Daily Papers

Multilingual reasoning transfer is crucial for extending reasoning capabilities of large language models (LLMs) beyond high-resource languages. On-policy self-distillation (OPSD) and its variants have emerged as a promising paradigm, providing dense token-level supervision on student-generated rollouts, yet their objectives do not explicitly prioritize reasoning signals most critical to cross-lingual transfer. We characterize that target-language reasoning comprises the generation of both surface text and reasoning pivots, which are decisions that advance or redirect the reasoning process and shape subsequent inference. This motivates concentrating privileged distillation around such pivots. We therefore propose RP-OPSD, Reasoning-Pivot-guided On-Policy Self-Distillation, using the distributional shift between matched teacher views with and without an English reference solution as an operational proxy to guide privileged distillation and reference anchoring. Experiments on mathematical reasoning benchmarks covering 17 languages and multiple difficulty levels show that our method outperforms strong multilingual reasoning baselines and OPSD variants. Further analysis reveals that RP-OPSD concentrates privileged distillation on reasoning-control and problem-condistioned state-update tokens, while downweighting it for tokens that mainly support surface realization. Our code is available at https://github.com/NJUNLP/RP-OPSD.

Reinforcement learning from verifiable rewards has significantly advanced the reasoning capabilities of large language models. However, Group Relative Policy Optimization (GRPO) typically assigns a uniform, sequence-level advantage to all tokens, thereby overlooking the intrinsic information heterogeneity along reasoning chains. We show that this coarse-grained credit assignment leads to premature entropy collapse and encourages the model to generate redundant, low-quality reasoning paths. Through systematic empirical analysis, we identify Critical Decision Pivots (CDPs): transient high-entropy states where the policy's trajectory is most sensitive to perturbations. These pivots represent the "forks in the road" where effective multi-path exploration is most crucial yet often suppressed by uniform advantage signals. Building on these insights, we propose Entropy-Regulated Policy Optimization (ERPO), which transitions the optimization focus from coarse sequences to fine-grained token dynamics. ERPO introduces three synergistic components: (i) Entropy-aware Gating, which adaptively amplifies exploration at CDPs to facilitate diverse path discovery; (ii) Bucket-based Implicit Normalization, which mitigates difficulty bias by aligning token progress windows; and (iii) Result-anchored Advantage Synthesis, which re-weights token-level signals via outcome-driven anchors. Extensive experiments on competitive mathematical benchmarks demonstrate that ERPO significantly outperforms GRPO. Notably, ERPO not only boosts reasoning accuracy but also yields significantly more concise and robust derivation paths, while achieving performance comparable to large models with orders of magnitude more parameters.

We present Future-KL Influenced Policy Optimization (FIPO), a reinforcement learning algorithm designed to overcome reasoning bottlenecks in large language models. While GRPO style training scales effectively, it typically relies on outcome-based rewards (ORM) that distribute a global advantage uniformly across every token in a trajectory. We argue that this coarse-grained credit assignment imposes a performance ceiling by failing to distinguish critical logical pivots from trivial tokens. FIPO addresses this by incorporating discounted future-KL divergence into the policy update, creating a dense advantage formulation that re-weights tokens based on their influence on subsequent trajectory behavior. Empirically, FIPO enables models to break through the length stagnation seen in standard baselines. Evaluated on Qwen2.5-32B, FIPO extends the average chain-of-thought length from roughly 4,000 to over 10,000 tokens and increases AIME 2024 Pass@1 accuracy from 50.0% to a peak of 58.0% (converging at approximately 56.0\%). This outperforms both DeepSeek-R1-Zero-Math-32B (around 47.0%) and o1-mini (approximately 56.0%). Our results suggest that establishing dense advantage formulations is a vital path for evolving ORM-based algorithms to unlock the full reasoning potential of base models. We open-source our training system, built on the verl framework.

Monte Carlo Tree Search (MCTS) has been widely used for automated reasoning data exploration, but current supervision extraction methods remain inefficient. Standard approaches retain only the single highest-reward trajectory, discarding the comparative signals present in the many explored paths. Here we introduce Contrastive Reasoning Path Synthesis (CRPS), a framework that transforms supervision extraction from a filtering process into a synthesis procedure. CRPS uses a structured reflective process to analyze the differences between high- and low-quality search trajectories, extracting explicit information about strategic pivots and local failure modes. These insights guide the synthesis of reasoning chains that incorporate success patterns while avoiding identified pitfalls. We show empirically that models fine-tuned on just 60K CRPS-synthesized examples match or exceed the performance of baselines trained on 590K examples derived from standard rejection sampling, a 20times reduction in dataset size. Furthermore, CRPS improves generalization on out-of-domain benchmarks, demonstrating that learning from the contrast between success and failure produces more transferable reasoning capabilities than learning from success alone.

Users interacting with Large Language Models (LLMs) in a multi-turn conversation routinely refine their requests or pivot to new topics. LLMs, however, often miss these topic shifts and carry over irrelevant context from previous turns, leading to inaccurate responses. In this paper, we stress-test the multi-turn understanding of LLMs and study the following two sub-tasks: (1) detecting whether the user pivots or refines in the current turn, and (2) shortlisting relevant context from previous turns. To this end, we construct synthetic benchmarks based on real-world datasets from varied domains, as to simulate context shifts of different levels of difficulty. We then evaluate the zero-shot performance of ten LLMs (open-weight, closed-source and reasoning), and demonstrate that only some reasoning and strongly instructed LLMs are accurate in detecting pivots; open-weight LLMs struggle with the task and frequently carry stale context even with explicit cues; and all models suffer from a position bias. Based on the results, we discuss key takeaways for improving long-term robustness in multi-turn capabilities for LLMs.

Recent advances in text-to-video generation have demonstrated the utility of powerful diffusion models. Nevertheless, the problem is not trivial when shaping diffusion models to animate static image (i.e., image-to-video generation). The difficulty originates from the aspect that the diffusion process of subsequent animated frames should not only preserve the faithful alignment with the given image but also pursue temporal coherence among adjacent frames. To alleviate this, we present TRIP, a new recipe of image-to-video diffusion paradigm that pivots on image noise prior derived from static image to jointly trigger inter-frame relational reasoning and ease the coherent temporal modeling via temporal residual learning. Technically, the image noise prior is first attained through one-step backward diffusion process based on both static image and noised video latent codes. Next, TRIP executes a residual-like dual-path scheme for noise prediction: 1) a shortcut path that directly takes image noise prior as the reference noise of each frame to amplify the alignment between the first frame and subsequent frames; 2) a residual path that employs 3D-UNet over noised video and static image latent codes to enable inter-frame relational reasoning, thereby easing the learning of the residual noise for each frame. Furthermore, both reference and residual noise of each frame are dynamically merged via attention mechanism for final video generation. Extensive experiments on WebVid-10M, DTDB and MSR-VTT datasets demonstrate the effectiveness of our TRIP for image-to-video generation. Please see our project page at https://trip-i2v.github.io/TRIP/.

Reasoning is a cognitive process of using evidence to reach a sound conclusion. The reasoning capability is essential for large language models (LLMs) to serve as the brain of the artificial general intelligence agent. Recent studies reveal that fine-tuning LLMs on data with the chain of thought (COT) reasoning process can significantly enhance their reasoning capabilities. However, we find that the fine-tuned LLMs suffer from an Assessment Misalignment problem, i.e., they frequently assign higher scores to subpar COTs, leading to potential limitations in their reasoning abilities. To address this problem, we introduce an Alignment Fine-Tuning (AFT) paradigm, which involves three steps: 1) fine-tuning LLMs with COT training data; 2) generating multiple COT responses for each question, and categorizing them into positive and negative ones based on whether they achieve the correct answer; 3) calibrating the scores of positive and negative responses given by LLMs with a novel constraint alignment loss. Specifically, the constraint alignment loss has two objectives: a) Alignment, which guarantees that positive scores surpass negative scores to encourage answers with high-quality COTs; b) Constraint, which keeps the negative scores confined to a reasonable range to prevent the model degradation. Beyond just the binary positive and negative feedback, the constraint alignment loss can be seamlessly adapted to the ranking situations when ranking feedback is accessible. Furthermore, we also delve deeply into recent ranking-based alignment methods, such as DPO, RRHF, and PRO, and discover that the constraint, which has been overlooked by these approaches, is also crucial for their performance. Extensive experiments on four reasoning benchmarks with both binary and ranking feedback demonstrate the effectiveness of AFT.

Time series reasoning treats time as a first-class axis and incorporates intermediate evidence directly into the answer. This survey defines the problem and organizes the literature by reasoning topology with three families: direct reasoning in one step, linear chain reasoning with explicit intermediates, and branch-structured reasoning that explores, revises, and aggregates. The topology is crossed with the main objectives of the field, including traditional time series analysis, explanation and understanding, causal inference and decision making, and time series generation, while a compact tag set spans these axes and captures decomposition and verification, ensembling, tool use, knowledge access, multimodality, agent loops, and LLM alignment regimes. Methods and systems are reviewed across domains, showing what each topology enables and where it breaks down in faithfulness or robustness, along with curated datasets, benchmarks, and resources that support study and deployment (https://github.com/blacksnail789521/Time-Series-Reasoning-Survey). Evaluation practices that keep evidence visible and temporally aligned are highlighted, and guidance is distilled on matching topology to uncertainty, grounding with observable artifacts, planning for shift and streaming, and treating cost and latency as design budgets. We emphasize that reasoning structures must balance capacity for grounding and self-correction against computational cost and reproducibility, while future progress will likely depend on benchmarks that tie reasoning quality to utility and on closed-loop testbeds that trade off cost and risk under shift-aware, streaming, and long-horizon settings. Taken together, these directions mark a shift from narrow accuracy toward reliability at scale, enabling systems that not only analyze but also understand, explain, and act on dynamic worlds with traceable evidence and credible outcomes.

Reasoning is a fundamental aspect of human intelligence that plays a crucial role in activities such as problem solving, decision making, and critical thinking. In recent years, large language models (LLMs) have made significant progress in natural language processing, and there is observation that these models may exhibit reasoning abilities when they are sufficiently large. However, it is not yet clear to what extent LLMs are capable of reasoning. This paper provides a comprehensive overview of the current state of knowledge on reasoning in LLMs, including techniques for improving and eliciting reasoning in these models, methods and benchmarks for evaluating reasoning abilities, findings and implications of previous research in this field, and suggestions on future directions. Our aim is to provide a detailed and up-to-date review of this topic and stimulate meaningful discussion and future work.

Perception-enhanced pre-training, particularly through grounding techniques, is widely adopted to enhance the performance of graphical user interface (GUI) agents. However, in resource-constrained scenarios, the format discrepancy between coordinate-oriented grounding and action-oriented reasoning limits the effectiveness of grounding for reasoning tasks. To address this challenge, we propose a query-oriented pivot approach called query inference, which serves as a bridge between GUI grounding and reasoning. By inferring potential user queries from a screenshot and its associated element coordinates, query inference improves the understanding of coordinates while aligning more closely with reasoning tasks. Experimental results show that query inference outperforms previous grounding techniques under the same training data scale. Notably, query inference achieves comparable or even better performance to large-scale grounding-enhanced OS-Atlas with less than 0.1% of training data. Furthermore, we explore the impact of reasoning formats and demonstrate that integrating additional semantic information into the input further boosts reasoning performance. The code is publicly available at https://github.com/ZrW00/GUIPivot.

This paper presents ReasonFormer, a unified reasoning framework for mirroring the modular and compositional reasoning process of humans in complex decision-making. Inspired by dual-process theory in cognitive science, the representation module (automatic thinking) and reasoning modules (controlled thinking) are decoupled to capture different levels of cognition. Upon the top of the representation module, the pre-trained reasoning modules are modular and professional in specific and fundamental reasoning skills (e.g., logic, simple QA, etc). To mimic the controlled compositional thinking process, different reasoning modules are dynamically activated and composed in both parallel and cascaded manners to control what reasoning skills are activated and how deep the reasoning process will be reached to solve the current problems. The unified reasoning framework solves multiple tasks with a single model, and is trained and inferred in an end-to-end manner. Evaluated on 11 datasets requiring different reasoning skills and complexity, ReasonFormer demonstrates substantial performance boosts, revealing the compositional reasoning ability. Few-shot experiments exhibit better generalization ability by learning to compose pre-trained skills for new tasks with limited data, and decoupling the representation module and the reasoning modules. Further analysis shows the modularity of reasoning modules as different tasks activate distinct reasoning skills at different reasoning depths.

Large language models (LLMs) have been routinely used to solve various tasks using step-by-step reasoning. However, the structure of intermediate reasoning steps, or thoughts, is rigid and unidirectional, such as chains, trees, or acyclic-directed graphs. Consequently, the resulting inflexible and forward-only reasoning may not address challenging tasks and fail when the LLM frequently gives false responses, i.e., ``hallucinations''. This paper proposes a new reasoning framework, called Thought Rollback (TR), allowing LLMs to adaptively build thought structure while maintaining effective reasoning toward problem-solving under ``hallucinations''. The core mechanism of TR is rolling back thoughts, which allows LLMs to perform error analysis on thoughts, and thus roll back to any previously mistaken thought for revision. Subsequently, by including such trial-and-error in the prompt to guide the LLM, each rollback leads to one more reliable reasoning path. Therefore, starting with a simple prompt without human annotations, LLM with TR adaptively and gradually explores thoughts for a correct solution. Comprehensive experiments on mathematical problems and multi-task reasoning demonstrate the state-of-the-art performance of TR in terms of problem-solving rate and interaction cost. For instance, the solving rate of GPT-4 with TR outperforms the current best by 9% on the MATH dataset.

Large language models have demonstrated remarkable proficiency in long and complex reasoning tasks. However, they frequently exhibit a problematic reliance on familiar reasoning patterns, a phenomenon we term reasoning rigidity. Despite explicit instructions from users, these models often override clearly stated conditions and default to habitual reasoning trajectories, leading to incorrect conclusions. This behavior presents significant challenges, particularly in domains such as mathematics and logic puzzle, where precise adherence to specified constraints is critical. To systematically investigate reasoning rigidity, a behavior largely unexplored in prior work, we introduce a expert-curated diagnostic set, . Our dataset includes specially modified variants of existing mathematical benchmarks, namely AIME and MATH500, as well as well-known puzzles deliberately redesigned to require deviation from familiar reasoning strategies. Using this dataset, we identify recurring contamination patterns that occur when models default to ingrained reasoning. Specifically, we categorize this contamination into three distinctive modes: (i) Interpretation Overload, (ii) Input Distrust, and (iii) Partial Instruction Attention, each causing models to ignore or distort provided instructions. We publicly release our diagnostic set to facilitate future research on mitigating reasoning rigidity in language models.

