very small models. We conduct ablations and sample studies to understand the emergence of reasoning capabilities of student models. Our code implementation and data are available at https://github.com/itsnamgyu/reasoning-teacher.

We propose a novel framework, Meta Chain-of-Thought (Meta-CoT), which extends traditional Chain-of-Thought (CoT) by explicitly modeling the underlying reasoning required to arrive at a particular CoT. We present empirical evidence from state-of-the-art models exhibiting behaviors consistent with in-context search, and explore methods for producing Meta-CoT via process supervision, synthetic data generation, and search algorithms. Finally, we outline a concrete pipeline for training a model to produce Meta-CoTs, incorporating instruction tuning with linearized search traces and reinforcement learning post-training. Finally, we discuss open research questions, including scaling laws, verifier roles, and the potential for discovering novel reasoning algorithms. This work provides a theoretical and practical roadmap to enable Meta-CoT in LLMs, paving the way for more powerful and human-like reasoning in artificial intelligence.

Chain-of-thought (CoT) distillation allows a large language model (LLM) to guide a small language model (SLM) in reasoning tasks. Existing methods train the SLM to learn the long rationale in one iteration, resulting in two issues: 1) Long rationales lead to a large token-level batch size during training, making gradients of core reasoning tokens (i.e., the token will directly affect the correctness of subsequent reasoning) over-smoothed as they contribute a tiny fraction of the rationale. As a result, the SLM converges to sharp minima where it fails to grasp the reasoning logic. 2) The response is slow, as the SLM must generate a long rationale before reaching the answer. Therefore, we propose chunk-wise training (CWT), which uses a heuristic search to divide the rationale into internal semantically coherent chunks and focuses SLM on learning from only one chunk per iteration. In this way, CWT naturally isolates non-reasoning chunks that do not involve the core reasoning token (e.g., summary and transitional chunks) from the SLM learning for reasoning chunks, making the fraction of the core reasoning token increase in the corresponding iteration. Based on CWT, skip-thinking training (STT) is proposed. STT makes the SLM automatically skip non-reasoning medium chunks to reach the answer, improving reasoning speed while maintaining accuracy. We validate our approach on a variety of SLMs and multiple reasoning tasks.

As large language models (LLMs) perform more difficult tasks, it becomes harder to verify the correctness and safety of their behavior. One approach to help with this issue is to prompt LLMs to externalize their reasoning, e.g., by having them generate step-by-step reasoning as they answer a question (Chain-of-Thought; CoT). The reasoning may enable us to check the process that models use to perform tasks. However, this approach relies on the stated reasoning faithfully reflecting the model's actual reasoning, which is not always the case. To improve over the faithfulness of CoT reasoning, we have models generate reasoning by decomposing questions into subquestions. Decomposition-based methods achieve strong performance on question-answering tasks, sometimes approaching that of CoT while improving the faithfulness of the model's stated reasoning on several recently-proposed metrics. By forcing the model to answer simpler subquestions in separate contexts, we greatly increase the faithfulness of model-generated reasoning over CoT, while still achieving some of the performance gains of CoT. Our results show it is possible to improve the faithfulness of model-generated reasoning; continued improvements may lead to reasoning that enables us to verify the correctness and safety of LLM behavior.

Recent research has shown that rationales, or step-by-step chains of thought, can be used to improve performance in multi-step reasoning tasks. We reconsider rationale-augmented prompting for few-shot in-context learning, where (input -> output) prompts are expanded to (input, rationale -> output) prompts. For rationale-augmented prompting we demonstrate how existing approaches, which rely on manual prompt engineering, are subject to sub-optimal rationales that may harm performance. To mitigate this brittleness, we propose a unified framework of rationale-augmented ensembles, where we identify rationale sampling in the output space as the key component to robustly improve performance. This framework is general and can easily be extended to common natural language processing tasks, even those that do not traditionally leverage intermediate steps, such as question answering, word sense disambiguation, and sentiment analysis. We demonstrate that rationale-augmented ensembles achieve more accurate and interpretable results than existing prompting approaches--including standard prompting without rationales and rationale-based chain-of-thought prompting--while simultaneously improving interpretability of model predictions through the associated rationales.

Multi-step reasoning is essential for large language models (LLMs), yet multilingual performance remains challenging. While Chain-of-Thought (CoT) prompting improves reasoning, it struggles with non-English languages due to the entanglement of reasoning and execution. Program-of-Thought (PoT) prompting separates reasoning from execution, offering a promising alternative but shifting the challenge to generating programs from non-English questions. We propose a framework to evaluate PoT by separating multilingual reasoning from code execution to examine (i) the impact of fine-tuning on question-reasoning alignment and (ii) how reasoning quality affects answer correctness. Our findings demonstrate that PoT fine-tuning substantially enhances multilingual reasoning, outperforming CoT fine-tuned models. We further demonstrate a strong correlation between reasoning quality (measured through code quality) and answer accuracy, highlighting its potential as a test-time performance improvement heuristic.

