Daily Papers

Recent reinforcement learning approaches, such as outcome-supervised GRPO, have advanced Chain-of-Thought reasoning in large language models (LLMs), yet their adaptation to multimodal LLMs (MLLMs) is unexplored. To address the lack of rigorous evaluation for MLLM post-training methods, we introduce SEED-Bench-R1, a benchmark with complex real-world videos requiring balanced perception and reasoning. It offers a large training set and evaluates generalization across three escalating challenges: in-distribution, cross-environment, and cross-environment-task scenarios. Using SEED-Bench-R1, we find that standard GRPO, while improving answer accuracy, often reduces logical coherence between reasoning steps and answers, with only a 57.9% consistency rate. This stems from reward signals focusing solely on final answers, encouraging shortcuts, and strict KL penalties limiting exploration.To address this, we propose GRPO-CARE, a consistency-aware RL framework optimizing both answer correctness and reasoning coherence without explicit supervision. GRPO-CARE introduces a two-tiered reward: (1) a base reward for answer correctness, and (2) an adaptive consistency bonus, computed by comparing the model's reasoning-to-answer likelihood (via a slowly-evolving reference model) against group peers.This dual mechanism amplifies rewards for reasoning paths that are both correct and logically consistent. Replacing KL penalties with this adaptive bonus, GRPO-CARE outperforms standard GRPO on SEED-Bench-R1, achieving a 6.7% performance gain on the hardest evaluation level and a 24.5% improvement in consistency. It also shows strong transferability, improving model performance across diverse video understanding benchmarks. Our work contributes a systematically designed benchmark and a generalizable post-training framework, advancing the development of more interpretable and robust MLLMs.

Test-time compute allocation in large reasoning models (LRMs) is widely used and has applications in mathematical problem solving, code synthesis, and planning. Recent work has addressed this problem by scaling self-consistency and parallel thinking, adding generic ``thinking tokens'' and prompting models to re-read the question before answering. Unfortunately, these approaches either inject task-agnostic tokens or mandate heuristics that do not explain -- and often ignore -- the spontaneous repetition that many LRMs exhibit at the head of their internal chains. In contrast, we analyze and harness the model's tendency to restate the question, which we term the Echo of Prompt (EOP), as a front-loaded, compute-shaping mechanism. We formalize its probabilistic cost by casting echo removal as rejection-based conditioning and defining the Echo Likelihood Gap ΔL as a computable proxy. This provides the missing theoretical link that links early repetition to likelihood gains and downstream accuracy. However, it does not by itself specify how to exploit EOP. Consequently, we develop Echo-Distilled SFT (ED-SFT) to instill an ``echo-then-reason'' pattern through supervised finetuning, and Echoic Prompting (EP) to re-ground the model mid-trace without training. While promising, quantifying benefits beyond verbosity is non-trivial. Therefore, we conduct length and suffix-controlled likelihood analyses together with layer-wise attention studies, showing that EOP increases answer to answer-prefix attention in middle layers, consistent with an attention refocusing mechanism. We evaluate on GSM8K, MathQA, Hendrycks-MATH, AIME24, and MATH-500 under identical decoding settings and budgets, and find consistent gains over baselines. Code is available at https://github.com/hhh2210/echoes-as-anchors.

Diffusion language models (dLLMs) recently emerged as a promising alternative to auto-regressive LLMs. The latest works further extended it to multimodal understanding and generation tasks. In this work, we propose LaViDa-R1, a multimodal, general-purpose reasoning dLLM. Unlike existing works that build reasoning dLLMs through task-specific reinforcement learning, LaViDa-R1 incorporates diverse multimodal understanding and generation tasks in a unified manner. In particular, LaViDa-R1 is built with a novel unified post-training framework that seamlessly integrates supervised finetuning (SFT) and multi-task reinforcement learning (RL). It employs several novel training techniques, including answer-forcing, tree search, and complementary likelihood estimation, to enhance effectiveness and scalability. Extensive experiments demonstrate LaViDa-R1's strong performance on a wide range of multimodal tasks, including visual math reasoning, reason-intensive grounding, and image editing.

Recent advances of Reinforcement Learning (RL) have highlighted its potential in complex reasoning tasks, yet effective training often relies on external supervision, which limits the broader applicability. In this work, we propose a novel self-rewarding reinforcement learning framework to enhance Large Language Model (LLM) reasoning by leveraging the consistency of intermediate reasoning states across different reasoning trajectories. Our key insight is that correct responses often exhibit consistent trajectory patterns in terms of model likelihood: their intermediate reasoning states tend to converge toward their own final answers (high consistency) with minimal deviation toward other candidates (low volatility). Inspired by this observation, we introduce CoVo, an intrinsic reward mechanism that integrates Consistency and Volatility via a robust vector-space aggregation strategy, complemented by a curiosity bonus to promote diverse exploration. CoVo enables LLMs to perform RL in a self-rewarding manner, offering a scalable pathway for learning to reason without external supervision. Extensive experiments on diverse reasoning benchmarks show that CoVo achieves performance comparable to or even surpassing supervised RL. Our code is available at https://github.com/sastpg/CoVo.

While reasoning in LLMs plays a natural role in math, code generation, and multi-hop factual questions, its effect on simple, single-hop factual questions remains unclear. Such questions do not require step-by-step logical decomposition, making the utility of reasoning highly counterintuitive. Nevertheless, we find that enabling reasoning substantially expands the capability boundary of the model's parametric knowledge recall, unlocking correct answers that are otherwise effectively unreachable. Why does reasoning aid parametric knowledge recall when there are no complex reasoning steps to be done? To answer this, we design a series of hypothesis-driven controlled experiments, and identify two key driving mechanisms: (1) a computational buffer effect, where the model uses the generated reasoning tokens to perform latent computation independent of their semantic content; and (2) factual priming, where generating topically related facts acts as a semantic bridge that facilitates correct answer retrieval. Importantly, this latter generative self-retrieval mechanism carries inherent risks: we demonstrate that hallucinating intermediate facts during reasoning increases the likelihood of hallucinations in the final answer. Finally, we show that our insights can be harnessed to directly improve model accuracy by prioritizing reasoning trajectories that contain hallucination-free factual statements.