Hierarchical reasoning model (HRM) achieves extraordinary performance on various reasoning tasks, significantly outperforming large language model-based reasoners. To understand the strengths and potential failure modes of HRM, we conduct a mechanistic study on its reasoning patterns and find three surprising facts: (a) Failure of extremely simple puzzles, e.g., HRM can fail on a puzzle with only one unknown cell. We attribute this failure to the violation of the fixed point property, a fundamental assumption of HRM. (b) "Grokking" dynamics in reasoning steps, i.e., the answer is not improved uniformly, but instead there is a critical reasoning step that suddenly makes the answer correct; (c) Existence of multiple fixed points. HRM "guesses" the first fixed point, which could be incorrect, and gets trapped there for a while or forever. All facts imply that HRM appears to be "guessing" instead of "reasoning". Leveraging this "guessing" picture, we propose three strategies to scale HRM's guesses: data augmentation (scaling the quality of guesses), input perturbation (scaling the number of guesses by leveraging inference randomness), and model bootstrapping (scaling the number of guesses by leveraging training randomness). On the practical side, by combining all methods, we develop Augmented HRM, boosting accuracy on Sudoku-Extreme from 54.5% to 96.9%. On the scientific side, our analysis provides new insights into how reasoning models "reason".

Reasoning is a fundamental cognitive process that enables logical inference, problem-solving, and decision-making. With the rapid advancement of large language models (LLMs), reasoning has emerged as a key capability that distinguishes advanced AI systems from conventional models that empower chatbots. In this survey, we categorize existing methods along two orthogonal dimensions: (1) Regimes, which define the stage at which reasoning is achieved (either at inference time or through dedicated training); and (2) Architectures, which determine the components involved in the reasoning process, distinguishing between standalone LLMs and agentic compound systems that incorporate external tools, and multi-agent collaborations. Within each dimension, we analyze two key perspectives: (1) Input level, which focuses on techniques that construct high-quality prompts that the LLM condition on; and (2) Output level, which methods that refine multiple sampled candidates to enhance reasoning quality. This categorization provides a systematic understanding of the evolving landscape of LLM reasoning, highlighting emerging trends such as the shift from inference-scaling to learning-to-reason (e.g., DeepSeek-R1), and the transition to agentic workflows (e.g., OpenAI Deep Research, Manus Agent). Additionally, we cover a broad spectrum of learning algorithms, from supervised fine-tuning to reinforcement learning such as PPO and GRPO, and the training of reasoners and verifiers. We also examine key designs of agentic workflows, from established patterns like generator-evaluator and LLM debate to recent innovations. ...

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.

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.

We consider the question: when a large language reasoning model makes a choice, did it think first and then decide to, or decide first and then think? In this paper, we present evidence that detectable, early-encoded decisions shape chain-of-thought in reasoning models. Specifically, we show that a simple linear probe successfully decodes tool-calling decisions from pre-generation activations with very high confidence, and in some cases, even before a single reasoning token is produced. Activation steering supports this causally: perturbing the decision direction leads to inflated deliberation, and flips behavior in many examples (between 7 - 79% depending on model and benchmark). We also show through behavioral analysis that, when steering changes the decision, the chain-of-thought process often rationalizes the flip rather than resisting it. Together, these results suggest that reasoning models can encode action choices before they begin to deliberate in text.

Reasoning LLMs often spend substantial tokens on long intermediate reasoning traces (e.g., chain-of-thought) when solving new problems. We propose to summarize and store reusable reasoning skills distilled from extensive deliberation and trial-and-error exploration, and to retrieve these skills at inference time to guide future reasoning. Unlike the prevailing reasoning from scratch paradigm, our approach first recalls relevant skills for each query, helping the model avoid redundant detours and focus on effective solution paths. We evaluate our method on coding and mathematical reasoning tasks, and find that it significantly reduces reasoning tokens while improving overall performance. The resulting lower per-request cost indicates strong practical and economic potential for real-world deployment.

Recently, slow-thinking reasoning systems, such as o1, have demonstrated remarkable capabilities in solving complex reasoning tasks. These systems typically engage in an extended thinking process before responding to a query, allowing them to generate more thorough, accurate, and well-reasoned solutions. These systems are primarily developed and maintained by industry, with their core techniques not publicly disclosed. In response, an increasing number of studies from the research community aim to explore the technical foundations underlying these powerful reasoning systems. Building on these prior efforts, this paper presents a reproduction report on implementing o1-like reasoning systems. We introduce an "imitate, explore, and self-improve" framework as our primary technical approach to train the reasoning model. In the initial phase, we use distilled long-form thought data to fine-tune the reasoning model, enabling it to invoke a slow-thinking mode. The model is then encouraged to explore challenging problems by generating multiple rollouts, which can result in increasingly more high-quality trajectories that lead to correct answers. Furthermore, the model undergoes self-improvement by iteratively refining its training dataset. To verify the effectiveness of this approach, we conduct extensive experiments on three challenging benchmarks. The experimental results demonstrate that our approach achieves competitive performance compared to industry-level reasoning systems on these benchmarks.

This work characterizes large language models' chain-of-thought generation as a structured trajectory through representation space. We show that mathematical reasoning traverses functionally ordered, step-specific subspaces that become increasingly separable with layer depth. This structure already exists in base models, while reasoning training primarily accelerates convergence toward termination-related subspaces rather than introducing new representational organization. While early reasoning steps follow similar trajectories, correct and incorrect solutions diverge systematically at late stages. This late-stage divergence enables mid-reasoning prediction of final-answer correctness with ROC-AUC up to 0.87. Furthermore, we introduce trajectory-based steering, an inference-time intervention framework that enables reasoning correction and length control based on derived ideal trajectories. Together, these results establish reasoning trajectories as a geometric lens for interpreting, predicting, and controlling LLM reasoning behavior.

Do reasoning models have "Aha!" moments? Prior work suggests that models like DeepSeek-R1-Zero undergo sudden mid-trace realizations that lead to accurate outputs, implying an intrinsic capacity for self-correction. Yet, it remains unclear whether such intrinsic shifts in reasoning strategy actually improve performance. Here, we study mid-reasoning shifts and instrument training runs to detect them. Our analysis spans 1M+ reasoning traces, hundreds of training checkpoints, three reasoning domains, and multiple decoding temperatures and model architectures. We find that reasoning shifts are rare, do not become more frequent with training, and seldom improve accuracy, indicating that they do not correspond to prior perceptions of model insight. However, their effect varies with model uncertainty. Building on this finding, we show that artificially triggering extrinsic shifts under high entropy reliably improves accuracy. Our results show that mid-reasoning shifts are symptoms of unstable inference behavior rather than an intrinsic mechanism for self-correction.

Large Reasoning Models (LRMs) increasingly rely on reasoning traces with complex internal structures. However, existing work lacks a unified answer to three fundamental questions: (1) what defines high-quality reasoning, (2) how to reliably evaluate long, implicitly structured reasoning traces, and (3) how to use such evaluation signals for reasoning optimization. To address these challenges, we provide a unified perspective. (1) We introduce the ME^2 principle to characterize reasoning quality along macro- and micro-level concerning efficiency and effectiveness. (2) Built on this principle, we model reasoning traces as directed acyclic graphs (DAGs) and develop a DAG-based pairwise evaluation method, capturing complex reasoning structures. (3) Based on this method, we construct the TRM-Preference dataset and train a Thinking Reward Model (TRM) to evaluate reasoning quality at scale. Experiments show that thinking rewards serve as an effective optimization signal. At test time, selecting better reasoning leads to better outcomes (up to 19.3\% gain), and during RL training, thinking rewards enhance reasoning and performance (up to 3.9\% gain) across diverse tasks. Code and data are available at https://github.com/Simplified-Reasoning/TRM.

Reasoning is a distinctive human capacity, enabling us to address complex problems by breaking them down into a series of manageable cognitive steps. Yet, complex logical reasoning is still cumbersome for language models. Based on the dual process theory in cognitive science, we are the first to unravel the cognitive reasoning abilities of language models. Our framework employs an iterative methodology to construct a Cognitive Tree (CogTree). The root node of this tree represents the initial query, while the leaf nodes consist of straightforward questions that can be answered directly. This construction involves two main components: the implicit extraction module (referred to as the intuitive system) and the explicit reasoning module (referred to as the reflective system). The intuitive system rapidly generates multiple responses by utilizing in-context examples, while the reflective system scores these responses using comparative learning. The scores guide the intuitive system in its subsequent generation step. Our experimental results on two popular and challenging reasoning tasks indicate that it is possible to achieve a performance level comparable to that of GPT-3.5 (with 175B parameters), using a significantly smaller language model that contains fewer parameters (<=7B) than 5% of GPT-3.5.

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.

With the growing accessibility and wide adoption of large language models, concerns about their safety and alignment with human values have become paramount. In this paper, we identify a concerning phenomenon: Reasoning-Induced Misalignment (RIM), in which misalignment emerges when reasoning capabilities strengthened-particularly when specific types of reasoning patterns are introduced during inference or training. Beyond reporting this vulnerability, we provide the first mechanistic account of its origins. Through representation analysis, we discover that specific attention heads facilitate refusal by reducing their attention to CoT tokens, a mechanism that modulates the model's rationalization process during inference. During training, we find significantly higher activation entanglement between reasoning and safety in safety-critical neurons than in control neurons, particularly after fine-tuning with those identified reasoning patterns. This entanglement strongly correlates with catastrophic forgetting, providing a neuron-level explanation for RIM.

Human reasoning often involves working over limited information to arrive at probabilistic conclusions. In its simplest form, this involves making an inference that is not strictly entailed by a premise, but rather only likely given the premise. While reasoning LLMs have demonstrated strong performance on logical and mathematical tasks, their behavior on such open-ended, non-deterministic inferences remains largely unexplored. We introduce ProbCOPA, a dataset of 210 handcrafted probabilistic inferences in English, each annotated for inference likelihood by 25--30 human participants. We find that human responses are graded and varied, revealing probabilistic judgments of the inferences in our dataset. Comparing these judgments with responses from eight state-of-the-art reasoning LLMs, we show that models consistently fail to produce human-like distributions. Finally, analyzing LLM reasoning chains, we find evidence of a common reasoning pattern used to evaluate such inferences. Our findings reveal persistent differences between humans and LLMs, and underscore the need to evaluate reasoning beyond deterministic settings.

Reasoning large language models have recently achieved state-of-the-art performance in many fields. However, their long-form chain-of-thought reasoning creates interpretability challenges as each generated token depends on all previous ones, making the computation harder to decompose. We argue that analyzing reasoning traces at the sentence level is a promising approach to understanding reasoning processes. We present three complementary attribution methods: (1) a black-box method measuring each sentence's counterfactual importance by comparing final answers across 100 rollouts conditioned on the model generating that sentence or one with a different meaning; (2) a white-box method of aggregating attention patterns between pairs of sentences, which identified ``broadcasting'' sentences that receive disproportionate attention from all future sentences via ``receiver'' attention heads; (3) a causal attribution method measuring logical connections between sentences by suppressing attention toward one sentence and measuring the effect on each future sentence's tokens. Each method provides evidence for the existence of thought anchors, reasoning steps that have outsized importance and that disproportionately influence the subsequent reasoning process. These thought anchors are typically planning or backtracking sentences. We provide an open-source tool (www.thought-anchors.com) for visualizing the outputs of our methods, and present a case study showing converging patterns across methods that map how a model performs multi-step reasoning. The consistency across methods demonstrates the potential of sentence-level analysis for a deeper understanding of reasoning models.

Mathematical reasoning, a core ability of human intelligence, presents unique challenges for machines in abstract thinking and logical reasoning. Recent large pre-trained language models such as GPT-3 have achieved remarkable progress on mathematical reasoning tasks written in text form, such as math word problems (MWP). However, it is unknown if the models can handle more complex problems that involve math reasoning over heterogeneous information, such as tabular data. To fill the gap, we present Tabular Math Word Problems (TabMWP), a new dataset containing 38,431 open-domain grade-level problems that require mathematical reasoning on both textual and tabular data. Each question in TabMWP is aligned with a tabular context, which is presented as an image, semi-structured text, and a structured table. There are two types of questions: free-text and multi-choice, and each problem is annotated with gold solutions to reveal the multi-step reasoning process. We evaluate different pre-trained models on TabMWP, including the GPT-3 model in a few-shot setting. As earlier studies suggest, since few-shot GPT-3 relies on the selection of in-context examples, its performance is unstable and can degrade to near chance. The unstable issue is more severe when handling complex problems like TabMWP. To mitigate this, we further propose a novel approach, PromptPG, which utilizes policy gradient to learn to select in-context examples from a small amount of training data and then constructs the corresponding prompt for the test example. Experimental results show that our method outperforms the best baseline by 5.31% on the accuracy metric and reduces the prediction variance significantly compared to random selection, which verifies its effectiveness in selecting in-context examples.

The rapid evolution of video generative models has shifted their focus from producing visually plausible outputs to tackling tasks requiring physical plausibility and logical consistency. However, despite recent breakthroughs such as Veo 3's chain-of-frames reasoning, it remains unclear whether these models can exhibit reasoning capabilities similar to large language models (LLMs). Existing benchmarks predominantly evaluate visual fidelity and temporal coherence, failing to capture higher-order reasoning abilities. To bridge this gap, we propose TiViBench, a hierarchical benchmark specifically designed to evaluate the reasoning capabilities of image-to-video (I2V) generation models. TiViBench systematically assesses reasoning across four dimensions: i) Structural Reasoning & Search, ii) Spatial & Visual Pattern Reasoning, iii) Symbolic & Logical Reasoning, and iv) Action Planning & Task Execution, spanning 24 diverse task scenarios across 3 difficulty levels. Through extensive evaluations, we show that commercial models (e.g., Sora 2, Veo 3.1) demonstrate stronger reasoning potential, while open-source models reveal untapped potential that remains hindered by limited training scale and data diversity. To further unlock this potential, we introduce VideoTPO, a simple yet effective test-time strategy inspired by preference optimization. By performing LLM self-analysis on generated candidates to identify strengths and weaknesses, VideoTPO significantly enhances reasoning performance without requiring additional training, data, or reward models. Together, TiViBench and VideoTPO pave the way for evaluating and advancing reasoning in video generation models, setting a foundation for future research in this emerging field.