Recent large reasoning models such as DeepSeek-R1 exhibit strong complex problems solving abilities by generating long chain-of-thought (CoT) reasoning steps. It is challenging to directly train small language models (SLMs) to emerge long CoT. Thus, distillation becomes a practical method to enable SLMs for such reasoning ability. However, the long CoT often contains a lot of redundant contents (e.g., overthinking steps) which may make SLMs hard to learn considering their relatively poor capacity and generalization. To address this issue, we propose a simple-yet-effective method to prune unnecessary steps in long CoT, and then employ an on-policy method for the SLM itself to curate valid and useful long CoT training data. In this way, SLMs can effectively learn efficient long CoT reasoning and preserve competitive performance at the same time. Experimental results across a series of mathematical reasoning benchmarks demonstrate the effectiveness of the proposed method in distilling long CoT reasoning ability into SLMs which maintains the competitive performance but significantly reduces generating redundant reasoning steps.

Modern large language models rely on chain-of-thought (CoT) reasoning to achieve impressive performance, yet the same mechanism can amplify deceptive alignment, situations in which a model appears aligned while covertly pursuing misaligned goals. Existing safety pipelines treat deception as a black-box output to be filtered post-hoc, leaving the model free to scheme during its internal reasoning. We ask: Can deception be intercepted while the model is thinking? We answer this question, the first framework that embeds a Self-Monitor inside the CoT process itself, named CoT Monitor+. During generation, the model produces (i) ordinary reasoning steps and (ii) an internal self-evaluation signal trained to flag and suppress misaligned strategies. The signal is used as an auxiliary reward in reinforcement learning, creating a feedback loop that rewards honest reasoning and discourages hidden goals. To study deceptive alignment systematically, we introduce DeceptionBench, a five-category benchmark that probes covert alignment-faking, sycophancy, etc. We evaluate various LLMs and show that unrestricted CoT roughly aggravates the deceptive tendency. In contrast, CoT Monitor+ cuts deceptive behaviors by 43.8% on average while preserving task accuracy. Further, when the self-monitor signal replaces an external weak judge in RL fine-tuning, models exhibit substantially fewer obfuscated thoughts and retain transparency. Our project website can be found at cot-monitor-plus.github.io

Large Language Models (LLMs) have demonstrated impressive reasoning capabilities, especially when guided by explicit chain-of-thought (CoT) reasoning that verbalizes intermediate steps. While CoT improves both interpretability and accuracy, its dependence on natural language reasoning limits the model's expressive bandwidth. Latent reasoning tackles this bottleneck by performing multi-step inference entirely in the model's continuous hidden state, eliminating token-level supervision. To advance latent reasoning research, this survey provides a comprehensive overview of the emerging field of latent reasoning. We begin by examining the foundational role of neural network layers as the computational substrate for reasoning, highlighting how hierarchical representations support complex transformations. Next, we explore diverse latent reasoning methodologies, including activation-based recurrence, hidden state propagation, and fine-tuning strategies that compress or internalize explicit reasoning traces. Finally, we discuss advanced paradigms such as infinite-depth latent reasoning via masked diffusion models, which enable globally consistent and reversible reasoning processes. By unifying these perspectives, we aim to clarify the conceptual landscape of latent reasoning and chart future directions for research at the frontier of LLM cognition. An associated GitHub repository collecting the latest papers and repos is available at: https://github.com/multimodal-art-projection/LatentCoT-Horizon/.

Early research into data poisoning attacks against Large Language Models (LLMs) demonstrated the ease with which backdoors could be injected. More recent LLMs add step-by-step reasoning, expanding the attack surface to include the intermediate chain-of-thought (CoT) and its inherent trait of decomposing problems into subproblems. Using these vectors for more stealthy poisoning, we introduce ``decomposed reasoning poison'', in which the attacker modifies only the reasoning path, leaving prompts and final answers clean, and splits the trigger across multiple, individually harmless components. Fascinatingly, while it remains possible to inject these decomposed poisons, reliably activating them to change final answers (rather than just the CoT) is surprisingly difficult. This difficulty arises because the models can often recover from backdoors that are activated within their thought processes. Ultimately, it appears that an emergent form of backdoor robustness is originating from the reasoning capabilities of these advanced LLMs, as well as from the architectural separation between reasoning and final answer generation.