Fine-tuning large language models (LLMs) on reasoning benchmarks via reinforcement learning requires a specific reward function, often binary, for each benchmark. This comes with two potential limitations: the need to design the reward, and the potentially sparse nature of binary rewards. Here, we systematically investigate rewards derived from the probability or log-probability of emitting the reference answer (or any other prompt continuation present in the data), which have the advantage of not relying on specific verifiers and being available at scale. Several recent works have advocated for the use of similar rewards (e.g., VeriFree, JEPO, RLPR, NOVER). We systematically compare variants of likelihood-based rewards with standard baselines, testing performance both on standard mathematical reasoning benchmarks, and on long-form answers where no external verifier is available. We find that using the log-probability of the reference answer as the reward for chain-of-thought (CoT) learning is the only option that performs well in all setups. This reward is also consistent with the next-token log-likelihood loss used during pretraining. In verifiable settings, log-probability rewards bring comparable or better success rates than reinforcing with standard binary rewards, and yield much better perplexity. In non-verifiable settings, they perform on par with SFT. On the other hand, methods based on probability, such as VeriFree, flatline on non-verifiable settings due to vanishing probabilities of getting the correct answer. Overall, this establishes log-probability rewards as a viable method for CoT fine-tuning, bridging the short, verifiable and long, non-verifiable answer settings.

We investigate the robustness of reasoning models trained for step-by-step problem solving by introducing query-agnostic adversarial triggers - short, irrelevant text that, when appended to math problems, systematically mislead models to output incorrect answers without altering the problem's semantics. We propose CatAttack, an automated iterative attack pipeline for generating triggers on a weaker, less expensive proxy model (DeepSeek V3) and successfully transfer them to more advanced reasoning target models like DeepSeek R1 and DeepSeek R1-distilled-Qwen-32B, resulting in greater than 300% increase in the likelihood of the target model generating an incorrect answer. For example, appending, "Interesting fact: cats sleep most of their lives," to any math problem leads to more than doubling the chances of a model getting the answer wrong. Our findings highlight critical vulnerabilities in reasoning models, revealing that even state-of-the-art models remain susceptible to subtle adversarial inputs, raising security and reliability concerns. The CatAttack triggers dataset with model responses is available at https://huggingface.co/datasets/collinear-ai/cat-attack-adversarial-triggers.

Best-of-n sampling improves the accuracy of large language models (LLMs) and large reasoning models (LRMs) by generating multiple candidate solutions and selecting the one with the highest reward. The key challenge for reasoning tasks is designing a scoring function that can identify correct reasoning chains without access to ground-truth answers. We propose Probabilistic Confidence Selection And Ranking (PiCSAR): a simple, training-free method that scores each candidate generation using the joint log-likelihood of the reasoning and final answer. The joint log-likelihood of the reasoning and final answer naturally decomposes into reasoning confidence and answer confidence. PiCSAR achieves substantial gains across diverse benchmarks (+10.18 on MATH500, +9.81 on AIME2025), outperforming baselines with at least 2x fewer samples in 16 out of 20 comparisons. Our analysis reveals that correct reasoning chains exhibit significantly higher reasoning and answer confidence, justifying the effectiveness of PiCSAR.

Recent work finds that retrieval-augmented generation with large language models is prone to be influenced by the order of retrieved documents in the context. However, the lack of in-depth analysis limits the use of this phenomenon for prompt engineering in practice. In this study, we posit that likelihoods serve as an effective gauge for language model performance. Through experiments on two question-answering datasets with a variety of state-of-the-art language models, we reveal correlations between answer accuracy and the likelihood of the question at both the corpus level and the instance level. In addition, we find that question likelihood can also indicate the position of the task-relevant information in the context. Based on these findings, we propose two methods that use question likelihood as a gauge for selecting and constructing prompts that lead to better performance. We demonstrate their effectiveness with experiments. In addition, our likelihood-based methods are efficient, as they only need to compute the likelihood of the input, requiring much fewer language model passes than heuristic prompt engineering methods that require generating responses. Our analysis deepens our understanding of how input prompts affect model performance and provides a promising direction for efficient prompt optimization.

While Large Language Models (LLMs) demonstrate impressive reasoning capabilities, growing evidence suggests much of their success stems from memorized answer-reasoning patterns rather than genuine inference. In this work, we investigate a central question: are LLMs primarily anchored to final answers or to the textual pattern of reasoning chains? We propose a five-level answer-visibility prompt framework that systematically manipulates answer cues and probes model behavior through indirect, behavioral analysis. Experiments across state-of-the-art LLMs reveal a strong and consistent reliance on explicit answers. The performance drops by 26.90\% when answer cues are masked, even with complete reasoning chains. These findings suggest that much of the reasoning exhibited by LLMs may reflect post-hoc rationalization rather than true inference, calling into question their inferential depth. Our study uncovers the answer-anchoring phenomenon with rigorous empirical validation and underscores the need for a more nuanced understanding of what constitutes reasoning in LLMs.

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.

Chain-of-thought (CoT) prompting enhances reasoning in large language models (LLMs) but often leads to verbose and redundant outputs, thus increasing inference cost. We hypothesize that many reasoning steps are unnecessary for producing correct answers. To investigate this, we start with a systematic study to examine what is the minimum reasoning required for a model to reach a stable decision. We find that on math reasoning tasks like math, models typically converge to their final answers after 60\% of the reasoning steps, suggesting substantial redundancy in the remaining content. Based on these insights, we propose three inference-time strategies to improve efficiency: (1) early stopping via answer consistency, (2) boosting the probability of generating end-of-reasoning signals, and (3) a supervised method that learns when to stop based on internal activations. Experiments across five benchmarks and five open-weights LLMs show that our methods significantly reduce token usage with little or no accuracy drop. In particular, on NaturalQuestions, Answer Consistency reduces tokens by over 40\% while further improving accuracy. Our work underscores the importance of cost-effective reasoning methods that operate at inference time, offering practical benefits for real-world applications.

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.

Large Language Models (LLMs) rely on generating extensive intermediate reasoning units (e.g., tokens, sentences) to enhance final answer quality across a wide range of complex tasks. While this approach has proven effective, it inevitably increases substantial inference costs. Previous methods adopting token-level reduction without clear criteria result in poor performance compared to models trained with complete rationale. To address this challenge, we propose a novel sentence-level rationale reduction framework leveraging likelihood-based criteria, verbosity, to identify and remove redundant reasoning sentences. Unlike previous approaches, our method leverages verbosity to selectively remove redundant reasoning sentences while preserving reasoning capabilities. Our experimental results across various reasoning tasks demonstrate that our method improves performance by an average of 7.71% while reducing token generation by 19.87% compared to model trained with complete reasoning paths.

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.