Despite the success of test-time scaling, Large Reasoning Models (LRMs) frequently encounter repetitive loops that lead to computational waste and inference failure. In this paper, we identify a distinct failure mode termed Circular Reasoning. Unlike traditional model degeneration, this phenomenon manifests as a self-reinforcing trap where generated content acts as a logical premise for its own recurrence, compelling the reiteration of preceding text. To systematically analyze this phenomenon, we introduce LoopBench, a dataset designed to capture two distinct loop typologies: numerical loops and statement loops. Mechanistically, we characterize circular reasoning as a state collapse exhibiting distinct boundaries, where semantic repetition precedes textual repetition. We reveal that reasoning impasses trigger the loop onset, which subsequently persists as an inescapable cycle driven by a self-reinforcing V-shaped attention mechanism. Guided by these findings, we employ the Cumulative Sum (CUSUM) algorithm to capture these precursors for early loop prediction. Experiments across diverse LRMs validate its accuracy and elucidate the stability of long-chain reasoning.

Recent studies have shown that Large Language Models (LLMs) can achieve strong reasoning performance by incorporating functional symbolic representations that abstractly describe graph traversal algorithms and step-by-step reasoning in few-shot learning settings. However, it remains unclear how LLMs genuinely understand the abstract meaning of each reasoning step and the overall algorithm from only a limited number of demonstrations. This work aims to localize the attention heads responsible for individual reasoning steps and characterize the types of information transferred among them. We first align constituent reasoning steps with their corresponding token logits under a symbolic-aided Chain-of-Thought (CoT) prompting framework. Our analysis shows that token positions that steer the reasoning process are associated with low confidence scores caused by constraints on satisfying reasoning behavior patterns in demonstrations. We then adopt causal mediation analysis techniques to identify the attention heads responsible for these patterns. In addition, our findings indicate that LLMs retrieve factual and rule-based information for individual sub-reasoning tasks through specialized attention heads (approximately 3% total heads), whereas higher layers predominantly facilitate information integration and the emergence of global reasoning strategies (e.g., graph traversal algorithms) that coordinate multiple intermediate reasoning steps to solve the overall task.

Human reasoning relies on constructing and manipulating mental models-simplified internal representations of situations that we use to understand and solve problems. Conceptual diagrams (for example, sketches drawn by humans to aid reasoning) externalize these mental models, abstracting irrelevant details to efficiently capture relational and spatial information. In contrast, Large Language Models (LLMs) and Large Multimodal Models (LMMs) predominantly reason through textual representations, limiting their effectiveness in complex multi-step combinatorial and planning tasks. In this paper, we propose a zero-shot fully automatic framework that enables LMMs to reason through multiple chains of self-generated intermediate conceptual diagrams, significantly enhancing their combinatorial planning capabilities. Our approach does not require any human initialization beyond a natural language description of the task. It integrates both textual and diagrammatic reasoning within an optimized graph-of-thought inference framework, enhanced by beam search and depth-wise backtracking. Evaluated on multiple challenging PDDL planning domains, our method substantially improves GPT-4o's performance (for example, from 35.5% to 90.2% in Blocksworld). On more difficult planning domains with solution depths up to 40, our approach outperforms even the o1-preview reasoning model (for example, over 13% improvement in Parking). These results highlight the value of conceptual diagrams as a complementary reasoning medium in LMMs.

Reasoning is central to human intelligence, enabling structured problem-solving across diverse tasks. Recent advances in large language models (LLMs) have greatly enhanced their reasoning abilities in arithmetic, commonsense, and symbolic domains. However, effectively extending these capabilities into multimodal contexts-where models must integrate both visual and textual inputs-continues to be a significant challenge. Multimodal reasoning introduces complexities, such as handling conflicting information across modalities, which require models to adopt advanced interpretative strategies. Addressing these challenges involves not only sophisticated algorithms but also robust methodologies for evaluating reasoning accuracy and coherence. This paper offers a concise yet insightful overview of reasoning techniques in both textual and multimodal LLMs. Through a thorough and up-to-date comparison, we clearly formulate core reasoning challenges and opportunities, highlighting practical methods for post-training optimization and test-time inference. Our work provides valuable insights and guidance, bridging theoretical frameworks and practical implementations, and sets clear directions for future research.

Achieving human-level intelligence requires refining the transition from the fast, intuitive System 1 to the slower, more deliberate System 2 reasoning. While System 1 excels in quick, heuristic decisions, System 2 relies on logical reasoning for more accurate judgments and reduced biases. Foundational Large Language Models (LLMs) excel at fast decision-making but lack the depth for complex reasoning, as they have not yet fully embraced the step-by-step analysis characteristic of true System 2 thinking. Recently, reasoning LLMs like OpenAI's o1/o3 and DeepSeek's R1 have demonstrated expert-level performance in fields such as mathematics and coding, closely mimicking the deliberate reasoning of System 2 and showcasing human-like cognitive abilities. This survey begins with a brief overview of the progress in foundational LLMs and the early development of System 2 technologies, exploring how their combination has paved the way for reasoning LLMs. Next, we discuss how to construct reasoning LLMs, analyzing their features, the core methods enabling advanced reasoning, and the evolution of various reasoning LLMs. Additionally, we provide an overview of reasoning benchmarks, offering an in-depth comparison of the performance of representative reasoning LLMs. Finally, we explore promising directions for advancing reasoning LLMs and maintain a real-time https://github.com/zzli2022/Awesome-Slow-Reason-System{GitHub Repository} to track the latest developments. We hope this survey will serve as a valuable resource to inspire innovation and drive progress in this rapidly evolving field.

Large reasoning models (LRMs) show strong capabilities in complex reasoning, yet their marginal gains on evidence-dependent factual questions are limited. We find this limitation is partially attributable to a reasoning-answer hit gap, where the model identifies the correct facts during reasoning but fails to incorporate them into the final response, thereby reducing factual fidelity. To address this issue, we propose MR-ALIGN, a Meta-Reasoning informed alignment framework that enhances factuality without relying on external verifiers. MR-ALIGN quantifies state transition probabilities along the model's thinking process and constructs a transition-aware implicit reward that reinforces beneficial reasoning patterns while suppressing defective ones at the atomic thinking segments. This re-weighting reshapes token-level signals into probability-aware segment scores, encouraging coherent reasoning trajectories that are more conducive to factual correctness. Empirical evaluations across four factual QA datasets and one long-form factuality benchmark show that MR-ALIGN consistently improves accuracy and truthfulness while reducing misleading reasoning. These results highlight that aligning the reasoning process itself, rather than merely the outputs, is pivotal for advancing factuality in LRMs.

Reasoning, a crucial ability for complex problem-solving, plays a pivotal role in various real-world settings such as negotiation, medical diagnosis, and criminal investigation. It serves as a fundamental methodology in the field of Artificial General Intelligence (AGI). With the ongoing development of foundation models, e.g., Large Language Models (LLMs), there is a growing interest in exploring their abilities in reasoning tasks. In this paper, we introduce seminal foundation models proposed or adaptable for reasoning, highlighting the latest advancements in various reasoning tasks, methods, and benchmarks. We then delve into the potential future directions behind the emergence of reasoning abilities within foundation models. We also discuss the relevance of multimodal learning, autonomous agents, and super alignment in the context of reasoning. By discussing these future research directions, we hope to inspire researchers in their exploration of this field, stimulate further advancements in reasoning with foundation models, and contribute to the development of AGI.

Existing works of reasoning segmentation often fall short in complex cases, particularly when addressing complicated queries and out-of-domain images. Inspired by the chain-of-thought reasoning, where harder problems require longer thinking steps/time, this paper aims to explore a system that can think step-by-step, look up information if needed, generate results, self-evaluate its own results, and refine the results, in the same way humans approach harder questions. We introduce CoT-Seg, a training-free framework that rethinks reasoning segmentation by combining chain-of-thought reasoning with self-correction. Instead of fine-tuning, CoT-Seg leverages the inherent reasoning ability of pre-trained MLLMs (GPT-4o) to decompose queries into meta-instructions, extract fine-grained semantics from images, and identify target objects even under implicit or complex prompts. Moreover, CoT-Seg incorporates a self-correction stage: the model evaluates its own segmentation against the original query and reasoning trace, identifies mismatches, and iteratively refines the mask. This tight integration of reasoning and correction significantly improves reliability and robustness, especially in ambiguous or error-prone cases. Furthermore, our CoT-Seg framework allows easy incorporation of retrieval-augmented reasoning, enabling the system to access external knowledge when the input lacks sufficient information. To showcase CoT-Seg's ability to handle very challenging cases ,we introduce a new dataset ReasonSeg-Hard. Our results highlight that combining chain-of-thought reasoning, self-correction, offers a powerful paradigm for vision-language integration driven segmentation.

Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis of inferring, learning, and exploiting laws, axioms, and symbol manipulation rules. In this paper, we present a new challenge for the evaluation (and eventually the design) of neural architectures and similar system, developing a task suite of mathematics problems involving sequential questions and answers in a free-form textual input/output format. The structured nature of the mathematics domain, covering arithmetic, algebra, probability and calculus, enables the construction of training and test splits designed to clearly illuminate the capabilities and failure-modes of different architectures, as well as evaluate their ability to compose and relate knowledge and learned processes. Having described the data generation process and its potential future expansions, we conduct a comprehensive analysis of models from two broad classes of the most powerful sequence-to-sequence architectures and find notable differences in their ability to resolve mathematical problems and generalize their knowledge.

Large Reasoning Models (LRMs) have shown impressive capabilities in multi-step reasoning tasks. However, alongside these successes, a more deceptive form of model error has emerged--Reasoning Hallucination--where logically coherent but factually incorrect reasoning traces lead to persuasive yet faulty conclusions. Unlike traditional hallucinations, these errors are embedded within structured reasoning, making them more difficult to detect and potentially more harmful. In this work, we investigate reasoning hallucinations from a mechanistic perspective. We propose the Reasoning Score, which quantifies the depth of reasoning by measuring the divergence between logits obtained from projecting late layers of LRMs to the vocabulary space, effectively distinguishing shallow pattern-matching from genuine deep reasoning. Using this score, we conduct an in-depth analysis on the ReTruthQA dataset and identify two key reasoning hallucination patterns: early-stage fluctuation in reasoning depth and incorrect backtracking to flawed prior steps. These insights motivate our Reasoning Hallucination Detection (RHD) framework, which achieves state-of-the-art performance across multiple domains. To mitigate reasoning hallucinations, we further introduce GRPO-R, an enhanced reinforcement learning algorithm that incorporates step-level deep reasoning rewards via potential-based shaping. Our theoretical analysis establishes stronger generalization guarantees, and experiments demonstrate improved reasoning quality and reduced hallucination rates.

Chain-of-Thought (CoT) reasoning has significantly advanced state-of-the-art AI capabilities. However, recent studies have shown that CoT reasoning is not always faithful when models face an explicit bias in their prompts, i.e., the CoT can give an incorrect picture of how models arrive at conclusions. We go further and show that unfaithful CoT can also occur on realistic prompts with no artificial bias. We find that when separately presented with the questions "Is X bigger than Y?" and "Is Y bigger than X?", models sometimes produce superficially coherent arguments to justify systematically answering Yes to both questions or No to both questions, despite such responses being logically contradictory. We show preliminary evidence that this is due to models' implicit biases towards Yes or No, thus labeling this unfaithfulness as Implicit Post-Hoc Rationalization. Our results reveal that several production models exhibit surprisingly high rates of post-hoc rationalization in our settings: GPT-4o-mini (13%) and Haiku 3.5 (7%). While frontier models are more faithful, especially thinking ones, none are entirely faithful: Gemini 2.5 Flash (2.17%), ChatGPT-4o (0.49%), DeepSeek R1 (0.37%), Gemini 2.5 Pro (0.14%), and Sonnet 3.7 with thinking (0.04%). We also investigate Unfaithful Illogical Shortcuts, where models use subtly illogical reasoning to try to make a speculative answer to hard maths problems seem rigorously proven. Our findings raise challenges for strategies for detecting undesired behavior in LLMs via the chain of thought.

Reasoning, as an essential ability for complex problem-solving, can provide back-end support for various real-world applications, such as medical diagnosis, negotiation, etc. This paper provides a comprehensive survey of cutting-edge research on reasoning with language model prompting. We introduce research works with comparisons and summaries and provide systematic resources to help beginners. We also discuss the potential reasons for emerging such reasoning abilities and highlight future research directions. Resources are available at https://github.com/zjunlp/Prompt4ReasoningPapers (updated periodically).

Recent scholarship on reasoning in LLMs has supplied evidence of impressive performance and flexible adaptation to machine generated or human feedback. Nonmonotonic reasoning, crucial to human cognition for navigating the real world, remains a challenging, yet understudied task. In this work, we study nonmonotonic reasoning capabilities of seven state-of-the-art LLMs in one abstract and one commonsense reasoning task featuring generics, such as 'Birds fly', and exceptions, 'Penguins don't fly' (see Fig. 1). While LLMs exhibit reasoning patterns in accordance with human nonmonotonic reasoning abilities, they fail to maintain stable beliefs on truth conditions of generics at the addition of supporting examples ('Owls fly') or unrelated information ('Lions have manes'). Our findings highlight pitfalls in attributing human reasoning behaviours to LLMs, as well as assessing general capabilities, while consistent reasoning remains elusive.

Large Language Models (LLMs) exhibit impressive reasoning abilities, yet their reliance on structured step-by-step processing reveals a critical limitation. While human cognition fluidly adapts between intuitive, heuristic (System 1) and analytical, deliberative (System 2) reasoning depending on the context, LLMs lack this dynamic flexibility. This rigidity can lead to brittle and unreliable performance when faced with tasks that deviate from their trained patterns. To address this, we create a dataset of 2,000 samples with valid System 1 and System 2 answers, explicitly align LLMs with these reasoning styles, and evaluate their performance across reasoning benchmarks. Our results reveal an accuracy-efficiency trade-off: System 2-aligned models excel in arithmetic and symbolic reasoning, while System 1-aligned models perform better in commonsense tasks. A mechanistic analysis of model responses shows that System 1 models employ more definitive answers, whereas System 2 models demonstrate greater uncertainty. Interpolating between these extremes produces a monotonic transition in reasoning accuracy, preserving coherence. This work challenges the assumption that step-by-step reasoning is always optimal and highlights the need for adapting reasoning strategies based on task demands.