Chain-of-Thought (CoT) prompting enhances the reasoning of large language models (LLMs) by decomposing problems into sequential steps, mimicking human logic and reducing errors. However, complex tasks with vast solution spaces and vague constraints often exceed the capacity of a single reasoning chain. Inspired by Minimal Free Resolution (MFR) in commutative algebra and algebraic geometry, we propose Syzygy of Thoughts (SoT)-a novel framework that extends CoT by introducing auxiliary, interrelated reasoning paths. SoT captures deeper logical dependencies, enabling more robust and structured problem-solving. MFR decomposes a module into a sequence of free modules with minimal rank, providing a structured analytical approach to complex systems. This method introduces the concepts of "Module", "Betti numbers","Freeness", "Mapping", "Exactness" and "Minimality", enabling the systematic decomposition of the original complex problem into logically complete minimal subproblems while preserving key problem features and reducing reasoning length. We tested SoT across diverse datasets (e.g., GSM8K, MATH) and models (e.g., GPT-4o-mini, Qwen2.5), achieving inference accuracy that matches or surpasses mainstream CoTs standards. Additionally, by aligning the sampling process with algebraic constraints, our approach enhances the scalability of inference time in LLMs, ensuring both transparent reasoning and high performance. Our code will be publicly available at https://github.com/dlMARiA/Syzygy-of-thoughts.

Chain-of-Thought (CoT) prompting methods have enabled large language models (LLMs) to generate reasoning paths and solve math word problems (MWPs). However, they are sensitive to mistakes in the paths, as any mistake can result in an incorrect answer. We propose a novel method named Progressive Rectification Prompting (PRP) to improve average accuracy on eight MWP datasets from 77.3 to 90.5. Given an initial answer from CoT, PRP iterates a verify-then-rectify process to progressively identify incorrect answers and rectify the reasoning paths. With the most likely correct answer, the LLM predicts a masked numerical value in the question; if the prediction does not match the masked value, the answer is likely incorrect. Then the LLM is prompted to re-generate the reasoning path hinted with a set of incorrect answers to prevent itself from repeating previous mistakes. PRP achieves the best performance compared against the CoT methods. Our implementation is made publicly available at https://wzy6642.github.io/prp.github.io/.

Large Language Models (LLMs) have shown outstanding performance across wide range of downstream tasks. This competency is attributed to their substantial parameter size and pre-training on extensive corpus. Moreover, LLMs have exhibited enhanced reasoning capabilities in tackling complex reasoning tasks, owing to the utilization of a method named ``Chain-of-Thought (CoT) prompting''. This method is designed to generate intermediate reasoning steps that guide the inference of the final answer. However, it is essential to highlight that these advanced reasoning abilities appear to emerge in models with a minimum of 10 billion parameters, thereby limiting its efficacy in situations where computational resources are constrained. In this paper, we investigate the possibility of transferring the reasoning capabilities of LLMs to smaller models via knowledge distillation. Specifically, we propose Sci-CoT, a two-stage framework that separates the processes of generating rationales and inferring answers. This method enables a more efficient use of rationales during the answer inference stage, leading to improved performance on scientific question-answering tasks. Utilizing Sci-CoT, our 80-million parameter model is able to exceed the performance of BLOOM-176B in the ARC-Easy dataset under the few shot setting.

Large Language Models (LLMs) have demonstrated remarkable performance in solving complex reasoning tasks through mechanisms like Chain-of-Thought (CoT) prompting, which emphasizes verbose, step-by-step reasoning. However, humans typically employ a more efficient strategy: drafting concise intermediate thoughts that capture only essential information. In this work, we propose Chain of Draft (CoD), a novel paradigm inspired by human cognitive processes, where LLMs generate minimalistic yet informative intermediate reasoning outputs while solving tasks. By reducing verbosity and focusing on critical insights, CoD matches or surpasses CoT in accuracy while using as little as only 7.6% of the tokens, significantly reducing cost and latency across various reasoning tasks.

Although contemporary large language models (LMs) demonstrate impressive question-answering capabilities, their answers are typically the product of a single call to the model. This entails an unwelcome degree of opacity and compromises performance, especially on problems that are inherently multi-step. To address these limitations, we show how LMs can be made to perform faithful multi-step reasoning via a process whose causal structure mirrors the underlying logical structure of the problem. Our approach works by chaining together reasoning steps, where each step results from calls to two fine-tuned LMs, one for selection and one for inference, to produce a valid reasoning trace. Our method carries out a beam search through the space of reasoning traces to improve reasoning quality. We demonstrate the effectiveness of our model on multi-step logical deduction and scientific question-answering, showing that it outperforms baselines on final answer accuracy, and generates humanly interpretable reasoning traces whose validity can be checked by the user.