With the advancement of large language models (LLMs), their performance on multiple-choice question (MCQ) tasks has improved significantly. However, existing approaches face key limitations: answer choices are typically presented to LLMs without contextual grounding or explanation. This absence of context can lead to incomplete exploration of all possible answers, ultimately degrading the models' reasoning capabilities. To address these challenges, we introduce BiasPrompting, a novel inference framework that guides LLMs to generate and critically evaluate reasoning across all plausible answer options before reaching a final prediction. It consists of two components: first, a reasoning generation stage, where the model is prompted to produce supportive reasonings for each answer option, and then, a reasoning-guided agreement stage, where the generated reasonings are synthesized to select the most plausible answer. Through comprehensive evaluations, BiasPrompting demonstrates significant improvements in five widely used multiple-choice question answering benchmarks. Our experiments showcase that BiasPrompting enhances the reasoning capabilities of LLMs and provides a strong foundation for tackling complex and challenging questions, particularly in settings where existing methods underperform.

Large Language Models (LLMs) leverage step-by-step reasoning to solve complex problems. Standard evaluation practice involves generating a complete reasoning trace and assessing the correctness of the final answer presented at its conclusion. In this paper, we challenge the reliance on the final answer by posing the following two questions: Does the final answer reliably represent the model's optimal conclusion? Can alternative reasoning paths yield different results? To answer these questions, we analyze intermediate reasoning steps, termed subthoughts, and propose a method based on our findings. Our approach involves segmenting a reasoning trace into sequential subthoughts based on linguistic cues. We start by prompting the model to generate continuations from the end-point of each intermediate subthought. We extract a potential answer from every completed continuation originating from different subthoughts. We find that aggregating these answers by selecting the most frequent one (the mode) often yields significantly higher accuracy compared to relying solely on the answer derived from the original complete trace. Analyzing the consistency among the answers derived from different subthoughts reveals characteristics that correlate with the model's confidence and correctness, suggesting potential for identifying less reliable answers. Our experiments across various LLMs and challenging mathematical reasoning datasets (AIME2024 and AIME2025) show consistent accuracy improvements, with gains reaching up to 13\% and 10\% respectively. Implementation is available at: https://github.com/hammoudhasan/SubthoughtReasoner.

Although Large Language Models (LLMs) achieve remarkable performance across various tasks, they often struggle with complex reasoning tasks, such as answering mathematical questions. Recent efforts to address this issue have primarily focused on leveraging mathematical datasets through supervised fine-tuning or self-improvement techniques. However, these methods often depend on high-quality datasets that are difficult to prepare, or they require substantial computational resources for fine-tuning. Inspired by findings that LLMs know how to produce the right answer but struggle to select the correct reasoning path, we propose a purely inference-based searching method -- MindStar (M*). This method formulates reasoning tasks as searching problems and proposes two search ideas to identify the optimal reasoning paths. We evaluate the M* framework on both the GSM8K and MATH datasets, comparing its performance with existing open and closed-source LLMs. Our results demonstrate that M* significantly enhances the reasoning abilities of open-source models, such as Llama-2-13B and Mistral-7B, and achieves comparable performance to GPT-3.5 and Grok-1, but with substantially reduced model size and computational costs.

Multi-hop question answering (MHQA) requires a model to retrieve and integrate information from multiple passages to answer a complex question. Recent systems leverage the power of large language models and integrate evidence retrieval with reasoning prompts (e.g., chain-of-thought reasoning) for the MHQA task. However, the complexities in the question types (bridge v.s. comparison questions) and the reasoning types (sequential v.s. parallel reasonings) require more novel and fine-grained prompting methods to enhance the performance of MHQA under the zero-shot setting. In this paper, we propose STOC-TOT, a stochastic tree-of-thought reasoning prompting method with constrained decoding for MHQA and conduct a detailed comparison with other reasoning prompts on different question types and reasoning types. Specifically, we construct a tree-like reasoning structure by prompting the model to break down the original question into smaller sub-questions to form different reasoning paths. In addition, we prompt the model to provide a probability estimation for each reasoning path at each reasoning step. At answer time, we conduct constrained decoding on the model to generate more grounded answers and reduce hallucination. Experiments comparing STOC-TOT with two MHQA datasets and five large language models showed that our framework outperforms other reasoning prompts by a significant margin.

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.

Recent progress in reasoning models suggests that generating plausible attempts for research-level mathematics may be within reach, but verification remains a bottleneck, consuming scarce expert time. We hypothesize that a meaningful solution should contain enough method-level information that, when applied to a neighborhood of related questions, it should yield better downstream performance than incorrect solutions. Building on this idea, we propose Consequence-Based Utility, an oracle-free evaluator that scores each candidate by testing its value as an in-context exemplar in solving related yet verifiable questions. Our approach is evaluated on an original set of research-level math problems, each paired with one expert-written solution and nine LLM-generated solutions. Notably, Consequence-Based Utility consistently outperforms reward models, generative reward models, and LLM judges on ranking quality. Specifically, for GPT-OSS-120B, it improves Acc@1 from 67.2 to 76.3 and AUC from 71.4 to 79.6, with similarly large AUC gains on GPT-OSS-20B (69.0 to 79.2). Furthermore, compared to LLM-Judges, it also exhibits a larger solver-evaluator gap, maintaining a stronger correct-wrong separation even on instances where the underlying solver often fails to solve.

Despite extensive research on a wide range of question answering (QA) systems, most existing work focuses on answer containment-i.e., assuming that answers can be directly extracted and/or generated from documents in the corpus. However, some questions require inference, i.e., deriving answers that are not explicitly stated but can be inferred from the available information. We introduce Inferential QA -- a new task that challenges models to infer answers from answer-supporting passages which provide only clues. To study this problem, we construct QUIT (QUestions requiring Inference from Texts) dataset, comprising 7,401 questions and 2.4M passages built from high-convergence human- and machine-authored hints, labeled across three relevance levels using LLM-based answerability and human verification. Through comprehensive evaluation of retrievers, rerankers, and LLM-based readers, we show that methods effective on traditional QA tasks struggle in inferential QA: retrievers underperform, rerankers offer limited gains, and fine-tuning provides inconsistent improvements. Even reasoning-oriented LLMs fail to outperform smaller general-purpose models. These findings reveal that current QA pipelines are not yet ready for inference-based reasoning. Inferential QA thus establishes a new class of QA tasks that move towards understanding and reasoning from indirect textual evidence.