We study how large language models (LLMs) ``think'' through their representation space. We propose a novel geometric framework that models an LLM's reasoning as flows -- embedding trajectories evolving where logic goes. We disentangle logical structure from semantics by employing the same natural deduction propositions with varied semantic carriers, allowing us to test whether LLMs internalize logic beyond surface form. This perspective connects reasoning with geometric quantities such as position, velocity, and curvature, enabling formal analysis in representation and concept spaces. Our theory establishes: (1) LLM reasoning corresponds to smooth flows in representation space, and (2) logical statements act as local controllers of these flows' velocities. Using learned representation proxies, we design controlled experiments to visualize and quantify reasoning flows, providing empirical validation of our theoretical framework. Our work serves as both a conceptual foundation and practical tools for studying reasoning phenomenon, offering a new lens for interpretability and formal analysis of LLMs' behavior.

Reasoning-enhanced large language models (RLLMs), whether explicitly trained for reasoning or prompted via chain-of-thought (CoT), have achieved state-of-the-art performance on many complex reasoning tasks. However, we uncover a surprising and previously overlooked phenomenon: explicit CoT reasoning can significantly degrade instruction-following accuracy. Evaluating 15 models on two benchmarks: IFEval (with simple, rule-verifiable constraints) and ComplexBench (with complex, compositional constraints), we consistently observe performance drops when CoT prompting is applied. Through large-scale case studies and an attention-based analysis, we identify common patterns where reasoning either helps (e.g., with formatting or lexical precision) or hurts (e.g., by neglecting simple constraints or introducing unnecessary content). We propose a metric, constraint attention, to quantify model focus during generation and show that CoT reasoning often diverts attention away from instruction-relevant tokens. To mitigate these effects, we introduce and evaluate four strategies: in-context learning, self-reflection, self-selective reasoning, and classifier-selective reasoning. Our results demonstrate that selective reasoning strategies, particularly classifier-selective reasoning, can substantially recover lost performance. To our knowledge, this is the first work to systematically expose reasoning-induced failures in instruction-following and offer practical mitigation strategies.

Reasoning models are evaluated on single-turn benchmarks but deployed in multi-turn dialogue, where users push back on correct answers. Under sustained adversarial pressure we find a previously undocumented failure mode: the chain-of-thought stays factually correct from first turn to last while the emitted answer flips wrong. We call this unfaithful capitulation (UC) and isolate it with a 2times 2 latent-versus-behavioral framework that flip-rate metrics and single-turn faithfulness probes both miss. Across three datasets (MT-Consistency, MMLU-Pro, GSM8K), the latent-correct rate at the behavioral flip clusters near 50% in think mode and collapses to 11-15% under no_think -- paired, within-model causal evidence that reasoning creates the gap. Across models the effect tracks the reasoning channel (high in Qwen3-32B and GPT-OSS-20B, low in inline-CoT Gemma-4-31B-it). An independent GPT-4o judge corroborates 86% of UC labels; a token-level probe shows the answer-slot argmax is correct in 84% of UC cells; and a naive trace-anchored defense backfires. We release all trajectories, traces, and judge labels.

Recent advances in vision-language reasoning underscore the importance of thinking with images, where models actively ground their reasoning in visual evidence. Yet, prevailing frameworks treat visual actions as optional tools, boosting metrics but leaving reasoning ungrounded and crops ineffective. This gap gives rise to the illusion of thinking with images: models seem visually grounded but rely on context-agnostic actions that neither refine perception nor guide reasoning toward correct answers. We address this problem by reframing visual actions as core reasoning primitives rather than optional tools, which we term visual rationalization, the visual analogue of textual Chain-of-Thought. Building on this insight, we propose Visual Rationale Learning (ViRL), an end-to-end paradigm that grounds training in the visual rationale itself. ViRL integrates (1) Process Supervision with ground-truth rationales, (2) Objective Alignment via step-level reward shaping, and (3) Fine-Grained Credit Assignment to distinguish correct, redundant, and erroneous actions. By ensuring each action contributes meaningfully to the reasoning chain, ViRL enables models to "get the right answer for the right visual reason". Trained purely with end-to-end RL, ViRL achieves state-of-the-art results across benchmarks spanning perception, hallucination, and reasoning. This work establishes visual rationalization as a task-agnostic, process-grounded paradigm for building transparent, verifiable, and trustworthy vision-language models.

We present SpinBench, a cognitively grounded diagnostic benchmark for evaluating spatial reasoning in vision language models (VLMs). SpinBench is designed around the core challenge of spatial reasoning: perspective taking, the ability to reason about how scenes and object relations change under viewpoint transformation. Since perspective taking requires multiple cognitive capabilities, such as recognizing objects across views, relative positions grounding, and mentally simulating transformations, SpinBench introduces a set of fine-grained diagnostic categories. Our categories target translation, rotation, object relative pose, and viewpoint change, and are progressively structured so that single-object simpler tasks scaffold toward the most demanding multi-object perspective-taking setting. We evaluate 37 state-of-the-art VLMs, both proprietary and open source. Results reveal systematic weaknesses: strong egocentric bias, poor rotational understanding, and inconsistencies under symmetrical and syntactic reformulations. Scaling analysis shows both smooth improvements and emergent capabilities. While human subjects achieve high accuracy (91.2\%), task difficulty as measured by human response time shows strong correlation with VLM accuracy, indicating that SpinBench captures spatial reasoning challenges shared across humans and VLMs. We believe SpinBench provides critical insights into spatial reasoning in VLMs and highlights key gaps in their ability to reason about physical space. Our website can be found at https://spinbench25.github.io/.

Pre-trained language models (PLMs) have shown impressive performance in various language tasks. However, they are prone to spurious correlations, and often generate illusory information. In real-world applications, PLMs should justify decisions with formalized, coherent reasoning chains, but this challenge remains under-explored. Cognitive psychology theorizes that humans are capable of utilizing fast and intuitive heuristic thinking to make decisions based on past experience, then rationalizing the decisions through slower and deliberative analytic reasoning. We incorporate these interlinked dual processes in fine-tuning and in-context learning with PLMs, applying them to two language understanding tasks that require coherent physical commonsense reasoning. We show that our proposed Heuristic-Analytic Reasoning (HAR) strategies drastically improve the coherence of rationalizations for model decisions, yielding state-of-the-art results on Tiered Reasoning for Intuitive Physics (TRIP). We also find that this improved coherence is a direct result of more faithful attention to relevant language context in each step of reasoning. Our findings suggest that human-like reasoning strategies can effectively improve the coherence and reliability of PLM reasoning.

Studies of human reasoning have shown that people are typically stronger at evaluating reasoning than producing it from scratch. In contrast, large reasoning models (LRMs) are trained to excel at producing long chains of reasoning to solve complex problems. How then do LRMs perform at evaluating reasons? We investigate this with the Valid-Answer-Invalid-Reasoning (VAIR) dataset: math problems and solutions with trivial reasoning flaws but valid answers, designed to isolate reasoning evaluation from the confound of reasoning production. Unlike humans, who we find are only 6% worse at grading than solving such problems, we find a substantial production-evaluation gap in LRMs: frontier models score as low as 48% when evaluating VAIR solutions, despite near-perfect solution production. Why this enigma? Through chain-of-thought (CoT) analysis, we find evidence of an answer confirmation bias: LRMs often produce then check for the correct answer instead of carefully verifying each step, fabricating rationalizations even when noticing anomalous reasoning. Linear probes corroborate this, showing that while LRM activations encode some representation of valid reasoning, they fail to robustly represent VAIR solutions as invalid. Causal patching of the final answer's representations causes LRM verdicts and activations to flip, demonstrating that answer validity is responsible for models' confirmation biases. These findings indicate an outstanding limitation in dominant approaches to reasoning training, which incentivize LRMs to produce and confirm reasoning towards correct answers, but not to robustly evaluate the underlying reasons.

In this work, we use large language models (LLMs) to augment and accelerate research on the P versus NP problem, one of the most important open problems in theoretical computer science and mathematics. Specifically, we propose Socratic reasoning, a general framework that promotes in-depth thinking with LLMs for complex problem-solving. Socratic reasoning encourages LLMs to recursively discover, solve, and integrate problems while facilitating self-evaluation and refinement. Our pilot study on the P vs. NP problem shows that GPT-4 successfully produces a proof schema and engages in rigorous reasoning throughout 97 dialogue turns, concluding "P neq NP", which is in alignment with (Xu and Zhou, 2023). The investigation uncovers novel insights within the extensive solution space of LLMs, shedding light on LLM for Science.

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.

Logical reasoning is central to complex human activities, such as thinking, debating, and planning; it is also a central component of many AI systems as well. In this paper, we investigate the extent to which encoder-only transformer language models (LMs) can reason according to logical rules. We ask whether those LMs can deduce theorems in propositional calculus and first-order logic; if their relative success in these problems reflects general logical capabilities; and which layers contribute the most to the task. First, we show for several encoder-only LMs that they can be trained, to a reasonable degree, to determine logical validity on various datasets. Next, by cross-probing fine-tuned models on these datasets, we show that LMs have difficulty in transferring their putative logical reasoning ability, which suggests that they may have learned dataset-specific features, instead of a general capability. Finally, we conduct a layerwise probing experiment, which shows that the hypothesis classification task is mostly solved through higher layers.

Mathematical reasoning is a hallmark of human intelligence, requiring logical deduction, symbolic manipulation, and abstract thinking. Recent multimodal large language models (MLLMs) have demonstrated strong performance on geometry problems through multi-step reasoning. To better emulate human problem-solving, intermediate steps can incorporate auxiliary visual constructions, such as additional lines or points, which improve geometric interpretation and educational clarity. In this work, we introduce the GeoMathCode, where programmatic representations serve as intermediate visual outputs. We further conduct an in-depth analysis of the underlying reasoning geometry. Experimental results show that reasoning and code generation steps can be disentangled in the latent space, while supervised fine-tuning (SFT) makes the reasoning manifold more structured and informative. Moreover, hierarchical syntactic code structures emerge as disentangled latent subspaces, and contain more mathematical symbolic information than visual representations.

People's decision-making abilities often fail to improve or may even erode when they rely on AI for decision-support, even when the AI provides informative explanations. We argue this is partly because people intuitively seek contrastive explanations, which clarify the difference between the AI's decision and their own reasoning, while most AI systems offer "unilateral" explanations that justify the AI's decision but do not account for users' thinking. To align human-AI knowledge on decision tasks, we introduce a framework for generating human-centered contrastive explanations that explain the difference between AI's choice and a predicted, likely human choice about the same task. Results from a large-scale experiment (N = 628) demonstrate that contrastive explanations significantly enhance users' independent decision-making skills compared to unilateral explanations, without sacrificing decision accuracy. Amid rising deskilling concerns, our research demonstrates that incorporating human reasoning into AI design can foster human skill development.

Large reasoning models (LRMs) achieve strong reasoning performance by emitting long chains of thought. Yet, these verbose traces slow down inference and often drift into unnecessary detail, known as the overthinking phenomenon. To better understand LRMs' behavior, we systematically analyze the token-level misalignment between reasoning and non-reasoning models. While it is expected that their primary difference lies in the stylistic "thinking cues", LRMs uniquely exhibit two pivotal, previously under-explored phenomena: a Global Misalignment Rebound, where their divergence from non-reasoning models persists or even grows as response length increases, and more critically, a Local Misalignment Diminish, where the misalignment concentrates at the "thinking cues" each sentence starts with but rapidly declines in the remaining of the sentence. Motivated by the Local Misalignment Diminish, we propose FoReaL-Decoding, a collaborative fast-slow thinking decoding method for cost-quality trade-off. In FoReaL-Decoding, a Leading model leads the first few tokens for each sentence, and then a weaker draft model completes the following tokens to the end of each sentence. FoReaL-Decoding adopts a stochastic gate to smoothly interpolate between the small and the large model. On four popular math-reasoning benchmarks (AIME24, GPQA-Diamond, MATH500, AMC23), FoReaL-Decoding reduces theoretical FLOPs by 30 to 50% and trims CoT length by up to 40%, while preserving 86 to 100% of model performance. These results establish FoReaL-Decoding as a simple, plug-and-play route to controllable cost-quality trade-offs in reasoning-centric tasks.

Deductive reasoning plays a pivotal role in the formulation of sound and cohesive arguments. It allows individuals to draw conclusions that logically follow, given the truth value of the information provided. Recent progress in the domain of large language models (LLMs) has showcased their capability in executing deductive reasoning tasks. Nonetheless, a significant portion of research primarily assesses the accuracy of LLMs in solving such tasks, often overlooking a deeper analysis of their reasoning behavior. In this study, we draw upon principles from cognitive psychology to examine inferential strategies employed by LLMs, through a detailed evaluation of their responses to propositional logic problems. Our findings indicate that LLMs display reasoning patterns akin to those observed in humans, including strategies like supposition following or chain construction. Moreover, our research demonstrates that the architecture and scale of the model significantly affect its preferred method of reasoning, with more advanced models tending to adopt strategies more frequently than less sophisticated ones. Importantly, we assert that a model's accuracy, that is the correctness of its final conclusion, does not necessarily reflect the validity of its reasoning process. This distinction underscores the necessity for more nuanced evaluation procedures in the field.

Recent studies have shown that Large Language Models (LLMs) augmented with chain-of-thought (CoT) reasoning demonstrate impressive problem-solving abilities. However, in this work, we identify a recurring issue where these models occasionally generate overly short reasoning, leading to degraded performance on even simple mathematical problems. Specifically, we investigate how reasoning length is embedded in the hidden representations of reasoning models and its impact on accuracy. Our analysis reveals that reasoning length is governed by a linear direction in the representation space, allowing us to induce overly short reasoning by steering the model along this direction. Building on this insight, we introduce ThinkEdit, a simple yet effective weight-editing approach to mitigate the issue of overly short reasoning. We first identify a small subset of attention heads (approximately 2%) that predominantly drive short reasoning behavior. We then edit the output projection weights of these heads to suppress the short reasoning direction. With changes to only 0.1% of the model's parameters, ThinkEdit effectively reduces overly short reasoning and yields notable accuracy gains for short reasoning outputs (+5.44%), along with an overall improvement across multiple math benchmarks (+2.43%). Our findings provide new mechanistic insights into how reasoning length is controlled within LLMs and highlight the potential of fine-grained model interventions to improve reasoning quality. Our code is available at https://github.com/Trustworthy-ML-Lab/ThinkEdit

While recent success of large reasoning models (LRMs) significantly advanced LLMs' reasoning capability by optimizing the final answer accuracy using reinforcement learning, they may also drastically increase the output length due to overthinking, characterized by unnecessarily complex reasoning paths that waste computation and potentially degrade the performance. We hypothesize that such inefficiencies stem from LRMs' limited capability to dynamically select the proper modular reasoning strategies, termed thinking patterns at the right position. To investigate this hypothesis, we propose a dynamic optimization framework that segments model-generated reasoning paths into distinct thinking patterns, systematically identifying and promoting beneficial patterns that improve the answer while removing detrimental ones. Empirical analysis confirms that our optimized thinking paths yield more concise yet sufficiently informative trajectories, enhancing reasoning efficiency by reducing attention FLOPs by up to 47% while maintaining accuracy for originally correct responses. Moreover, a non-trivial portion of originally incorrect responses are transformed into correct ones, achieving a 15.6% accuracy improvement with reduced length. Motivated by the improvement brought by the optimized thinking paths, we apply a preference optimization technique supported by a pairwise dataset contrasting suboptimal and optimal reasoning paths. Experimental evaluations across multiple mathematical reasoning benchmarks reveal that our method notably reduces computational overhead while simultaneously improving reasoning accuracy, achieving up to a 12% accuracy improvement and reducing token usage from approximately 5,000 to 3,000 tokens.