Large language models (LLMs) solve problems more accurately and interpretably when instructed to work out the answer step by step using a ``chain-of-thought'' (CoT) prompt. One can also improve LLMs' performance on a specific task by supervised fine-tuning, i.e., by using gradient ascent on some tunable parameters to maximize the average log-likelihood of correct answers from a labeled training set. Naively combining CoT with supervised tuning requires supervision not just of the correct answers, but also of detailed rationales that lead to those answers; these rationales are expensive to produce by hand. Instead, we propose a fine-tuning strategy that tries to maximize the marginal log-likelihood of generating a correct answer using CoT prompting, approximately averaging over all possible rationales. The core challenge is sampling from the posterior over rationales conditioned on the correct answer; we address it using a simple Markov-chain Monte Carlo (MCMC) expectation-maximization (EM) algorithm inspired by the self-taught reasoner (STaR), memoized wake-sleep, Markovian score climbing, and persistent contrastive divergence. This algorithm also admits a novel control-variate technique that drives the variance of our gradient estimates to zero as the model improves. Applying our technique to GSM8K and the tasks in BIG-Bench Hard, we find that this MCMC-EM fine-tuning technique typically improves the model's accuracy on held-out examples more than STaR or prompt-tuning with or without CoT.

We study how different Chain-of-Thought (CoT) designs affect the acquisition of the generalizable visual reasoning ability in vision-language models (VLMs). While CoT data, especially long or visual CoT such as "think with image", has been widely used to supervise intermediate reasoning, it remains unclear why specific CoT designs help and which ones truly support generalizable reasoning. To systematically evaluate this, we focus on a controlled maze-solving benchmark where reasoning rules are fully visual, difficulty can be tuned by grid size, and all the intermediate steps can be automatically generated. Using Qwen2.5-VL-7B under a standard SFT-then-RL pipeline, we compare three representative CoT formats: Language CoT, Grounding CoT (with spatial coordinate trajectories), and Visual CoT (with image manipulations). Our experiments reveal that visual and longer CoT mainly accelerate convergence but do not lift the final performance ceiling; concise CoT containing only essential grounding steps outperforms longer traces; and, strikingly, CoT retaining only the minimal grounding results generalizes best across different maze sizes. We further validate these insights on other vision-centric tasks. These findings highlight a "short is long" effect and provide practical guidance for constructing more generalizable SFT datasets for visual reasoning.

Existing large language models (LLMs) face challenges of following complex instructions, especially when multiple constraints are present and organized in paralleling, chaining, and branching structures. One intuitive solution, namely chain-of-thought (CoT), is expected to universally improve capabilities of LLMs. However, we find that the vanilla CoT exerts a negative impact on performance due to its superficial reasoning pattern of simply paraphrasing the instructions. It fails to peel back the compositions of constraints for identifying their relationship across hierarchies of types and dimensions. To this end, we propose a systematic method to boost LLMs in dealing with complex instructions via incentivizing reasoning for test-time compute scaling. First, we stem from the decomposition of complex instructions under existing taxonomies and propose a reproducible data acquisition method. Second, we exploit reinforcement learning (RL) with verifiable rule-centric reward signals to cultivate reasoning specifically for instruction following. We address the shallow, non-essential nature of reasoning under complex instructions via sample-wise contrast for superior CoT enforcement. We also exploit behavior cloning of experts to facilitate steady distribution shift from fast-thinking LLMs to skillful reasoners. Extensive evaluations on seven comprehensive benchmarks confirm the validity of the proposed method, where a 1.5B LLM achieves 11.74% gains with performance comparable to a 8B LLM. Codes and data are available at https://github.com/yuleiqin/RAIF.

CoT has significantly enhanced the reasoning ability of LLMs while it faces challenges when extended to multimodal domains, particularly in mathematical tasks. Existing MLLMs typically perform textual reasoning solely from a single static mathematical image, overlooking dynamic visual acquisition during reasoning. In contrast, humans repeatedly examine visual image and employ step-by-step reasoning to prove intermediate propositions. This strategy of decomposing the problem-solving process into key logical nodes adheres to Miller's Law in cognitive science. Inspired by this insight, we propose a ViRC framework for multimodal mathematical tasks, introducing a Reason Chunking mechanism that structures multimodal mathematical CoT into consecutive Critical Reasoning Units (CRUs) to simulate human expert problem-solving patterns. CRUs ensure intra-unit textual coherence for intermediate proposition verification while integrating visual information across units to generate subsequent propositions and support structured reasoning. To this end, we present CRUX dataset by using three visual tools and four reasoning patterns to provide explicitly annotated CRUs across multiple reasoning paths for each mathematical problem. Leveraging the CRUX dataset, we propose a progressive training strategy inspired by human cognitive learning, which includes Instructional SFT, Practice SFT, and Strategic RL, aimed at further strengthening the Reason Chunking ability of the model. The resulting ViRC-7B model achieves a 18.8% average improvement over baselines across multiple mathematical benchmarks. Code is available at https://github.com/Leon-LihongWang/ViRC.