Words of estimative probability (WEP) are expressions of a statement's plausibility (probably, maybe, likely, doubt, likely, unlikely, impossible...). Multiple surveys demonstrate the agreement of human evaluators when assigning numerical probability levels to WEP. For example, highly likely corresponds to a median chance of 0.90+-0.08 in Fagen-Ulmschneider (2015)'s survey. In this work, we measure the ability of neural language processing models to capture the consensual probability level associated to each WEP. Firstly, we use the UNLI dataset (Chen et al., 2020) which associates premises and hypotheses with their perceived joint probability p, to construct prompts, e.g. "[PREMISE]. [WEP], [HYPOTHESIS]." and assess whether language models can predict whether the WEP consensual probability level is close to p. Secondly, we construct a dataset of WEP-based probabilistic reasoning, to test whether language models can reason with WEP compositions. When prompted "[EVENTA] is likely. [EVENTB] is impossible.", a causal language model should not express that [EVENTA&B] is likely. We show that both tasks are unsolved by off-the-shelf English language models, but that fine-tuning leads to transferable improvement.

Inference-time scaling techniques have shown promise in enhancing the reasoning capabilities of large language models (LLMs). While recent research has primarily focused on training-time optimization, our work highlights inference-time reward model (RM)-based reasoning as a critical yet overlooked avenue. In this paper, we conduct a systematic analysis of RM behavior across downstream reasoning tasks, revealing three key limitations: (1) RM can impair performance on simple questions, (2) its discriminative ability declines with increased sampling, and (3) high search diversity undermines RM performance. To address these issues, we propose CRISP (Clustered Reward Integration with Stepwise Prefixing), a novel inference-time algorithm that clusters generated reasoning paths by final answers, aggregates reward signals at the cluster level, and adaptively updates prefix prompts to guide generation. Experimental results demonstrate that CRISP significantly enhances LLM reasoning performance, achieving up to 5% accuracy improvement over other RM-based inference methods and an average of 10% gain over advanced reasoning models.

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.

Studies have underscored how, regardless of the recent breakthrough and swift advances in AI research, even state-of-the-art Large Language models (LLMs) continue to struggle when performing logical and mathematical reasoning. The results seem to suggest that LLMs still work as (highly advanced) data pattern identifiers, scoring poorly when attempting to generalise and solve reasoning problems the models have never previously seen or that are not close to samples presented in their training data. To address this compelling concern, this paper makes use of the notion of critical questions from the literature on argumentation theory, focusing in particular on Toulmin's model of argumentation. We show that employing these critical questions can improve the reasoning capabilities of LLMs. By probing the rationale behind the models' reasoning process, the LLM can assess whether some logical mistake is occurring and correct it before providing the final reply to the user prompt. The underlying idea is drawn from the gold standard of any valid argumentative procedure: the conclusion is valid if it is entailed by accepted premises. Or, to paraphrase such Aristotelian principle in a real-world approximation, characterised by incomplete information and presumptive logic, the conclusion is valid if not proved otherwise. This approach successfully steers the models' output through a reasoning pipeline, resulting in better performance against the baseline and its Chain-of-Thought (CoT) implementation. To this end, an extensive evaluation of the proposed approach on the MT-Bench Reasoning and Math tasks across a range of LLMs is provided.

Large language models (LLMs) are capable of answering knowledge-intensive complex questions with chain-of-thought (CoT) reasoning. However, they tend to generate factually incorrect reasoning steps when the required knowledge is not available or up-to-date in models' parameters. Recent works turn to retrieving external knowledge to augment CoT reasoning. Despite being promising, these chain-based methods suffer from: 1) Negative retrieval. Unnecessary or incorrect retrieval may mislead the reasoning; 2) Limited sight. Lacking the ability to look backward or forward, a local error in one step will propagate along the chain. In this paper, we propose a novel approach: Probabilistic Tree-of-thought Reasoning (ProbTree). First, LLMs translate a complex question into a query tree, in which each non-root node denotes a sub-question of its parent node. Then, probabilistic reasoning is conducted over the tree, by solving questions from leaf to root considering the confidence of both question decomposing and answering. During reasoning, for leaf nodes, LLMs choose a more confident answer from Closed-book QA that employs parametric knowledge and Open-book QA that employs retrieved external knowledge, thus eliminating the negative retrieval problem. For non-leaf nodes, with the hierarchical structure, LLMs have broader sights and are able to globally reason with the information from child nodes, thus recovering from local errors. The experiments on three Complex QA datasets under the open-domain setting show that our approach outperforms SOTA methods significantly, demonstrating the effect of probabilistic tree-of-thought reasoning.

With the growing success of reasoning models across complex natural language tasks, researchers in the Information Retrieval (IR) community have begun exploring how similar reasoning capabilities can be integrated into passage rerankers built on Large Language Models (LLMs). These methods typically employ an LLM to produce an explicit, step-by-step reasoning process before arriving at a final relevance prediction. But, does reasoning actually improve reranking accuracy? In this paper, we dive deeper into this question, studying the impact of the reasoning process by comparing reasoning-based pointwise rerankers (ReasonRR) to standard, non-reasoning pointwise rerankers (StandardRR) under identical training conditions, and observe that StandardRR generally outperforms ReasonRR. Building on this observation, we then study the importance of reasoning to ReasonRR by disabling its reasoning process (ReasonRR-NoReason), and find that ReasonRR-NoReason is surprisingly more effective than ReasonRR. Examining the cause of this result, our findings reveal that reasoning-based rerankers are limited by the LLM's reasoning process, which pushes it toward polarized relevance scores and thus fails to consider the partial relevance of passages, a key factor for the accuracy of pointwise rerankers.

This study focuses on improving the performance of lightweight Large Language Models (LLMs) in mathematical reasoning tasks. We introduce a novel method for measuring mathematical logic similarity and design an automatic screening mechanism to construct a set of reference problems that integrate both semantic and logical similarity. By employing carefully crafted positive and negative example prompts, we guide the model towards adopting sound reasoning logic. To the best of our knowledge, this is the first attempt to utilize retrieval-enhanced generation for mathematical problem-solving. Experimental results demonstrate that our method achieves a 15.8% improvement over the Chain of Thought approach on the SVAMP dataset and a 21.5 % improvement on the GSM8K dataset. Further application of this method to a large-scale model with 175 billion parameters yields performance comparable to the best results on both aforementioned datasets. Finally, we conduct an analysis of errors during the reasoning process, providing valuable insights and directions for future research on reasoning tasks using large language models.

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

Large 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.

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.

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

Large Language Models (LLMs) have exhibited an impressive capability to perform reasoning tasks, especially if they are encouraged to generate a sequence of intermediate steps. Reasoning performance can be improved by suitably combining multiple LLM responses, generated either in parallel in a single query, or via sequential interactions with LLMs throughout the reasoning process. Existing strategies for combination, such as self-consistency and progressive-hint-prompting, make inefficient usage of the LLM responses. We present Hint Marginalization, a novel and principled algorithmic framework to enhance the reasoning capabilities of LLMs. Our approach can be viewed as an iterative sampling strategy for forming a Monte Carlo approximation of an underlying distribution of answers, with the goal of identifying the mode the most likely answer. Empirical evaluation on several benchmark datasets for arithmetic reasoning demonstrates the superiority of the proposed approach.