We present Hermes 4, a family of hybrid reasoning models that combine structured, multi-turn reasoning with broad instruction-following ability. We describe the challenges encountered during data curation, synthesis, training, and evaluation, and outline the solutions employed to address these challenges at scale. We comprehensively evaluate across mathematical reasoning, coding, knowledge, comprehension, and alignment benchmarks, and we report both quantitative performance and qualitative behavioral analysis. To support open research, all model weights are published publicly at https://huggingface.co/collections/NousResearch/hermes-4-collection-68a731bfd452e20816725728

Large language models (LLMs) have demonstrated impressive capabilities in various reasoning tasks, aided by techniques like chain-of-thought (CoT) prompting that elicits verbalized reasoning. However, LLMs often generate text with obvious mistakes and contradictions, raising doubts about their ability to robustly process and utilize generated rationales. In this work, we investigate CoT reasoning in LLMs through the lens of internal representations, focusing on how these representations are influenced by generated rationales. Our preliminary analysis reveals that while generated rationales improve answer accuracy, inconsistencies emerge between the model's internal representations in middle layers and those in final layers, potentially undermining the reliability of their reasoning processes. To address this, we propose internal consistency as a measure of the model's confidence by examining the agreement of latent predictions decoded from intermediate layers. Extensive empirical studies across different models and datasets demonstrate that internal consistency effectively distinguishes between correct and incorrect reasoning paths. Motivated by this, we propose a new approach to calibrate CoT reasoning by up-weighting reasoning paths with high internal consistency, resulting in a significant boost in reasoning performance. Further analysis uncovers distinct patterns in attention and feed-forward modules across layers, providing insights into the emergence of internal inconsistency. In summary, our results demonstrate the potential of using internal representations for self-evaluation of LLMs.

Recent advances in reasoning models have demonstrated significant improvements in accuracy, particularly for complex tasks such as mathematical reasoning, by employing detailed and comprehensive reasoning processes. However, generating these lengthy reasoning sequences is computationally expensive and time-consuming. To address this inefficiency, we leverage the inherent parallelizability of certain tasks to accelerate the reasoning process. Specifically, when multiple parallel reasoning branches exist, we decode multiple tokens per step using a specialized attention mask, processing them within a single sequence, avoiding additional memory usage. Experimental results show that our method achieves over 100% speedup in decoding time while maintaining the answer quality.

Knights and knaves problems represent a classic genre of logical puzzles where characters either tell the truth or lie. The objective is to logically deduce each character's identity based on their statements. The challenge arises from the truth-telling or lying behavior, which influences the logical implications of each statement. Solving these puzzles requires not only direct deductions from individual statements, but the ability to assess the truthfulness of statements by reasoning through various hypothetical scenarios. As such, knights and knaves puzzles serve as compelling examples of suppositional reasoning. In this paper, we introduce TruthQuest, a benchmark for suppositional reasoning based on the principles of knights and knaves puzzles. Our benchmark presents problems of varying complexity, considering both the number of characters and the types of logical statements involved. Evaluations on TruthQuest show that large language models like Llama 3 and Mixtral-8x7B exhibit significant difficulties solving these tasks. A detailed error analysis of the models' output reveals that lower-performing models exhibit a diverse range of reasoning errors, frequently failing to grasp the concept of truth and lies. In comparison, more proficient models primarily struggle with accurately inferring the logical implications of potentially false statements.

As AI systems progress, we rely more on them to make decisions with us and for us. To ensure that such decisions are aligned with human values, it is imperative for us to understand not only what decisions they make but also how they come to those decisions. Reasoning language models, which provide both final responses and (partially transparent) intermediate thinking traces, present a timely opportunity to study AI procedural reasoning. Unlike math and code problems which often have objectively correct answers, moral dilemmas are an excellent testbed for process-focused evaluation because they allow for multiple defensible conclusions. To do so, we present MoReBench: 1,000 moral scenarios, each paired with a set of rubric criteria that experts consider essential to include (or avoid) when reasoning about the scenarios. MoReBench contains over 23 thousand criteria including identifying moral considerations, weighing trade-offs, and giving actionable recommendations to cover cases on AI advising humans moral decisions as well as making moral decisions autonomously. Separately, we curate MoReBench-Theory: 150 examples to test whether AI can reason under five major frameworks in normative ethics. Our results show that scaling laws and existing benchmarks on math, code, and scientific reasoning tasks fail to predict models' abilities to perform moral reasoning. Models also show partiality towards specific moral frameworks (e.g., Benthamite Act Utilitarianism and Kantian Deontology), which might be side effects of popular training paradigms. Together, these benchmarks advance process-focused reasoning evaluation towards safer and more transparent AI.

Reasoning is an essential component of human intelligence as it plays a fundamental role in our ability to think critically, support responsible decisions, and solve challenging problems. Traditionally, AI has addressed reasoning in the context of logic-based representations of knowledge. However, the recent leap forward in natural language processing, with the emergence of language models based on transformers, is hinting at the possibility that these models exhibit reasoning abilities, particularly as they grow in size and are trained on more data. Despite ongoing discussions about what reasoning is in language models, it is still not easy to pin down to what extent these models are actually capable of reasoning. The goal of this workshop is to create a platform for researchers from different disciplines and/or AI perspectives, to explore approaches and techniques with the aim to reconcile reasoning between language models using transformers and using logic-based representations. The specific objectives include analyzing the reasoning abilities of language models measured alongside KR methods, injecting KR-style reasoning abilities into language models (including by neuro-symbolic means), and formalizing the kind of reasoning language models carry out. This exploration aims to uncover how language models can effectively integrate and leverage knowledge and reasoning with it, thus improving their application and utility in areas where precision and reliability are a key requirement.

While Large Reasoning Models (LRMs) have demonstrated success in complex reasoning tasks through long chain-of-thought (CoT) reasoning, their inference often involves excessively verbose reasoning traces, resulting in substantial inefficiency. To address this, we propose Distilled Reasoning Pruning (DRP), a hybrid framework that combines inference-time pruning with tuning-based distillation, two widely used strategies for efficient reasoning. DRP uses a teacher model to perform skill-aware step decomposition and content pruning, and then distills the pruned reasoning paths into a student model, enabling it to reason both efficiently and accurately. Across several challenging mathematical reasoning datasets, we find that models trained with DRP achieve substantial improvements in token efficiency without sacrificing accuracy. Specifically, DRP reduces average token usage on GSM8K from 917 to 328 while improving accuracy from 91.7% to 94.1%, and achieves a 43% token reduction on AIME with no performance drop. Further analysis shows that aligning the reasoning structure of training CoTs with the student's reasoning capacity is critical for effective knowledge transfer and performance gains.

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.

Spatial reasoning is a core aspect of human intelligence that allows perception, inference and planning in 3D environments. However, current vision-language models (VLMs) struggle to maintain geometric coherence and cross-view consistency for spatial reasoning in multi-view settings. We attribute this gap to the lack of fine-grained benchmarks that isolate multi-view reasoning from single-view perception and temporal factors. To address this, we present ReMindView-Bench, a cognitively grounded benchmark for evaluating how VLMs construct, align and maintain spatial mental models across complementary viewpoints. ReMindView-Bench systematically varies viewpoint spatial pattern and query type to probe key factors of spatial cognition. Evaluations of 15 current VLMs reveals consistent failures in cross-view alignment and perspective-taking in multi-view spatial reasoning, motivating deeper analysis on the reasoning process. Explicit phase-wise analysis using LLM-as-a-judge and self-consistency prompting shows that VLMs perform well on in-frame perception but degrade sharply when integrating information across views. Implicit analysis, including linear probing and entropy dynamics, further show progressive loss of task-relevant information and uncertainty separation between correct and incorrect trajectories. These results provide a cognitively grounded diagnosis of VLM spatial reasoning and reveal how multi-view spatial mental models are formed, degraded and destabilized across reasoning phases. The ReMindView-Bench benchmark is available at https://huggingface.co/datasets/Xue0823/ReMindView-Bench, and the source codes of benchmark construction and VLM reasoning analysis are available at https://github.com/pittisl/ReMindView-Bench.

Remarkable progress has been made on automated reasoning with natural text, by using Language Models (LMs) and methods such as Chain-of-Thought and Selection-Inference. These techniques search for proofs in the forward direction from axioms to the conclusion, which suffers from a combinatorial explosion of the search space, and thus high failure rates for problems requiring longer chains of reasoning. The classical automated reasoning literature has shown that reasoning in the backward direction (i.e. from the intended conclusion to supporting axioms) is significantly more efficient at proof-finding. Importing this intuition into the LM setting, we develop a Backward Chaining algorithm, called LAMBADA, that decomposes reasoning into four sub-modules. These sub-modules are simply implemented by few-shot prompted LM inference. We show that LAMBADA achieves sizable accuracy boosts over state-of-the-art forward reasoning methods on challenging logical reasoning datasets, particularly when deep and accurate proof chains are required.

Reasoning is a central capability of human intelligence. In recent years, with the advent of large-scale datasets, pretrained large language models have emerged with new capabilities, including reasoning. However, these models still struggle with long-term, complex reasoning tasks, such as playing chess. Based on the observation that expert chess players employ a dual approach combining long-term strategic play with short-term tactical play along with language explanation, we propose improving the reasoning capability of large language models in chess by integrating annotated strategy and tactic. Specifically, we collect a dataset named MATE, which consists of 1 million chess positions with candidate moves annotated by chess experts for strategy and tactics. We finetune the LLaMA-3-8B model and compare it against state-of-the-art commercial language models in the task of selecting better chess moves. Our experiments show that our models perform better than GPT, Claude, and Gemini models. We find that language explanations can enhance the reasoning capability of large language models.

Chain-of-thought (CoT) reasoning is the dominant paradigm for inference-time scaling in language models, yet the causal influence of individual steps on the final answer poorly understood. We estimate each step's causal importance via early exit and use this measure to study how answers form across the reasoning traces of several model families. Across diverse tasks, we find that reasoning typically crosses a commitment boundary -- a sharp transition from transient intermediate guesses to a stable, high-confidence answer. This transition often happens in a single step, well before the model's reasoning block ends, and is followed by epiphenomenal CoT steps that leave the final answer probability unaltered. Using attention probes, we show that answer-formation stages can be linearly decoded from intermediate reasoning steps with high accuracy and generalize robustly to unseen reasoning tasks. We exploit this signal to early-exit reasoning blocks at the commitment boundary, reducing the length of CoTs up to 55\% on average with negligible impact on model performance.

Reasoning is a fundamental capability for solving complex multi-step problems, particularly in visual contexts where sequential step-wise understanding is essential. Existing approaches lack a comprehensive framework for evaluating visual reasoning and do not emphasize step-wise problem-solving. To this end, we propose a comprehensive framework for advancing step-by-step visual reasoning in large language models (LMMs) through three key contributions. First, we introduce a visual reasoning benchmark specifically designed to evaluate multi-step reasoning tasks. The benchmark presents a diverse set of challenges with eight different categories ranging from complex visual perception to scientific reasoning with over 4k reasoning steps in total, enabling robust evaluation of LLMs' abilities to perform accurate and interpretable visual reasoning across multiple steps. Second, we propose a novel metric that assesses visual reasoning quality at the granularity of individual steps, emphasizing both correctness and logical coherence. The proposed metric offers deeper insights into reasoning performance compared to traditional end-task accuracy metrics. Third, we present a new multimodal visual reasoning model, named LlamaV-o1, trained using a multi-step curriculum learning approach, where tasks are progressively organized to facilitate incremental skill acquisition and problem-solving. The proposed LlamaV-o1 is designed for multi-step reasoning and learns step-by-step through a structured training paradigm. Extensive experiments show that our LlamaV-o1 outperforms existing open-source models and performs favorably against close-source proprietary models. Compared to the recent Llava-CoT, our LlamaV-o1 achieves an average score of 67.3 with an absolute gain of 3.8\% across six benchmarks while being 5 times faster during inference scaling. Our benchmark, model, and code are publicly available.

Large Vision-Language Models (LVLMs) excel in multimodal reasoning and have shown impressive performance on various multimodal benchmarks. However, most of these benchmarks evaluate models primarily through multiple-choice or short-answer formats, which do not take the reasoning process into account. Although some benchmarks assess the reasoning process, their methods are often overly simplistic and only examine reasoning when answers are incorrect. This approach overlooks scenarios where flawed reasoning leads to correct answers. In addition, these benchmarks do not consider the impact of intermodal relationships on reasoning. To address this issue, we propose the Reasoning Process Tree Score (RPTS), a tree structure-based metric to assess reasoning processes. Specifically, we organize the reasoning steps into a reasoning tree and leverage its hierarchical information to assign weighted faithfulness scores to each reasoning step. By dynamically adjusting these weights, RPTS not only evaluates the overall correctness of the reasoning, but also pinpoints where the model fails in the reasoning. To validate RPTS in real-world multimodal scenarios, we construct a new benchmark, RPTS-Eval, comprising 374 images and 390 reasoning instances. Each instance includes reliable visual-textual clues that serve as leaf nodes of the reasoning tree. Furthermore, we define three types of intermodal relationships to investigate how intermodal interactions influence the reasoning process. We evaluated representative LVLMs (e.g., GPT4o, Llava-Next), uncovering their limitations in multimodal reasoning and highlighting the differences between open-source and closed-source commercial LVLMs. We believe that this benchmark will contribute to the advancement of research in the field of multimodal reasoning.