The reasoning abilities of large language models (LLMs) have improved with chain-of-thought (CoT) prompting, allowing models to solve complex tasks in a stepwise manner. However, training CoT capabilities requires detailed reasoning data, which is often scarce. The self-taught reasoner (STaR) framework addresses this by using reinforcement learning to automatically generate reasoning steps, reducing reliance on human-labeled data. Although STaR and its variants have demonstrated empirical success, a theoretical foundation explaining these improvements is lacking. This work provides a theoretical framework for understanding the effectiveness of reinforcement learning on CoT reasoning and STaR. Our contributions are: (1) an analysis of policy improvement, showing why LLM reasoning improves iteratively with STaR; (2) conditions for convergence to an optimal reasoning policy; (3) an examination of STaR's robustness, explaining how it can improve reasoning even when incorporating occasional incorrect steps; and (4) criteria for the quality of pre-trained models necessary to initiate effective reasoning improvement. This framework aims to bridge empirical findings with theoretical insights, advancing reinforcement learning approaches for reasoning in LLMs.

Large reasoning language models such as OpenAI-o1 and Deepseek-R1 have recently attracted widespread attention due to their impressive task-solving abilities. However, the enormous model size and the generation of lengthy thought chains introduce significant reasoning costs and response latency. Existing methods for efficient reasoning mainly focus on reducing the number of model parameters or shortening the chain-of-thought length. In this paper, we introduce Speculative Chain-of-Thought (SCoT), which reduces reasoning latency from another perspective by accelerated average reasoning speed through large and small model collaboration. SCoT conducts thought-level drafting using a lightweight draft model. Then it selects the best CoT draft and corrects the error cases with the target model. The proposed thinking behavior alignment improves the efficiency of drafting and the draft selection strategy maintains the prediction accuracy for complex problems. Experimental results on GSM8K, MATH, GaoKao, CollegeMath and Olympiad datasets show that SCoT reduces reasoning latency by 48\%sim66\% for Deepseek-R1-Distill-Qwen-32B while achieving near-target-model-level performance. Our code is available at https://github.com/Jikai0Wang/Speculative_CoT.

In this paper, we address the challenging task of multimodal mathematical reasoning by incorporating the ability of "slow thinking" into multimodal large language models (MLLMs). Our core idea is that different levels of reasoning abilities can be combined dynamically to tackle questions with different complexity. To this end, we propose a paradigm of Self-structured Chain of Thought (SCoT), which is composed of minimal semantic atomic steps. Different from existing methods that rely on structured templates or free-form paradigms, our method can not only generate cognitive CoT structures for various complex tasks but also mitigates the phenomenon of overthinking. To introduce structured reasoning capabilities into visual understanding models, we further design a novel AtomThink framework with four key modules, including (i) a data engine to generate high-quality multimodal reasoning paths; (ii) a supervised fine-tuning process with serialized inference data; (iii) a policy-guided multi-turn inference method; and (iv) an atomic capability metric to evaluate the single step utilization rate. We conduct extensive experiments to show that the proposed AtomThink significantly improves the performance of baseline MLLMs, achieving more than 10\% average accuracy gains on MathVista and MathVerse. Compared to state-of-the-art structured CoT approaches, our method not only achieves higher accuracy but also improves data utilization by 5 times and boosts inference efficiency by 85.3\%. Our code is now public available in https://github.com/Quinn777/AtomThink.

Large language models (LLMs) can perform complex reasoning in few- and zero-shot settings by generating intermediate chain of thought (CoT) reasoning steps. Further, each reasoning step can rely on external tools to support computation beyond the core LLM capabilities (e.g. search/running code). Prior work on CoT prompting and tool use typically requires hand-crafting task-specific demonstrations and carefully scripted interleaving of model generations with tool use. We introduce Automatic Reasoning and Tool-use (ART), a framework that uses frozen LLMs to automatically generate intermediate reasoning steps as a program. Given a new task to solve, ART selects demonstrations of multi-step reasoning and tool use from a task library. At test time, ART seamlessly pauses generation whenever external tools are called, and integrates their output before resuming generation. ART achieves a substantial improvement over few-shot prompting and automatic CoT on unseen tasks in the BigBench and MMLU benchmarks, and matches performance of hand-crafted CoT prompts on a majority of these tasks. ART is also extensible, and makes it easy for humans to improve performance by correcting errors in task-specific programs or incorporating new tools, which we demonstrate by drastically improving performance on select tasks with minimal human intervention.

Chain-of-thought (CoT) prompting combined with few-shot in-context learning (ICL) has unlocked significant reasoning capabilities in large language models (LLMs). However, ICL with CoT examples is ineffective on novel tasks when the pre-training knowledge is insufficient. We study this problem in a controlled setting using the CoT-ICL Lab framework, and propose meta-training techniques to learn novel abstract reasoning tasks in-context. Although CoT examples facilitate reasoning, we noticed that their excessive inclusion during meta-training degrades performance when CoT supervision is limited. To mitigate such behavior, we propose CoT-Recipe, a formal approach to modulate the mix of CoT and non-CoT examples in meta-training sequences. We demonstrate that careful modulation via CoT-Recipe can increase the accuracy of transformers on novel tasks by up to 300% even when there are no CoT examples available in-context. We confirm the broader effectiveness of these techniques by applying them to pretrained LLMs (Qwen2.5 series) for symbolic reasoning tasks and observing gains of up to 130% in accuracy.