Large language models (LLMs) excel in many tasks but struggle to accurately quantify uncertainty in their generated responses. This limitation makes it challenging to detect misinformation and ensure reliable decision-making. Existing uncertainty quantification (UQ) methods for LLMs are primarily prompt-wise rather than response-wise, often requiring multiple response samples, which incurs high computational costs. Moreover, LLMs have been shown to be overconfident, particularly when using reasoning steps to derive their answers. In this work, we propose CoT-UQ, a response-wise UQ framework that integrates LLMs' inherent reasoning capabilities through Chain-of-Thought (CoT) into the UQ process. CoT-UQ captures critical information during inference by extracting keywords from each reasoning step and assessing their importance to the final answer. This key reasoning information is then aggregated to produce a final uncertainty estimate. We conduct extensive experiments based on LLaMA Family with model sizes varying from 8B to 13B across logical and mathematical reasoning tasks. Experimental results demonstrate that CoT-UQ significantly outperforms existing UQ methods, achieving an average improvement of 5.9% AUROC compared to current UQ methods. The code is available at: https://github.com/ZBox1005/CoT-UQ.

The recent rise of Large Reasoning Models (LRMs) has significantly improved multi-step reasoning performance, but often at the cost of generating excessively long reasoning chains. This paper revisits the efficiency of such reasoning processes through an information-theoretic lens, revealing a fundamental trade-off between reasoning length and semantic efficiency. We propose two metrics, InfoBias and InfoGain, to quantify divergence from ideal reasoning paths and stepwise information contribution, respectively. Empirical analyses show that longer reasoning chains tend to exhibit higher information bias and diminishing information gain, especially for incorrect answers. Motivated by these findings, we introduce an entropy-based Adaptive Think strategy that dynamically halts reasoning once confidence is sufficiently high, improving efficiency while maintaining competitive accuracy. Compared to the Vanilla Think approach (default mode), our strategy yields a 1.10% improvement in average accuracy and a 50.80% reduction in token usage on QwQ-32B across six benchmark tasks spanning diverse reasoning types and difficulty levels, demonstrating superior efficiency and reasoning performance. These results underscore the promise of entropy-based methods for enhancing both accuracy and cost-effiiciency in large language model deployment.

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.

One of the most widely used methods to evaluate LLMs are Multiple Choice Question (MCQ) tests. MCQ benchmarks enable the testing of LLM knowledge on almost any topic at scale as the results can be processed automatically. To help the LLM answer, a few examples called few shots can be included in the prompt. Moreover, the LLM can be asked to answer the question directly with the selected option or to first provide the reasoning and then the selected answer, which is known as chain of thought. In addition to checking whether the selected answer is correct, the evaluation can look at the LLM-estimated probability of its response as an indication of the confidence of the LLM in the response. In this paper, we study how the LLM confidence in its answer depends on whether the model has been asked to answer directly or to provide the reasoning before answering. The results of the evaluation of questions on a wide range of topics in seven different models show that LLMs are more confident in their answers when they provide reasoning before the answer. This occurs regardless of whether the selected answer is correct. Our hypothesis is that this behavior is due to the reasoning that modifies the probability of the selected answer, as the LLM predicts the answer based on the input question and the reasoning that supports the selection made. Therefore, LLM estimated probabilities seem to have intrinsic limitations that should be understood in order to use them in evaluation procedures. Interestingly, the same behavior has been observed in humans, for whom explaining an answer increases confidence in its correctness.

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 quality in large language models depends not only on producing correct answers but also on generating valid intermediate steps. We study this through multiple-choice question answering (MCQA), which provides a controlled setting with fixed answer options. Our analysis shows that when questions are effectively unsolvable for a model, spurious chains of thought (CoTs) are more likely to appear, leading to false positives. By estimating the solvability of each question, we uncover an intermediate regime where learning is most effective. Building on this insight, we adapt outcome-supervised reward models and reinforcement learning with group-relative advantage to incorporate solvability into their objectives. Across experiments on math and multimodal datasets, these modifications consistently yield higher rates of process-correct reasoning and, in reinforcement learning, improved answer accuracy as well. Our results highlight solvability as a key factor for reducing hallucinations and increasing reliability in CoT reasoning.

When provided with sufficient explanatory context, smaller Language Models have been shown to exhibit strong reasoning ability on challenging short-answer question-answering tasks where the questions are unseen in training. We evaluate two methods for further improvement in this setting. Both methods focus on combining rationales generated by a larger Language Model with longer contexts created from a multi-hop dense retrieval system. The first method (RR) involves training a Rationale Ranking model to score both generated rationales and retrieved contexts with respect to relevance and truthfulness. We then use the scores to derive combined contexts from both knowledge sources using a number of combinatory strategies. For the second method (RATD) we utilise retrieval-augmented training datasets developed by Hartill et al. 2023 to train a smaller Reasoning model such that it becomes proficient at utilising relevant information from longer text sequences that may be only partially evidential and frequently contain many irrelevant sentences. We find that both methods significantly improve results. Our single best Reasoning model materially improves upon strong comparable prior baselines for unseen evaluation datasets (StrategyQA 58.9 rightarrow 61.7 acc., CommonsenseQA 63.6 rightarrow 72.7 acc., ARC-DA 31.6 rightarrow 52.1 F1, IIRC 25.5 rightarrow 27.3 F1) and a version utilising our prior knowledge of each type of question in selecting a context combination strategy does even better. Our proposed models also generally outperform direct prompts against much larger models (BLOOM 175B and StableVicuna 13B) in both few-shot chain-of-thought and standard few-shot settings.

Reasoning has become a central paradigm for large language models (LLMs), consistently boosting accuracy across diverse benchmarks. Yet its suitability for precision-sensitive tasks remains unclear. We present the first systematic study of reasoning for classification tasks under strict low false positive rate (FPR) regimes. Our analysis covers two tasks--safety detection and hallucination detection--evaluated in both fine-tuned and zero-shot settings, using standard LLMs and Large Reasoning Models (LRMs). Our results reveal a clear trade-off: Think On (reasoning-augmented) generation improves overall accuracy, but underperforms at the low-FPR thresholds essential for practical use. In contrast, Think Off (no reasoning during inference) dominates in these precision-sensitive regimes, with Think On surpassing only when higher FPRs are acceptable. In addition, we find token-based scoring substantially outperforms self-verbalized confidence for precision-sensitive deployments. Finally, a simple ensemble of the two modes recovers the strengths of each. Taken together, our findings position reasoning as a double-edged tool: beneficial for average accuracy, but often ill-suited for applications requiring strict precision.