Recent advancements in large reasoning models (LRMs) have significantly enhanced language models' capabilities in complex problem-solving by emulating human-like deliberative thinking. However, these models often exhibit overthinking (i.e., the generation of unnecessarily verbose and redundant content), which hinders efficiency and inflates inference cost. In this work, we explore the representational and behavioral origins of this inefficiency, revealing that LRMs inherently possess the capacity for more concise reasoning. Empirical analyses show that correct reasoning paths vary significantly in length, and the shortest correct responses often suffice, indicating untapped efficiency potential. Exploiting these findings, we propose two lightweight methods to enhance LRM efficiency. First, we introduce Efficiency Steering, a training-free activation steering technique that modulates reasoning behavior via a single direction in the model's representation space. Second, we develop Self-Rewarded Efficiency RL, a reinforcement learning framework that dynamically balances task accuracy and brevity by rewarding concise correct solutions. Extensive experiments on seven LRM backbones across multiple mathematical reasoning benchmarks demonstrate that our methods significantly reduce reasoning length while preserving or improving task performance. Our results highlight that reasoning efficiency can be improved by leveraging and guiding the intrinsic capabilities of existing models in a self-guided manner.

Reasoning models enhance performance by tackling problems in a step-by-step manner, decomposing them into sub-problems and exploring long chains of thought before producing an answer. However, applying extended reasoning to every step introduces substantial redundancy, as sub-problems vary widely in difficulty and complexity: a small number of pivotal steps are genuinely challenging and decisive for the final answer, while many others only involve straightforward revisions or simple computations. Therefore, a natural idea is to endow reasoning models with the ability to adaptively respond to this variation, rather than treating all steps with the same level of elaboration. To this end, we propose MixReasoning, a framework that dynamically adjusts the depth of reasoning within a single response. The resulting chain of thought then becomes a mixture of detailed reasoning on difficult steps and concise inference on simpler ones. Experiments on GSM8K, MATH-500, and AIME show that MixReasoning shortens reasoning length and substantially improves efficiency without compromising accuracy.

Recent reasoning Large Language Models produce a chain-of-thought (CoT) predominantly in English, even when prompted in non-English languages. Prior work suggests that forcing the CoT to remain in the input language (native reasoning) substantially degrades performance relative to allowing the model to reason in English before answering in the input language (English-pivoted reasoning). However, most studies of this native reasoning gap rely on inference-time interventions or limited native-language training data. We revisit this comparison at a larger scale and under comparable supervision. We construct long multilingual reasoning datasets across six languages (English, French, German, Spanish, Chinese and Swahili); fine-tune specialists in both native and English-pivoted regimes on top of Qwen/Qwen3-8B-Base, and evaluate across mathematics, science, general knowledge, and code. In this setting, the average native reasoning gap shrinks to 1.9--3.5\% across the five non-English languages, considerably smaller than previously reported. Weight-space analysis of the native specialists reveals aligned fine-tuning updates in the middle layers and divergence in the outer layers. This points to a largely language-agnostic reasoning core surrounded by language-specific layers. Exploiting this structure, we introduce a Layer Swap: transferring the English specialist's stronger reasoning mid-layers into each native specialist, closing most of the native reasoning gap across the five non-English languages while preserving CoT in the target language. We release all models and datasets.

Recently developed large language models (LLMs) have been shown to perform remarkably well on a wide range of language understanding tasks. But, can they really "reason" over the natural language? This question has been receiving significant research attention and many reasoning skills such as commonsense, numerical, and qualitative have been studied. However, the crucial skill pertaining to 'logical reasoning' has remained underexplored. Existing work investigating this reasoning ability of LLMs has focused only on a couple of inference rules (such as modus ponens and modus tollens) of propositional and first-order logic. Addressing the above limitation, we comprehensively evaluate the logical reasoning ability of LLMs on 25 different reasoning patterns spanning over propositional, first-order, and non-monotonic logics. To enable systematic evaluation, we introduce LogicBench, a natural language question-answering dataset focusing on the use of a single inference rule. We conduct detailed analysis with a range of LLMs such as GPT-4, ChatGPT, Gemini, Llama-2, and Mistral using chain-of-thought prompting. Experimental results show that existing LLMs do not fare well on LogicBench; especially, they struggle with instances involving complex reasoning and negations. Furthermore, they sometimes overlook contextual information necessary for reasoning to arrive at the correct conclusion. We believe that our work and findings facilitate future research for evaluating and enhancing the logical reasoning ability of LLMs. Data and code are available at https://github.com/Mihir3009/LogicBench.

Recent advancements in large reasoning models (LRMs) have greatly improved their capabilities on complex reasoning tasks through Long Chains of Thought (CoTs). However, this approach often results in substantial redundancy, impairing computational efficiency and causing significant delays in real-time applications. Recent studies show that longer reasoning chains are frequently uncorrelated with correctness and can even be detrimental to accuracy. In a further in-depth analysis of this phenomenon, we surprisingly uncover and empirically verify that LRMs implicitly know the appropriate time to stop thinking, while this capability is obscured by current sampling paradigms. Motivated by this, we introduce SAGE (Self-Aware Guided Efficient Reasoning), a novel sampling paradigm that unleashes this efficient reasoning potential. Furthermore, integrating SAGE as mixed sampling into group-based reinforcement learning (SAGE-RL) enables SAGE-RL to effectively incorporate SAGE-discovered efficient reasoning patterns into standard pass@1 inference, markedly enhancing both the reasoning accuracy and efficiency of LRMs across multiple challenging mathematical benchmarks.

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.

Recent advancements in Large Language Models (LLMs) have significantly enhanced their ability to perform complex reasoning tasks, transitioning from fast and intuitive thinking (System 1) to slow and deep reasoning (System 2). While System 2 reasoning improves task accuracy, it often incurs substantial computational costs due to its slow thinking nature and inefficient or unnecessary reasoning behaviors. In contrast, System 1 reasoning is computationally efficient but leads to suboptimal performance. Consequently, it is critical to balance the trade-off between performance (benefits) and computational costs (budgets), giving rise to the concept of reasoning economy. In this survey, we provide a comprehensive analysis of reasoning economy in both the post-training and test-time inference stages of LLMs, encompassing i) the cause of reasoning inefficiency, ii) behavior analysis of different reasoning patterns, and iii) potential solutions to achieve reasoning economy. By offering actionable insights and highlighting open challenges, we aim to shed light on strategies for improving the reasoning economy of LLMs, thereby serving as a valuable resource for advancing research in this evolving area. We also provide a public repository to continually track developments in this fast-evolving field.

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.

Video reasoning, the task of enabling machines to infer from dynamic visual content through multi-step logic, is crucial for advanced AI. While the Chain-of-Thought (CoT) mechanism has enhanced reasoning in text-based tasks, its application to video understanding remains underexplored. This paper presents a systematic analysis revealing that CoT often degrades performance in video reasoning, generating verbose but misleading internal monologues, and leading to hallucinated visual details and overridden correct intuitions - a phenomenon we term "visual thinking drift". We explain this drift through a Bayesian lens, positing that CoT traces often diverge from actual visual evidence, instead amplifying internal biases or language priors, causing models to storytell rather than engage in grounded reasoning. To counteract this, we introduce Visual Evidence Reward (VER), a novel reinforcement learning framework that explicitly rewards the generation of reasoning traces that are verifiably grounded in visual evidence. Comprehensive evaluation across 10 diverse video understanding benchmarks demonstrates that our Video-VER consistently achieves top performance. Our work sheds light on the distinct challenges of video-centric reasoning and encourages the development of AI that robustly grounds its inferences in visual evidence - for large multimodal models that not only "think before answering", but also "see while thinking".

LLMs' decision-making process is opaque, prompting the need for explanation techniques like Chain-of-Thought. To investigate the relationship between answer and reasoning, we design a novel evaluation framework, MATCHA. In domains like education and healthcare, reasoning is key for model trustworthiness. MATCHA reveals that LLMs under input perturbations can give inconsistent or nonsensical reasoning. Additionally, we use LLM judges to assess reasoning robustness across models. Our results show that LLMs exhibit greater vulnerability to input perturbations for multi-step and commonsense tasks than compared to logical tasks. Also, we show non-trivial transfer rates of our successful examples to black-box models. Our evaluation framework helps to better understand LLM reasoning mechanisms and guides future models toward more robust and reasoning-driven architectures, enforcing answer-reasoning consistency.

Large-scale pre-trained language models (PLMs) bring new opportunities to challenging problems, especially those that need high-level intelligence, such as the math word problem (MWPs). However, directly applying existing PLMs to MWPs can fail as the generation process lacks sufficient supervision and thus lacks fast adaptivity as humans. We notice that human reasoning has a dual reasoning framework that consists of an immediate reaction system (system 1) and a delicate reasoning system (system 2), where the entire reasoning is determined by their interaction. This inspires us to develop a cooperative reasoning-induced PLM for solving MWPs, called Cooperative Reasoning (CoRe), resulting in a human-like reasoning architecture with system 1 as the generator and system 2 as the verifier. In our approach, the generator is responsible for generating reasoning paths, and the verifiers are used to supervise the evaluation in order to obtain reliable feedback for the generator. We evaluate our CoRe framework on several mathematical reasoning datasets and achieve decent improvement over state-of-the-art methods, up to 9.6% increase over best baselines. Our codes are available at https://github.com/TianHongZXY/CoRe

Recent advances in large Vision-Language Models (VLMs) have exhibited strong reasoning capabilities on complex visual tasks by thinking with images in their Chain-of-Thought (CoT), which is achieved by actively invoking tools to analyze visual inputs rather than merely perceiving them. However, existing models often struggle to reflect on and correct themselves when attempting incorrect reasoning trajectories. To address this limitation, we propose DRIM, a model that enables deep but reliable multi-turn reasoning when thinking with images in its multimodal CoT. Our pipeline comprises three stages: data construction, cold-start SFT and RL. Based on a high-resolution image dataset, we construct high-difficulty and verifiable visual question-answer pairs, where solving each task requires multi-turn tool calls to reach the correct answer. In the SFT stage, we collect tool trajectories as cold-start data, guiding a multi-turn reasoning pattern. In the RL stage, we introduce redundancy-penalized policy optimization, which incentivizes the model to develop a self-reflective reasoning pattern. The basic idea is to impose judgment on reasoning trajectories and penalize those that produce incorrect answers without sufficient multi-scale exploration. Extensive experiments demonstrate that DRIM achieves superior performance on visual understanding benchmarks.

Complex reasoning problems often involve implicit spatial, geometric, and structural relationships that are not explicitly encoded in text. While recent reasoning models have achieved strong performance across many domains, purely text-based reasoning struggles to represent global structural constraints in complex settings. In this paper, we introduce FIGR, which integrates active visual thinking into multi-turn reasoning via end-to-end reinforcement learning. FIGR externalizes intermediate structural hypotheses by constructing visual representations during problem solving. By adaptively regulating when and how visual reasoning should be invoked, FIGR enables more stable and coherent reasoning over global structural properties that are difficult to capture from text alone. Experiments on challenging mathematical reasoning benchmarks demonstrate that FIGR outperforms strong text-only chain-of-thought baselines. In particular, FIGR improves the base model by 13.12% on AIME 2025 and 11.00% on BeyondAIME, highlighting the effectiveness of figure-guided multimodal reasoning in enhancing the stability and reliability of complex reasoning.

Visual reasoning refers to the task of solving questions about visual information. Current visual reasoning methods typically employ pre-trained vision-language model (VLM) strategies or deep neural network approaches. However, existing efforts are constrained by limited reasoning interpretability, while hindering by the phenomenon of underspecification in the question text. Additionally, the absence of fine-grained visual knowledge limits the precise understanding of subject behavior in visual reasoning tasks. To address these issues, we propose VIKSER (Visual Knowledge-Driven Self-Reinforcing Reasoning Framework). Specifically, VIKSER, trained using knowledge distilled from large language models, extracts fine-grained visual knowledge with the assistance of visual relationship detection techniques. Subsequently, VIKSER utilizes fine-grained visual knowledge to paraphrase the question with underspecification. Additionally, we design a novel prompting method called Chain-of-Evidence (CoE), which leverages the power of ``evidence for reasoning'' to endow VIKSER with interpretable reasoning capabilities. Meanwhile, the integration of self-reflection technology empowers VIKSER with the ability to learn and improve from its mistakes. Experiments conducted on widely used datasets demonstrate that VIKSER achieves new state-of-the-art (SOTA) results in relevant tasks.

Humans have a powerful and mysterious capacity to reason. By working through a series of purely mental steps, we can make inferences we would not be capable of making directly -- despite the fact that we get no additional data from the world. Similarly, when large language models generate a series of intermediate steps (a chain of thought) before answering a question, they often produce better answers than they otherwise would. We investigate why and how chain-of-thought reasoning is useful in language models, testing the hypothesis that reasoning is effective when training data consists of local clusters of variables that influence each other strongly. These training conditions enable the chaining of accurate local inferences in order to estimate relationships between variables that were not seen together in training. We prove that there will exist a "reasoning gap", where reasoning through intermediate variables improves inference, for the simple case of an autoregressive density estimator trained on local samples from a chain-structured probabilistic model. We then test our hypothesis empirically in more complex models, training an autoregressive language model on samples from Bayes nets but only including a subset of variables in each sample. We test language models' ability to match conditional probabilities with and without intermediate reasoning steps, finding that intermediate steps are only helpful when the training data is locally structured with respect to dependencies between variables and that the combination of locally-structured observations and reasoning is much more data-efficient than training on all variables. Our results illustrate how the effectiveness of reasoning step by step is rooted in the local statistical structure of the training data.

Post-training has become a primary driver of recent progress in large reasoning models, and reasoning data are often the key variable determining whether this stage succeeds. Work on post-training reasoning data has grown rapidly, yet this literature remains scattered across dataset papers, reinforcement-learning recipes, reward-model studies, benchmarks, and frontier system reports. This paper is the first primer to synthesize over 150 key public studies and system reports on post-training reasoning data. We organize the field around four questions: what data objects exist, what makes them useful, how they are constructed, and how they scale. Together, this organization provides an attribution framework for future reasoning-data releases and post-training recipes.