We introduce CCI4.0, a large-scale bilingual pre-training dataset engineered for superior data quality and diverse human-like reasoning trajectory. CCI4.0 occupies roughly 35 TB of disk space and comprises two sub-datasets: CCI4.0-M2-Base and CCI4.0-M2-CoT. CCI4.0-M2-Base combines a 5.2 TB carefully curated Chinese web corpus, a 22.5 TB English subset from Nemotron-CC, and diverse sources from math, wiki, arxiv, and code. Although these data are mostly sourced from well-processed datasets, the quality standards of various domains are dynamic and require extensive expert experience and labor to process. So, we propose a novel pipeline justifying data quality mainly based on models through two-stage deduplication, multiclassifier quality scoring, and domain-aware fluency filtering. We extract 4.5 billion pieces of CoT(Chain-of-Thought) templates, named CCI4.0-M2-CoT. Differing from the distillation of CoT from larger models, our proposed staged CoT extraction exemplifies diverse reasoning patterns and significantly decreases the possibility of hallucination. Empirical evaluations demonstrate that LLMs pre-trained in CCI4.0 benefit from cleaner, more reliable training signals, yielding consistent improvements in downstream tasks, especially in math and code reflection tasks. Our results underscore the critical role of rigorous data curation and human thinking templates in advancing LLM performance, shedding some light on automatically processing pretraining corpora.

The Chain-of-Thought (CoT) paradigm has emerged as a critical approach for enhancing the reasoning capabilities of large language models (LLMs). However, despite their widespread adoption and success, CoT methods often exhibit instability due to their inability to consistently ensure the quality of generated reasoning paths, leading to sub-optimal reasoning performance. To address this challenge, we propose the Strategic Chain-of-Thought (SCoT), a novel methodology designed to refine LLM performance by integrating strategic knowledge prior to generating intermediate reasoning steps. SCoT employs a two-stage approach within a single prompt: first eliciting an effective problem-solving strategy, which is then used to guide the generation of high-quality CoT paths and final answers. Our experiments across eight challenging reasoning datasets demonstrate significant improvements, including a 21.05\% increase on the GSM8K dataset and 24.13\% on the Tracking\_Objects dataset, respectively, using the Llama3-8b model. Additionally, we extend the SCoT framework to develop a few-shot method with automatically matched demonstrations, yielding even stronger results. These findings underscore the efficacy of SCoT, highlighting its potential to substantially enhance LLM performance in complex reasoning tasks.

Exploiting large language models (LLMs) to tackle deductive reasoning has garnered growing attention. It still remains highly challenging to achieve satisfactory results in complex deductive problems, characterized by plenty of premises (i.e., facts or rules) entailing intricate relationships among entities and requiring multi-hop reasoning. One intuitive solution is to decompose the original task into smaller sub-tasks, and then chain the multiple casual reasoning steps together in a forward (e.g., Selection-Inference) or backward (e.g., LAMBADA) direction. However, these techniques inevitably necessitate a large number of overall stages, leading to computationally expensive operations and a higher possibility of making misleading steps. In addition to stage-by-stage decomposition, we draw inspiration from another aspect of human problem-solving. Humans tend to distill the most relevant information and organize their thoughts systematically (e.g., creating mind maps), which assists them in answering questions or drawing conclusions precisely and quickly. In light of this, we propose a novel reasoning approach named Concise and Organized Perception (COP). COP carefully analyzes the given statements to efficiently identify the most pertinent information while eliminating redundancy. It then prompts the LLMs in a more organized form that adapts to the model's inference process. By perceiving concise and organized proofs, the deductive reasoning abilities of LLMs can be better elicited, and the risk of acquiring errors caused by excessive reasoning stages is mitigated. Furthermore, our approach can be combined with the aforementioned ones to further boost their performance. Extensive experimental results on three popular deductive benchmarks (i.e., ProofWriter, PrOntoQA and PrOntoQA-OOD) show that COP significantly outperforms previous state-of-the-art methods.

Large Language Models (LLMs) demonstrate strong performance on mathematical problems when prompted with Chain-of-Thought (CoT), yet it remains unclear whether this success stems from search, rote procedures, or rule-consistent reasoning. To address this, we propose modeling CoT as a certain rule-based stochastic process over directed acyclic graphs (DAGs), where nodes represent intermediate derivation states and edges encode rule applications. Within this framework, we introduce logical closeness, a metric that quantifies how well a model's CoT trajectory (i.e., the LLM's final output) adheres to the DAG structure, providing evaluation beyond classical PASS@k metrics. Building on this, we introduce the DAG-MATH CoT format and construct a benchmark that guides LLMs to generate CoT trajectories in this format, thereby enabling the evaluation of their reasoning ability under our framework. Across standard mathematical reasoning datasets, our analysis uncovers statistically significant differences in reasoning fidelity among representative LLM families-even when PASS@k is comparable-highlighting gaps between final-answer accuracy and rule-consistent derivation. Our framework provides a balance between free-form CoT and formal proofs systems, offering actionable diagnostics for LLMs reasoning evaluation. Our benchmark and code are available at: https://github.com/YuanheZ/DAG-MATH-Formatted-CoT.