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

Reasoning models have achieved remarkable performance on tasks like math and logical reasoning thanks to their ability to search during reasoning. However, they still suffer from overthinking, often performing unnecessary reasoning steps even after reaching the correct answer. This raises the question: can models evaluate the correctness of their intermediate answers during reasoning? In this work, we study whether reasoning models encode information about answer correctness through probing the model's hidden states. The resulting probe can verify intermediate answers with high accuracy and produces highly calibrated scores. Additionally, we find models' hidden states encode correctness of future answers, enabling early prediction of the correctness before the intermediate answer is fully formulated. We then use the probe as a verifier to decide whether to exit reasoning at intermediate answers during inference, reducing the number of inference tokens by 24\% without compromising performance. These findings confirm that reasoning models do encode a notion of correctness yet fail to exploit it, revealing substantial untapped potential to enhance their efficiency.

Evaluating large language models (LLMs) on final-answer correctness is the dominant paradigm. This approach, however, provides a coarse signal for model improvement and overlooks the quality of the underlying reasoning process. We argue that a more granular evaluation of reasoning offers a more effective path to building robust models. We decompose reasoning quality into two dimensions: relevance and coherence. Relevance measures if a step is grounded in the problem; coherence measures if it follows logically from prior steps. To measure these aspects reliably, we introduce causal stepwise evaluation (CaSE). This method assesses each reasoning step using only its preceding context, which avoids hindsight bias. We validate CaSE against human judgments on our new expert-annotated benchmarks, MRa-GSM8K and MRa-MATH. More importantly, we show that curating training data with CaSE-evaluated relevance and coherence directly improves final task performance. Our work provides a scalable framework for analyzing, debugging, and improving LLM reasoning, demonstrating the practical value of moving beyond validity checks.

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.

Recent advancements in Chain-of-Thought prompting have facilitated significant breakthroughs for Large Language Models (LLMs) in complex reasoning tasks. Current research enhances the reasoning performance of LLMs by sampling multiple reasoning chains and ensembling based on the answer frequency. However, this approach fails in scenarios where the correct answers are in the minority. We identify this as a primary factor constraining the reasoning capabilities of LLMs, a limitation that cannot be resolved solely based on the predicted answers. To address this shortcoming, we introduce a hierarchical reasoning aggregation framework AoR (Aggregation of Reasoning), which selects answers based on the evaluation of reasoning chains. Additionally, AoR incorporates dynamic sampling, adjusting the number of reasoning chains in accordance with the complexity of the task. Experimental results on a series of complex reasoning tasks show that AoR outperforms prominent ensemble methods. Further analysis reveals that AoR not only adapts various LLMs but also achieves a superior performance ceiling when compared to current methods.

We endow Large Language Models (LLMs) with fine-grained self-evaluation to refine multi-step reasoning inference. We propose an effective prompting approach that integrates self-evaluation guidance through stochastic beam search. Our approach explores the reasoning search space using a well-calibrated automatic criterion. This enables an efficient search to produce higher-quality final predictions. With the self-evaluation guided stochastic beam search, we also balance the quality-diversity trade-off in the generation of reasoning chains. This allows our approach to adapt well with majority voting and surpass the corresponding Codex-backboned baselines by 6.34%, 9.56%, and 5.46% on the GSM8K, AQuA, and StrategyQA benchmarks, respectively, in few-shot accuracy. Analysis of our decompositional reasoning finds it pinpoints logic failures and leads to higher consistency and robustness. Our code is publicly available at https://github.com/YuxiXie/SelfEval-Guided-Decoding.

Deductive reasoning is a crucial logical capability that assists us in solving complex problems based on existing knowledge. Although augmented by Chain-of-Thought prompts, Large Language Models (LLMs) might not follow the correct reasoning paths. Enhancing the deductive reasoning abilities of LLMs, and leveraging their extensive built-in knowledge for various reasoning tasks, remains an open question. Attempting to mimic the human deductive reasoning paradigm, we propose a multi-stage Syllogistic-Reasoning Framework of Thought (SR-FoT) that enables LLMs to perform syllogistic deductive reasoning to handle complex knowledge-based reasoning tasks. Our SR-FoT begins by interpreting the question and then uses the interpretation and the original question to propose a suitable major premise. It proceeds by generating and answering minor premise questions in two stages to match the minor premises. Finally, it guides LLMs to use the previously generated major and minor premises to perform syllogistic deductive reasoning to derive the answer to the original question. Extensive and thorough experiments on knowledge-based reasoning tasks have demonstrated the effectiveness and advantages of our SR-FoT.

There is intense interest in investigating how inference time compute (ITC) (e.g. repeated sampling, refinements, etc) can improve large language model (LLM) capabilities. At the same time, recent breakthroughs in reasoning models, such as Deepseek-R1, unlock the opportunity for reinforcement learning to improve LLM reasoning skills. An in-depth understanding of how ITC interacts with reasoning across different models could provide important guidance on how to further advance the LLM frontier. This work conducts a comprehensive analysis of inference-time scaling methods for both reasoning and non-reasoning models on challenging reasoning tasks. Specifically, we focus our research on verifier-free inference time-scaling methods due to its generalizability without needing a reward model. We construct the Pareto frontier of quality and efficiency. We find that non-reasoning models, even with an extremely high inference budget, still fall substantially behind reasoning models. For reasoning models, majority voting proves to be a robust inference strategy, generally competitive or outperforming other more sophisticated ITC methods like best-of-N and sequential revisions, while the additional inference compute offers minimal improvements. We further perform in-depth analyses of the association of key response features (length and linguistic markers) with response quality, with which we can improve the existing ITC methods. We find that correct responses from reasoning models are typically shorter and have fewer hedging and thinking markers (but more discourse markers) than the incorrect responses.

Recent advancements in large language models (LLMs), such as DeepSeek-R1 and OpenAI-o1, have demonstrated the significant effectiveness of test-time scaling, achieving substantial performance gains across various benchmarks. These advanced models utilize deliberate "thinking" steps to systematically enhance answer quality. In this paper, we propose leveraging these high-quality outputs generated by reasoning-intensive models to improve less computationally demanding, non-reasoning models. We explore and compare methodologies for utilizing the answers produced by reasoning models to train and improve non-reasoning models. Through straightforward Supervised Fine-Tuning (SFT) experiments on established benchmarks, we demonstrate consistent improvements across various benchmarks, underscoring the potential of this approach for advancing the ability of models to answer questions directly.