Reasoning-specialized language models show large performance gains over base models, yet the internal changes responsible for improved multi-step reasoning remain poorly understood. It is unclear whether reasoning fine-tuning improves local token-level competence or globally reorganizes how models structure inference over time. We address this question by modeling Chain-of-Thought reasoning as a switching dynamical system (SDS), in which internal representations evolve under discrete latent policy states. Our framework combines time-aware contrastive representation learning with discrete regime discovery to recover latent policies from activation trajectories. Across four benchmarks and model scales from 1.5B to 32B parameters, reasoning-fine-tuned models exhibit richer latent-policy organization than their base counterparts, characterized by more differentiated transition structure and model-dependent changes in state utilization, persistence, and mixing. The recovered regimes exhibit functional specialization aligned with distinct reasoning stages, and extensive controls confirm that their structure is not explained by correctness, representation learning, or modeling priors, but depends on the coherent temporal organization of reasoning trajectories. Causal interventions further show that the regimes are functionally meaningful: state-swap ablations reduce one-step predictive fit, while transplanting reasoning dynamics into base models improves performance on challenging reasoning problems. Finally, SDS-guided pruning of failure-prone reasoning prefixes outperforms self-consistency in 11 of 12 model-dataset settings, with gains of up to 12.5 percentage points. Together, our results suggest that reasoning fine-tuning globally reorganizes latent dynamics, offering a new lens for mechanistic analysis and process-level control of reasoning models.

With the widespread adoption of large language models (LLMs), hallucinations, which are non-factual fabrications in model outputs, have become serious concerns. Reasoning capabilities have received attention as a self-verification process to improve output reliability. However, the effect of reasoning within a closed system where LLMs cannot rely on external tools or knowledge has yet to be clarified. We therefore conduct experiments under strict constraints (recommending peer-reviewed journal articles in computer science) to examine the effect of reasoning across multiple models (GPT-5.2 and Gemini 3 Flash). Our results reveal a problematic trade-off between constraint compliance and factual accuracy. Non-reasoning models exhibit high constraint violation rates (66-75%) but maintain factual accuracy, while reasoning models reduce violations (13-26%) but systematically distort known facts to satisfy constraints and increase complete fabrication. This trade-off pattern is consistent across both models despite different architectures, indicating a fundamental limitation of reasoning. Furthermore, reasoning does not uniformly improve output authenticity: effects diverge by model, reflecting different allocations of the compliance-truthfulness trade-off. These findings challenge the assumption that reasoning universally improves reliability: reasoning models trade honest constraint violations for detection-resistant distortions.

Reasoning stands as a cornerstone of intelligence, enabling the synthesis of existing knowledge to solve complex problems. Despite remarkable progress, existing reasoning benchmarks often fail to rigorously evaluate the nuanced reasoning capabilities required for complex, real-world problemsolving, particularly in multi-disciplinary and multimodal contexts. In this paper, we introduce a graduate-level, multi-disciplinary, EnglishChinese benchmark, dubbed as Reasoning Bench (R-Bench), for assessing the reasoning capability of both language and multimodal models. RBench spans 1,094 questions across 108 subjects for language model evaluation and 665 questions across 83 subjects for multimodal model testing in both English and Chinese. These questions are meticulously curated to ensure rigorous difficulty calibration, subject balance, and crosslinguistic alignment, enabling the assessment to be an Olympiad-level multi-disciplinary benchmark. We evaluate widely used models, including OpenAI o1, GPT-4o, DeepSeek-R1, etc. Experimental results indicate that advanced models perform poorly on complex reasoning, especially multimodal reasoning. Even the top-performing model OpenAI o1 achieves only 53.2% accuracy on our multimodal evaluation. Data and code are made publicly available at here.

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.

We introduce S1-Bench, a novel benchmark designed to evaluate Large Reasoning Models' (LRMs) performance on simple tasks that favor intuitive system 1 thinking rather than deliberative system 2 reasoning. While LRMs have achieved significant breakthroughs in complex reasoning tasks through explicit chains of thought, their reliance on deep analytical thinking may limit their system 1 thinking capabilities. Moreover, a lack of benchmark currently exists to evaluate LRMs' performance in tasks that require such capabilities. To fill this gap, S1-Bench presents a set of simple, diverse, and naturally clear questions across multiple domains and languages, specifically designed to assess LRMs' performance in such tasks. Our comprehensive evaluation of 22 LRMs reveals significant lower efficiency tendencies, with outputs averaging 15.5 times longer than those of traditional small LLMs. Additionally, LRMs often identify correct answers early but continue unnecessary deliberation, with some models even producing numerous errors. These findings highlight the rigid reasoning patterns of current LRMs and underscore the substantial development needed to achieve balanced dual-system thinking capabilities that can adapt appropriately to task complexity.

Large reasoning models (LRMs) achieve strong performance on mathematical reasoning tasks, often attributed to their capability to generate explicit chain-of-thought (CoT) explanations. However, recent work shows that LRMs often arrive at the correct answer before completing these textual reasoning steps, indicating the presence of latent reasoning -- internal, non-verbal computation encoded in hidden states. While this phenomenon has been explored in English, its multilingual behavior remains largely unknown. In this paper, we conduct a systematic investigation of multilingual latent reasoning in LRMs across 11 languages. Using a truncation-based strategy, we examine how the correct answer emerges as the model is given only partial reasoning traces, allowing us to measure stepwise latent prediction formation. Our results reveal clear evidence of multilingual latent reasoning, though unevenly: strong in resource-rich languages, weaker in low-resource ones, and broadly less observable on harder benchmarks. To understand whether these differences reflect distinct internal mechanisms, we further perform representational analyses. Despite surface-level disparities, we find that the internal evolution of predictions is highly consistent across languages and broadly aligns with English -- a pattern suggesting an English-centered latent reasoning pathway.

Reasoning, the process of devising and executing complex goal-oriented action sequences, remains a critical challenge in AI. Current large language models (LLMs) primarily employ Chain-of-Thought (CoT) techniques, which suffer from brittle task decomposition, extensive data requirements, and high latency. Inspired by the hierarchical and multi-timescale processing in the human brain, we propose the Hierarchical Reasoning Model (HRM), a novel recurrent architecture that attains significant computational depth while maintaining both training stability and efficiency. HRM executes sequential reasoning tasks in a single forward pass without explicit supervision of the intermediate process, through two interdependent recurrent modules: a high-level module responsible for slow, abstract planning, and a low-level module handling rapid, detailed computations. With only 27 million parameters, HRM achieves exceptional performance on complex reasoning tasks using only 1000 training samples. The model operates without pre-training or CoT data, yet achieves nearly perfect performance on challenging tasks including complex Sudoku puzzles and optimal path finding in large mazes. Furthermore, HRM outperforms much larger models with significantly longer context windows on the Abstraction and Reasoning Corpus (ARC), a key benchmark for measuring artificial general intelligence capabilities. These results underscore HRM's potential as a transformative advancement toward universal computation and general-purpose reasoning systems.

Logical reasoning is a critical benchmark for evaluating the capabilities of large language models (LLMs), as it reflects their ability to derive valid conclusions from given premises. While the combination of test-time scaling with dedicated outcome or process reward models has opened up new avenues to enhance LLMs performance in complex reasoning tasks, this space is under-explored in deductive logical reasoning. We present a set of Outcome Reward Models (ORMs) for deductive reasoning. To train the ORMs we mainly generate data using Chain-of-Thought (CoT) with single and multiple samples. Additionally, we propose a novel tactic to further expand the type of errors covered in the training dataset of the ORM. In particular, we propose an echo generation technique that leverages LLMs' tendency to reflect incorrect assumptions made in prompts to extract additional training data, covering previously unexplored error types. While a standard CoT chain may contain errors likely to be made by the reasoner, the echo strategy deliberately steers the model toward incorrect reasoning. We show that ORMs trained on CoT and echo-augmented data demonstrate improved performance on the FOLIO, JustLogic, and ProverQA datasets across four different LLMs.

In most current research, large language models (LLMs) are able to perform reasoning tasks by generating chains of thought through the guidance of specific prompts. However, there still exists a significant discrepancy between their capability in solving complex reasoning problems and that of humans. At present, most approaches focus on chains of thought (COT) and tool use, without considering the adoption and application of human cognitive frameworks. It is well-known that when confronting complex reasoning challenges, humans typically employ various cognitive abilities, and necessitate interaction with all aspects of tools, knowledge, and the external environment information to accomplish intricate tasks. This paper introduces a novel intelligent framework, referred to as OlaGPT. OlaGPT carefully studied a cognitive architecture framework, and propose to simulate certain aspects of human cognition. The framework involves approximating different cognitive modules, including attention, memory, reasoning, learning, and corresponding scheduling and decision-making mechanisms. Inspired by the active learning mechanism of human beings, it proposes a learning unit to record previous mistakes and expert opinions, and dynamically refer to them to strengthen their ability to solve similar problems. The paper also outlines common effective reasoning frameworks for human problem-solving and designs Chain-of-Thought (COT) templates accordingly. A comprehensive decision-making mechanism is also proposed to maximize model accuracy. The efficacy of OlaGPT has been stringently evaluated on multiple reasoning datasets, and the experimental outcomes reveal that OlaGPT surpasses state-of-the-art benchmarks, demonstrating its superior performance. Our implementation of OlaGPT is available on GitHub: https://github.com/oladata-team/OlaGPT.

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.

Understanding how Large Language Models (LLMs) perform complex reasoning and their failure mechanisms is a challenge in interpretability research. To provide a measurable geometric analysis perspective, we define the concept of the Reasoning Manifold, a latent low-dimensional geometric structure formed by the internal representations corresponding to all correctly reasoned generations. This structure can be conceptualized as the embodiment of the effective thinking paths that the model has learned to successfully solve a given task. Based on this concept, we build REMA, a framework that explains the origins of failures by quantitatively comparing the spatial relationships of internal model representations corresponding to both erroneous and correct reasoning samples. Specifically, REMA first quantifies the geometric deviation of each erroneous representation by calculating its k-nearest neighbors distance to the approximated manifold formed by correct representations, thereby providing a unified failure signal. It then localizes the divergence points where these deviations first become significant by tracking this deviation metric across the model's layers and comparing it against a baseline of internal fluctuations from correct representations, thus identifying where the reasoning chain begins to go off-track. Our extensive experiments on diverse language and multimodal models and tasks demonstrate the low-dimensional nature of the reasoning manifold and the high separability between erroneous and correct reasoning representations. The results also validate the effectiveness of the REMA framework in analyzing the origins of reasoning failures. This research connects abstract reasoning failures to measurable geometric deviations in representations, providing new avenues for in-depth understanding and diagnosis of the internal computational processes of black-box models.

Reasoning is a core capability in artificial intelligence systems, for which large language models (LLMs) have recently shown remarkable progress. However, most work focuses exclusively on deductive reasoning, which is problematic since other types of reasoning are also essential in solving real-world problems, and they are less explored. This work focuses on evaluating LLMs' inductive and abductive reasoning capabilities. We introduce a programmable and synthetic dataset, InAbHyD (pronounced in-a-bid), where each reasoning example consists of an incomplete world model and a set of observations. The task for the intelligent agent is to produce hypotheses to explain observations under the incomplete world model to solve each reasoning example. We propose a new metric to evaluate the quality of hypotheses based on Occam's Razor. We evaluate and analyze some state-of-the-art LLMs. Our analysis shows that LLMs can perform inductive and abductive reasoning in simple scenarios, but struggle with complex world models and producing high-quality hypotheses, even with popular reasoning-enhancing techniques such as in-context learning and RLVR.

Scaling inference through long chains-of-thought (CoTs) has unlocked impressive reasoning capabilities in large language models (LLMs), yet the reasoning process remains almost exclusively English-centric. We construct translated versions of two popular English reasoning datasets, fine-tune Qwen 2.5 (7B) and Qwen 3 (8B) models, and present a systematic study of long CoT generation across French, Japanese, Latvian, and Swahili. Our experiments reveal three key findings. First, the efficacy of using English as a pivot language varies by language: it provides no benefit for French, improves performance when used as the reasoning language for Japanese and Latvian, and proves insufficient for Swahili where both task comprehension and reasoning remain poor. Second, extensive multilingual pretraining in Qwen 3 narrows but does not eliminate the cross-lingual performance gap. A lightweight fine-tune using only 1k traces still improves performance by over 30\% in Swahili. Third, data quality versus scale trade-offs are language dependent: small, carefully curated datasets suffice for English and French, whereas larger but noisier corpora prove more effective for Swahili and Latvian. Together, these results clarify when and why long CoTs transfer across languages and provide translated datasets to foster equitable multilingual reasoning research.

Recent advances in large language models (LLMs) have demonstrated that reinforcement learning with verifiable rewards (RLVR) can significantly enhance reasoning abilities by directly optimizing correctness, rather than relying solely on supervised imitation. This paradigm has been extended to multimodal LLMs for complex video and image understanding tasks. However, while outcome-driven RL improves answer accuracy, it can inadvertently decouple the reasoning chain from the final answer, leading to situations where models produce inconsistency between the reasoning trace and final answer. In our experiments on multiple-choice visual question-answering tasks, the standard GRPO method yields only 79.7\% consistency on MMVU between the reasoning steps and the chosen answers, indicating frequent mismatches between answers and reasoning. To this end, we propose Answer-Consistent Reinforcement Learning (ACRE) that modifies the GRPO algorithm with an auxiliary consistency check. After the model generates a chain of thought and an initial answer for a given question, we shuffle the answer options and prompt the model again with the same reasoning trace to predict a second answer. We design a consistency-verification reward that grants a high reward only if both the original and the post-shuffle answers agree and are correct; otherwise, a lower reward is assigned accordingly. This mechanism penalizes reasoning-answer misalignment and discourages the model from relying on spurious patterns, such as option ordering biases. We evaluate ACRE on challenging Video Reasoning benchmarks and multimodal math reasoning benchmarks, achieving an average 2.2\% and 1.5\% improvement for Video Reasoning and Math Reasoning tasks over the GRPO baseline.

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

While Large Reasoning Models (LRMs) generate extensive chain-of-thought reasoning, we lack a principled framework for understanding how these thoughts are structured. In this paper, we introduce a novel approach by applying Schoenfeld's Episode Theory, a classic cognitive framework for human mathematical problem-solving, to analyze the reasoning traces of LRMs. We annotated thousands of sentences and paragraphs from model-generated solutions to math problems using seven cognitive labels (e.g., Plan, Implement, Verify). The result is the first publicly available benchmark for the fine-grained analysis of machine reasoning, including a large annotated corpus and detailed annotation guidebooks. Our preliminary analysis reveals distinct patterns in LRM reasoning, such as the transition dynamics between cognitive states. This framework provides a theoretically grounded methodology for interpreting LRM cognition and enables future work on more controllable and transparent reasoning systems.