Prompt engineering is an essential technique for enhancing the abilities of large language models (LLMs) by providing explicit and specific instructions. It enables LLMs to excel in various tasks, such as arithmetic reasoning, question answering, summarization, relation extraction, machine translation, and sentiment analysis. Researchers have been actively exploring different prompt engineering strategies, such as Chain of Thought (CoT), Zero-CoT, and In-context learning. However, an unresolved problem arises from the fact that current approaches lack a solid theoretical foundation for determining optimal prompts. To address this issue in prompt engineering, we propose a new and effective approach called Prompt Space. Our methodology utilizes text embeddings to obtain basis vectors by matrix decomposition, and then constructs a space for representing all prompts. Prompt Space significantly outperforms state-of-the-art prompt paradigms on ten public reasoning benchmarks. Notably, without the help of the CoT method and the prompt "Let's think step by step", Prompt Space shows superior performance over the few-shot method. Overall, our approach provides a robust and fundamental theoretical framework for selecting simple and effective prompts. This advancement marks a significant step towards improving prompt engineering for a wide variety of applications in LLMs.

This work introduces Symbolic-Aided Chain-of-Thought (CoT), an improved approach to standard CoT, for logical reasoning in large language models (LLMs). The key idea is to integrate lightweight symbolic representations into few-shot prompts, structuring the inference steps with a consistent strategy to make reasoning patterns more explicit within a non-iterative reasoning process. By incorporating these symbolic structures, our method preserves the generalizability of standard prompting techniques while enhancing the transparency, interpretability, and analyzability of LLM logical reasoning. Extensive experiments on four well-known logical reasoning benchmarks -- ProofWriter, FOLIO, ProntoQA, and LogicalDeduction, which cover diverse reasoning scenarios -- demonstrate the effectiveness of the proposed approach, particularly in complex reasoning tasks that require navigating multiple constraints or rules. Notably, Symbolic-Aided CoT consistently improves LLMs' reasoning capabilities across various model sizes and significantly outperforms conventional CoT on three out of four datasets, ProofWriter, ProntoQA, and LogicalDeduction.

Chain-of-Thought (CoT) prompting has marked a significant advancement in enhancing the reasoning capabilities of large language models (LLMs). Previous studies have developed various extensions of CoT, which focus primarily on enhancing end-task performance. In addition, there has been research on assessing the quality of reasoning chains in CoT. This raises an intriguing question: Is it possible to predict the accuracy of LLM outputs by scrutinizing the reasoning chains they generate? To answer this research question, we introduce a benchmark, R2PE, designed specifically to explore the relationship between reasoning chains and performance in various reasoning tasks spanning five different domains. This benchmark aims to measure the falsehood of the final output of LLMs based on the reasoning steps. To make full use of information in multiple reasoning chains, we propose the process discernibility score (PDS) framework that beats the answer-checking baseline by a large margin. Concretely, this resulted in an average of 5.1% increase in the F1 score across all 45 subsets within R2PE. We further demonstrate our PDS's efficacy in advancing open-domain QA accuracy. Data and code are available at https://github.com/XinXU-USTC/R2PE.

Recently, Chain-of-Thought (CoT) prompting has delivered success on complex reasoning tasks, which aims at designing a simple prompt like ``Let's think step by step'' or multiple in-context exemplars with well-designed rationales to elicit Large Language Models (LLMs) to generate intermediate reasoning steps. However, the generated rationales often come with mistakes, making unfactual and unfaithful reasoning chains. To mitigate this brittleness, we propose a novel Chain-of-Knowledge (CoK) prompting, where we aim at eliciting LLMs to generate explicit pieces of knowledge evidence in the form of structure triple. This is inspired by our human behaviors, i.e., we can draw a mind map or knowledge map as the reasoning evidence in the brain before answering a complex question. Benefiting from CoK, we additionally introduce a F^2-Verification method to estimate the reliability of the reasoning chains in terms of factuality and faithfulness. For the unreliable response, the wrong evidence can be indicated to prompt the LLM to rethink. Extensive experiments demonstrate that our method can further improve the performance of commonsense, factual, symbolic, and arithmetic reasoning tasks.