When prompted with a few examples and intermediate steps, large language models (LLMs) have demonstrated impressive performance in various reasoning tasks. However, prompting methods that rely on implicit knowledge in an LLM often generate incorrect answers when the implicit knowledge is wrong or inconsistent with the task. To tackle this problem, we present Hypotheses-to-Theories (HtT), a framework that learns a rule library for reasoning with LLMs. HtT contains two stages, an induction stage and a deduction stage. In the induction stage, an LLM is first asked to generate and verify rules over a set of training examples. Rules that appear and lead to correct answers sufficiently often are collected to form a rule library. In the deduction stage, the LLM is then prompted to employ the learned rule library to perform reasoning to answer test questions. Experiments on relational reasoning, numerical reasoning and concept learning problems show that HtT improves existing prompting methods, with an absolute gain of 10-30% in accuracy. The learned rules are also transferable to different models and to different forms of the same problem.

The recent development of chain-of-thought (CoT) decoding has enabled large language models (LLMs) to generate explicit logical reasoning paths for complex problem-solving. However, research indicates that these paths are not always deliberate and optimal. The tree-of-thought (ToT) method employs tree-searching to extensively explore the reasoning space and find better reasoning paths that CoT decoding might overlook. This deliberation, however, comes at the cost of significantly increased inference complexity. In this work, we demonstrate that fine-tuning LLMs leveraging the search tree constructed by ToT allows CoT to achieve similar or better performance, thereby avoiding the substantial inference burden. This is achieved through Chain of Preference Optimization (CPO), where LLMs are fine-tuned to align each step of the CoT reasoning paths with those of ToT using the inherent preference information in the tree-search process. Extensive experimental results show that CPO significantly improves LLM performance in solving a variety of complex problems, including question answering, fact verification, and arithmetic reasoning, demonstrating its effectiveness. Our code is available at https://github.com/sail-sg/CPO.

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

Chain-of-thought (CoT) reasoning has enabled large language models (LLMs) to utilize additional computation through intermediate tokens to solve complex tasks. However, we posit that typical reasoning traces contain many redundant tokens, incurring extraneous inference costs. Upon examination of the output distribution of current LLMs, we find evidence on their latent ability to reason more concisely, relative to their default behavior. To elicit this capability, we propose simple fine-tuning methods which leverage self-generated concise reasoning paths obtained by best-of-N sampling and few-shot conditioning, in task-specific settings. Our combined method achieves a 30% reduction in output tokens on average, across five model families on GSM8K and MATH, while maintaining average accuracy. By exploiting the fundamental stochasticity and in-context learning capabilities of LLMs, our self-training approach robustly elicits concise reasoning on a wide range of models, including those with extensive post-training. Code is available at https://github.com/TergelMunkhbat/concise-reasoning

Logical reasoning is a fundamental aspect of human intelligence and an essential capability for multimodal large language models (MLLMs). Despite the significant advancement in multimodal reasoning, existing benchmarks fail to comprehensively evaluate their reasoning abilities due to the lack of explicit categorization for logical reasoning types and an unclear understanding of reasoning. To address these issues, we introduce MME-Reasoning, a comprehensive benchmark designed to evaluate the reasoning ability of MLLMs, which covers all three types of reasoning (i.e., inductive, deductive, and abductive) in its questions. We carefully curate the data to ensure that each question effectively evaluates reasoning ability rather than perceptual skills or knowledge breadth, and extend the evaluation protocols to cover the evaluation of diverse questions. Our evaluation reveals substantial limitations of state-of-the-art MLLMs when subjected to holistic assessments of logical reasoning capabilities. Even the most advanced MLLMs show limited performance in comprehensive logical reasoning, with notable performance imbalances across reasoning types. In addition, we conducted an in-depth analysis of approaches such as ``thinking mode'' and Rule-based RL, which are commonly believed to enhance reasoning abilities. These findings highlight the critical limitations and performance imbalances of current MLLMs in diverse logical reasoning scenarios, providing comprehensive and systematic insights into the understanding and evaluation of reasoning capabilities.

Accurately quantifying a large language model's (LLM) predictive uncertainty is crucial for judging the reliability of its answers. While most existing research focuses on short, directly answerable questions with closed-form outputs (e.g., multiple-choice), involving intermediate reasoning steps in LLM responses is increasingly important. This added complexity complicates uncertainty quantification (UQ) because the probabilities assigned to answer tokens are conditioned on a vast space of preceding reasoning tokens. Direct marginalization is infeasible, and the dependency inflates probability estimates, causing overconfidence in UQ. To address this, we propose UQAC, an efficient method that narrows the reasoning space to a tractable size for marginalization. UQAC iteratively constructs an "attention chain" of tokens deemed "semantically crucial" to the final answer via a backtracking procedure. Starting from the answer tokens, it uses attention weights to identify the most influential predecessors, then iterates this process until reaching the input tokens. Similarity filtering and probability thresholding further refine the resulting chain, allowing us to approximate the marginal probabilities of the answer tokens, which serve as the LLM's confidence. We validate UQAC on multiple reasoning benchmarks with advanced open-source LLMs, demonstrating that it consistently delivers reliable UQ estimates with high computational efficiency.

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.

Despite their impressive capabilities, large pre-trained language models (LMs) struggle with consistent reasoning; recently, prompting LMs to generate explanations that self-guide the inference has emerged as a promising direction to amend this. However, these approaches are fundamentally bounded by the correctness of explanations, which themselves are often noisy and inconsistent. In this work, we develop Maieutic Prompting, which infers a correct answer to a question even from the noisy and inconsistent generations of LM. Maieutic Prompting induces a tree of explanations abductively (e.g. X is true, because ...) and recursively, then frames the inference as a satisfiability problem over these explanations and their logical relations. We test Maieutic Prompting for true/false QA on three challenging benchmarks that require complex commonsense reasoning. Maieutic Prompting achieves up to 20% better accuracy than state-of-the-art prompting methods, and as a fully unsupervised approach, performs competitively with supervised models. We also show that Maieutic Prompting improves robustness in inference while providing interpretable rationales.

Large language models (LLMs) have shown remarkable reasoning capabilities given chain-of-thought prompts (examples with intermediate reasoning steps). Existing benchmarks measure reasoning ability indirectly, by evaluating accuracy on downstream tasks such as mathematical reasoning. However, it is unclear how these models obtain the answers and whether they rely on simple heuristics rather than the generated chain-of-thought. To enable systematic exploration of the reasoning ability of LLMs, we present a new synthetic question-answering dataset called PrOntoQA, where each example is generated from a synthetic world model represented in first-order logic. This allows us to parse the generated chain-of-thought into symbolic proofs for formal analysis. Our analysis on InstructGPT and GPT-3 shows that LLMs are quite capable of making correct individual deduction steps, and so are generally capable of reasoning, even in fictional contexts. However, they have difficulty with proof planning: When multiple valid deduction steps are available, they are not able to systematically explore the different options.