We study syllogistic reasoning in LLMs from the logical and natural language perspectives. In process, we explore fundamental reasoning capabilities of the LLMs and the direction this research is moving forward. To aid in our studies, we use 14 large language models and investigate their syllogistic reasoning capabilities in terms of symbolic inferences as well as natural language understanding. Even though this reasoning mechanism is not a uniform emergent property across LLMs, the perfect symbolic performances in certain models make us wonder whether LLMs are becoming more and more formal reasoning mechanisms, rather than making explicit the nuances of human reasoning.

When writing and talking, people sometimes pause to think. Although reasoning-focused works have often framed reasoning as a method of answering questions or completing agentic tasks, reasoning is implicit in almost all written text. For example, this applies to the steps not stated between the lines of a proof or to the theory of mind underlying a conversation. In the Self-Taught Reasoner (STaR, Zelikman et al. 2022), useful thinking is learned by inferring rationales from few-shot examples in question-answering and learning from those that lead to a correct answer. This is a highly constrained setting -- ideally, a language model could instead learn to infer unstated rationales in arbitrary text. We present Quiet-STaR, a generalization of STaR in which LMs learn to generate rationales at each token to explain future text, improving their predictions. We address key challenges, including 1) the computational cost of generating continuations, 2) the fact that the LM does not initially know how to generate or use internal thoughts, and 3) the need to predict beyond individual next tokens. To resolve these, we propose a tokenwise parallel sampling algorithm, using learnable tokens indicating a thought's start and end, and an extended teacher-forcing technique. Encouragingly, generated rationales disproportionately help model difficult-to-predict tokens and improve the LM's ability to directly answer difficult questions. In particular, after continued pretraining of an LM on a corpus of internet text with Quiet-STaR, we find zero-shot improvements on GSM8K (5.9%rightarrow10.9%) and CommonsenseQA (36.3%rightarrow47.2%) and observe a perplexity improvement of difficult tokens in natural text. Crucially, these improvements require no fine-tuning on these tasks. Quiet-STaR marks a step towards LMs that can learn to reason in a more general and scalable way.

To augment language models with the ability to reason, researchers usually prompt or finetune them to produce chain of thought reasoning steps before producing the final answer. However, although people use natural language to reason effectively, it may be that LMs could reason more effectively with some intermediate computation that is not in natural language. In this work, we explore an alternative reasoning approach: instead of explicitly producing the chain of thought reasoning steps, we use the language model's internal hidden states to perform implicit reasoning. The implicit reasoning steps are distilled from a teacher model trained on explicit chain-of-thought reasoning, and instead of doing reasoning "horizontally" by producing intermediate words one-by-one, we distill it such that the reasoning happens "vertically" among the hidden states in different layers. We conduct experiments on a multi-digit multiplication task and a grade school math problem dataset and find that this approach enables solving tasks previously not solvable without explicit chain-of-thought, at a speed comparable to no chain-of-thought.

Cartographic reasoning is the skill of interpreting geographic relationships by aligning legends, map scales, compass directions, map texts, and geometries across one or more map images. Although essential as a concrete cognitive capability and for critical tasks such as disaster response and urban planning, it remains largely unevaluated. Building on progress in chart and infographic understanding, recent large vision language model studies on map visual question-answering often treat maps as a special case of charts. In contrast, map VQA demands comprehension of layered symbology (e.g., symbols, geometries, and text labels) as well as spatial relations tied to orientation and distance that often span multiple maps and are not captured by chart-style evaluations. To address this gap, we introduce FRIEDA, a benchmark for testing complex open-ended cartographic reasoning in LVLMs. FRIEDA sources real map images from documents and reports in various domains and geographical areas. Following classifications in Geographic Information System (GIS) literature, FRIEDA targets all three categories of spatial relations: topological (border, equal, intersect, within), metric (distance), and directional (orientation). All questions require multi-step inference, and many require cross-map grounding and reasoning. We evaluate eleven state-of-the-art LVLMs under two settings: (1) the direct setting, where we provide the maps relevant to the question, and (2) the contextual setting, where the model may have to identify the maps relevant to the question before reasoning. Even the strongest models, Gemini-2.5-Pro and GPT-5-Think, achieve only 38.20% and 37.20% accuracy, respectively, far below human performance of 84.87%. These results reveal a persistent gap in multi-step cartographic reasoning, positioning FRIEDA as a rigorous benchmark to drive progress on spatial intelligence in LVLMs.

Deductive reasoning is the process of deriving conclusions strictly from the given premises, without relying on external knowledge. We define honesty in this setting as a model's ability to respond only when the conclusion is logically entailed by the premises, and to abstain otherwise. However, current language models often fail to reason honestly, producing unwarranted answers when the input is insufficient. To study this challenge, we formulate honest deductive reasoning as multi-step tasks where models must either derive the correct conclusion or abstain. We curate two datasets from graph structures, one for linear algebra and one for logical inference, and introduce unanswerable cases by randomly perturbing an edge in half of the instances. We find that prompting and existing training methods, including GRPO with or without supervised fine-tuning initialization, struggle on these tasks. In particular, GRPO optimize only for final task outcomes, leaving models vulnerable to collapse when negative rewards dominate early training. To address this, we propose ACNCHOR, a reinforcement learning method that injects ground truth trajectories into rollouts, preventing early training collapse. Our results demonstrate that this method stabilizes learning and significantly improves the overall reasoning performance, underscoring the importance of training dynamics for enabling honest deductive reasoning in language models.

A central question in artificial intelligence is the extent to which machine learning models comprehend mathematics. To address this, we propose a novel framework for measuring mathematical reasoning that moves beyond standard benchmarks to diagnose specific failure points. Our method first generates structured, step-by-step reasoning from gpt-3.5-turbo on the GSM8K dataset. We then use a more capable analyst model, gpt-4o-mini, to categorize errors and, crucially, perform an unsupervised clustering of every reasoning sentence to identify emergent "reasoning modes." This analysis reveals a cognitive profile with a stark, nonhuman-like brittleness: while the model achieves near-perfect accuracy on procedural modes like sequential calculation, its performance on modes requiring combinatorial reasoning with restrictions plummets. By identifying and quantifying the reliability of these distinct reasoning skills, our work provides a more granular method to evaluate mathematical comprehension and offers a precise roadmap for developing new capabilities and more reliable future applications.

Recent advances in test-time compute scaling have enabled Large Language Models (LLMs) to tackle deep reasoning tasks by generating a chain-of-thought (CoT) that includes trial and error, backtracking, and intermediate reasoning steps before producing the final answer. However, these techniques have been applied predominantly to popular languages, such as English, leaving reasoning in low-resource languages underexplored and misaligned. In this work, we investigate the multilingual mechanism by which LLMs internally operate in a latent space biased toward their inherently dominant language. To leverage this phenomenon for low-resource languages, we train models to generate the CoT in English while outputting the final response in the target language, given input in the low-resource language. Our experiments demonstrate that this approach, named English-Pivoted CoT Training, outperforms other baselines, including training to generate both the CoT and the final response solely in the target language, with up to 28.33% improvement. Further analysis provides novel insights into the relationships between reasoning and multilinguality of LLMs, prompting for better approaches in developing multilingual large reasoning models

Recent advancements in large language models (LLMs) often rely on generating intermediate reasoning steps to enhance accuracy. However, little work has examined how reasoning utility contributes to the final answer's correctness. Due to the stochastic nature of autoregressive generation, generating more context does not guarantee increased confidence in the answer. If we could predict, during generation, whether a reasoning step will be useful, we could stop early or prune ineffective steps, avoiding distractions in the final decision. We present an oracle study on MATH dataset, using Qwen2.5-32B and GPT-4o to generate reasoning chains, and then employing a separate model (Qwen3-8B) to quantify the utility of these chains for final accuracy. Specifically, we measure the model's uncertainty on the answer span Y at each reasoning step using conditional entropy (expected negative log-likelihood over the vocabulary) with context expanding step by step. Our results show a clear pattern: conditional entropy that decreases over steps is strongly associated with correct answers, whereas flat or increasing entropy often results in wrong answers. We also corroborate that incorrect reasoning paths tend to be longer than correct ones, suggesting that longer reasoning does not necessarily yield better outcomes. These findings serve as a foundation to inspire future work on designing efficient reasoning pipelines that detect and avoid unproductive reasoning early.

Recent advancements in reasoning-reinforced Large Language Models (LLMs) have shown remarkable capabilities in complex reasoning tasks. However, the mechanism underlying their utilization of different human reasoning skills remains poorly investigated, especially for multilingual commonsense reasoning that involves everyday knowledge across different languages and cultures. To address this gap, we propose a Multilingual and Scalable Benchmark for Skill-based Commonsense Reasoning (mSCoRe). Our benchmark incorporates three key components that are designed to systematically evaluate LLM's reasoning capabilities, including: (1) a novel taxonomy of reasoning skills that enables fine-grained analysis of models' reasoning processes, (2) a robust data synthesis pipeline tailored specifically for commonsense reasoning evaluation, and (3) a complexity scaling framework allowing task difficulty to scale dynamically alongside future improvements in LLM abilities. Extensive experiments on eights state-of-the-art LLMs of varying sizes and training approaches demonstrate that mSCoRe remains significantly challenging for current models, particularly at higher complexity levels. Our results reveal the limitations of such reasoning-reinforced models when confronted with nuanced multilingual general and cultural commonsense. We further provide detailed analysis on the models' reasoning processes, suggesting future directions for improving multilingual commonsense reasoning capabilities.

Large Language Models (LLMs) have demonstrated impressive reasoning abilities through test-time computation (TTC) techniques such as chain-of-thought prompting and tree-based reasoning. However, we argue that current reasoning LLMs (RLLMs) lack the ability to systematically explore the solution space. This paper formalizes what constitutes systematic problem solving and identifies common failure modes that reveal reasoning LLMs to be wanderers rather than systematic explorers. Through qualitative and quantitative analysis across multiple state-of-the-art LLMs, we uncover persistent issues: invalid reasoning steps, redundant explorations, hallucinated or unfaithful conclusions, and so on. Our findings suggest that current models' performance can appear to be competent on simple tasks yet degrade sharply as complexity increases. Based on the findings, we advocate for new metrics and tools that evaluate not just final outputs but the structure of the reasoning process itself.

While reinforcement learning has advanced the reasoning abilities of Large Language Models (LLMs), these gains are largely confined to English, creating a significant performance disparity across languages. To address this, we introduce Pivot-Based Reinforcement Learning with Semantically Verifiable Rewards (PB-RLSVR), a novel framework that enhances multilingual reasoning by circumventing the need for human-annotated data in target languages. Our approach employs a high-performing English LLM as a "pivot" model to generate reference responses for reasoning tasks. A multilingual model is then rewarded based on the semantic equivalence of its responses to the English reference, effectively transferring the pivot model's reasoning capabilities across languages. We investigate several cross-lingual semantic reward functions, including those based on embeddings and machine translation. Extensive experiments on a suite of multilingual reasoning benchmarks show that our method significantly narrows the performance gap between English and other languages, substantially outperforming traditional PPO baselines. Specifically, our PB-RLSVR framework improves the average multilingual performance of Llama-3.1-8B-Instruct and Qwen3-32B by 16.41% and 10.17%, respectively, demonstrating a powerful and data-efficient approach to building truly multilingual reasoning agents.

Large language models (LLMs) demonstrate significant reasoning capabilities, particularly through long chain-of-thought (CoT) processes, which can be elicited by reinforcement learning (RL). However, prolonged CoT reasoning presents limitations, primarily verbose outputs due to excessive introspection. The reasoning process in these LLMs often appears to follow a trial-and-error methodology rather than a systematic, logical deduction. In contrast, tree-of-thoughts (ToT) offers a conceptually more advanced approach by modeling reasoning as an exploration within a tree structure. This reasoning structure facilitates the parallel generation and evaluation of multiple reasoning branches, allowing for the active identification, assessment, and pruning of unproductive paths. This process can potentially lead to improved performance and reduced token costs. Building upon the long CoT capability of LLMs, we introduce tree-of-thoughts RL (ToTRL), a novel on-policy RL framework with a rule-based reward. ToTRL is designed to guide LLMs in developing the parallel ToT strategy based on the sequential CoT strategy. Furthermore, we employ LLMs as players in a puzzle game during the ToTRL training process. Solving puzzle games inherently necessitates exploring interdependent choices and managing multiple constraints, which requires the construction and exploration of a thought tree, providing challenging tasks for cultivating the ToT reasoning capability. Our empirical evaluations demonstrate that our ToTQwen3-8B model, trained with our ToTRL, achieves significant improvement in performance and reasoning efficiency on complex reasoning tasks.

With the development of large language models (LLMs), particularly with the introduction of the long reasoning chain technique, the reasoning ability of LLMs in complex problem-solving has been significantly enhanced. While acknowledging the power of long reasoning chains, we cannot help but wonder: Why do different reasoning chains perform differently in reasoning? What components of the reasoning chains play a key role? Existing studies mainly focus on evaluating reasoning chains from a functional perspective, with little attention paid to their structural mechanisms. To address this gap, this work is the first to analyze and evaluate the quality of the reasoning chain from a structural perspective. We apply persistent homology from Topological Data Analysis (TDA) to map reasoning steps into semantic space, extract topological features, and analyze structural changes. These changes reveal semantic coherence, logical redundancy, and identify logical breaks and gaps. By calculating homology groups, we assess connectivity and redundancy at various scales, using barcode and persistence diagrams to quantify stability and consistency. Our results show that the topological structural complexity of reasoning chains correlates positively with accuracy. More complex chains identify correct answers sooner, while successful reasoning exhibits simpler topologies, reducing redundancy and cycles, enhancing efficiency and interpretability. This work provides a new perspective on reasoning chain quality assessment and offers guidance for future optimization.

Large Reasoning Models (LRMs) have significantly enhanced their capabilities in complex problem-solving by introducing a thinking draft that enables multi-path Chain-of-Thought explorations before producing final answers. Ensuring the faithfulness of these intermediate reasoning processes is crucial for reliable monitoring, interpretation, and effective control. In this paper, we propose a systematic counterfactual intervention framework to rigorously evaluate thinking draft faithfulness. Our approach focuses on two complementary dimensions: (1) Intra-Draft Faithfulness, which assesses whether individual reasoning steps causally influence subsequent steps and the final draft conclusion through counterfactual step insertions; and (2) Draft-to-Answer Faithfulness, which evaluates whether final answers are logically consistent with and dependent on the thinking draft, by perturbing the draft's concluding logic. We conduct extensive experiments across six state-of-the-art LRMs. Our findings show that current LRMs demonstrate selective faithfulness to intermediate reasoning steps and frequently fail to faithfully align with the draft conclusions. These results underscore the need for more faithful and interpretable reasoning in advanced LRMs.