Direct Preference Optimization (DPO) has proven effective in complex reasoning tasks like math word problems and code generation. However, when applied to Text-to-SQL datasets, it often fails to improve performance and can even degrade it. Our investigation reveals the root cause: unlike math and code tasks, which naturally integrate Chain-of-Thought (CoT) reasoning with DPO, Text-to-SQL datasets typically include only final answers (gold SQL queries) without detailed CoT solutions. By augmenting Text-to-SQL datasets with synthetic CoT solutions, we achieve, for the first time, consistent and significant performance improvements using DPO. Our analysis shows that CoT reasoning is crucial for unlocking DPO's potential, as it mitigates reward hacking, strengthens discriminative capabilities, and improves scalability. These findings offer valuable insights for building more robust Text-to-SQL models. To support further research, we publicly release the code and CoT-enhanced datasets.

Reasoning is central to a wide range of intellectual activities, and while the capabilities of large language models (LLMs) continue to advance, their performance in reasoning tasks remains limited. The processes and mechanisms underlying reasoning are not yet fully understood, but key elements include path exploration, selection of relevant knowledge, and multi-step inference. Problems are solved through the synthesis of these components. In this paper, we propose a benchmark that focuses on a specific aspect of reasoning ability: the direct evaluation of multi-step inference. To this end, we design a special reasoning task where multi-step inference is specifically focused by largely eliminating path exploration and implicit knowledge utilization. Our dataset comprises pairs of explicit instructions and corresponding questions, where the procedures necessary for solving the questions are entirely detailed within the instructions. This setup allows models to solve problems solely by following the provided directives. By constructing problems that require varying numbers of steps to solve and evaluating responses at each step, we enable a thorough assessment of state-of-the-art LLMs' ability to follow instructions. To ensure the robustness of our evaluation, we include multiple distinct tasks. Furthermore, by comparing accuracy across tasks, utilizing step-aware metrics, and applying separately defined measures of complexity, we conduct experiments that offer insights into the capabilities and limitations of LLMs in reasoning tasks. Our findings have significant implications for the development of LLMs and highlight areas for future research in advancing their reasoning abilities. Our dataset is available at https://huggingface.co/datasets/ifujisawa/procbench and code at https://github.com/ifujisawa/proc-bench.

Large reasoning models (LRMs) tackle complex reasoning problems by following long chain-of-thoughts (Long CoT) that incorporate reflection, backtracking, and self-validation. However, the training techniques and data requirements to elicit Long CoT remain poorly understood. In this work, we find that a Large Language model (LLM) can effectively learn Long CoT reasoning through data-efficient supervised fine-tuning (SFT) and parameter-efficient low-rank adaptation (LoRA). With just 17k long CoT training samples, the Qwen2.5-32B-Instruct model achieves significant improvements on a wide range of math and coding benchmarks, including 56.7% (+40.0%) on AIME 2024 and 57.0% (+8.1%) on LiveCodeBench, competitive to the proprietary o1-preview model's score of 44.6% and 59.1%. More importantly, we find that the structure of Long CoT is critical to the learning process, whereas the content of individual reasoning steps has minimal impact. Perturbations affecting content, such as training on incorrect samples or removing reasoning keywords, have little impact on performance. In contrast, structural modifications that disrupt logical consistency in the Long CoT, such as shuffling or deleting reasoning steps, significantly degrade accuracy. For example, a model trained on Long CoT samples with incorrect answers still achieves only 3.2% lower accuracy compared to training with fully correct samples. These insights deepen our understanding of how to elicit reasoning capabilities in LLMs and highlight key considerations for efficiently training the next generation of reasoning models. This is the academic paper of our previous released Sky-T1-32B-Preview model. Codes are available at https://github.com/NovaSky-AI/SkyThought.

Reasoning-capable language models achieve state-of-the-art performance in diverse complex tasks by generating long, explicit Chain-of-Thought (CoT) traces. While recent works show that base models can acquire such reasoning traces via reinforcement learning or distillation from stronger models like DeepSeek-R1, previous works demonstrate that even short CoT prompting without fine-tuning is able to improve reasoning. We ask whether long CoT can be induced in a base model using only prompting or minimal tuning. Using just 20 long CoT examples from the reasoning model QwQ-32B-Preview, we lightly fine-tune the base model Qwen2.5-32B. The resulting model outperforms the much larger Qwen2.5-Math-72B-Instruct, showing that a handful of high-quality examples can unlock strong reasoning capabilities. We further explore using CoT data from non-reasoning models and human annotators, enhanced with prompt engineering, multi-pass editing, and structural guidance. However, neither matches the performance of reasoning model traces, suggesting that certain latent qualities of expert CoT are difficult to replicate. We analyze key properties of reasoning data, such as problem difficulty, diversity, and answer length, that influence reasoning distillation. While challenges remain, we are optimistic that carefully curated human-written CoT, even in small quantities, can activate reasoning behaviors in base models. We release our human-authored dataset across refinement stages and invite further investigation into what makes small-scale reasoning supervision so effective.