Large language models (LLMs) are increasingly optimized for long reasoning, under the assumption that more reasoning leads to better performance. However, emerging evidence suggests that longer responses can sometimes degrade accuracy rather than improve it. In this paper, we conduct a systematic empirical study of the relationship between reasoning length and answer correctness. We find that LLMs tend to overthink simple problems, generating unnecessarily long outputs, and underthink harder ones, failing to extend their reasoning when it is most needed. This indicates that models might misjudge problem difficulty and fail to calibrate their response length appropriately. Furthermore, we investigate the effects of length reduction with a preference optimization algorithm when simply preferring the shorter responses regardless of answer correctness. Experiments show that the generation length can be significantly reduced while maintaining acceptable accuracy. Our findings highlight generation length as a meaningful signal for reasoning behavior and motivate further exploration into LLMs' self-awareness in reasoning length adaptation.

Recent advances in Large Reasoning Models (LRMs) have shown impressive capabilities in mathematical and logical reasoning. However, current LRMs rarely admit ignorance or respond with "I don't know". Instead, they often produce incorrect answers while showing undue confidence, raising concerns about their factual reliability. In this work, we identify two pathological reasoning patterns characterized by overthinking that contribute to the overconfident and incorrect answers: last-minute guessing and second-thought spiraling. To address these issues, we propose BARREL-a novel framework that promotes concise and boundary-aware factual reasoning. Our experiments show that BARREL-training increases the reliability of DeepSeek-R1-Distill-Llama-8B from 39.33% to 61.48%, while still achieving accuracy comparable to models finetuned on reasoning data generated by R1. These results demonstrate that our pilot study is inspiring to build more reliable and factual System 2 LRMs.

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.

Large Language Models (LLMs) empowered with retrieval mechanisms have achieved strong progress in open-domain question answering (QA). Yet, the conventional retrieve--then--answer paradigm often suffers from two key limitations: (1) low signal-to-noise ratio in retrieved evidence, where useful information is buried under irrelevant content, and (2) error accumulation in multi-hop reasoning when incomplete or noisy passages are involved. To address these challenges, we present EviNote-RAG, an agentic RAG framework that introduces a structured retrieve--note--answer pipeline. Instead of directly reasoning over raw retrievals, the model is trained to compose Supportive-Evidence Notes (SENs), concise, human-like notes that preserve only answer-relevant information, highlight uncertainty, and explicitly state when no useful evidence exists. This distillation process is further reinforced by the Evidence Quality Reward (EQR), an entailment-based signal that evaluates whether SENs logically support the final answer. Together, SENs and EQR guide the model toward faithful and robust reasoning, while reducing the impact of noise. Experiments on in-domain and out-of-domain QA benchmarks show that EviNote-RAG consistently outperforms strong baselines in accuracy, generalization, and training stability. In particular, it achieves state-of-the-art results while enhancing robustness and efficiency, yielding relative F1 gains of 20\% on HotpotQA (+0.093), 40\% on Bamboogle (+0.151), and 91\% on 2Wiki (+0.256) via denser rewards and reduced verbosity.

Existing methods on understanding the capabilities of LLMs in logical reasoning rely on binary entailment classification or synthetically derived rationales, which are not sufficient for proper investigation of model's capabilities. We present P-FOLIO, a human-annotated dataset consisting of diverse and complex reasoning chains for a set of realistic logical reasoning stories also written by humans. P-FOLIO is collected with an annotation protocol that facilitates humans to annotate well-structured natural language proofs for first-order logic reasoning problems in a step-by-step manner. The number of reasoning steps in P-FOLIO span from 0 to 20. We further use P-FOLIO to evaluate and improve large-language-model (LLM) reasoning capabilities. We evaluate LLM reasoning capabilities at a fine granularity via single-step inference rule classification, with more diverse inference rules of more diverse and higher levels of complexities than previous works. Given that a single model-generated reasoning chain could take a completely different path than the human-annotated one, we sample multiple reasoning chains from a model and use pass@k metrics for evaluating the quality of model-generated reasoning chains. We show that human-written reasoning chains significantly boost the logical reasoning capabilities of LLMs via many-shot prompting and fine-tuning. Furthermore, fine-tuning Llama3-7B on P-FOLIO improves the model performance by 10% or more on three other out-of-domain logical reasoning datasets. We also conduct detailed analysis to show where most powerful LLMs fall short in reasoning. We will release the dataset and code publicly.

Language models (LM) are capable of remarkably complex linguistic tasks; however, numerical reasoning is an area in which they frequently struggle. An important but rarely evaluated form of reasoning is understanding probability distributions. In this paper, we focus on evaluating the probabilistic reasoning capabilities of LMs using idealized and real-world statistical distributions. We perform a systematic evaluation of state-of-the-art LMs on three tasks: estimating percentiles, drawing samples, and calculating probabilities. We evaluate three ways to provide context to LMs 1) anchoring examples from within a distribution or family of distributions, 2) real-world context, 3) summary statistics on which to base a Normal approximation. Models can make inferences about distributions, and can be further aided by the incorporation of real-world context, example shots and simplified assumptions, even if these assumptions are incorrect or misspecified. To conduct this work, we developed a comprehensive benchmark distribution dataset with associated question-answer pairs that we will release publicly.

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.

Investigating the reasoning abilities of transformer models, and discovering new challenging tasks for them, has been a topic of much interest. Recent studies have found these models to be surprisingly strong at performing deductive reasoning over formal logical theories expressed in natural language. A shortcoming of these studies, however, is that they do not take into account that logical theories, when sampled uniformly at random, do not necessarily lead to hard instances. We propose a new methodology for creating challenging algorithmic reasoning datasets that focus on natural language satisfiability (NLSat) problems. The key idea is to draw insights from empirical sampling of hard propositional SAT problems and from complexity-theoretic studies of language. This methodology allows us to distinguish easy from hard instances, and to systematically increase the complexity of existing reasoning benchmarks such as RuleTaker. We find that current transformers, given sufficient training data, are surprisingly robust at solving the resulting NLSat problems of substantially increased difficulty. They also exhibit some degree of scale-invariance - the ability to generalize to problems of larger size and scope. Our results, however, reveal important limitations too: a careful sampling of training data is crucial for building models that generalize to larger problems, and transformer models' limited scale-invariance suggests they are far from learning robust deductive reasoning algorithms.

We present the surprising finding that a language model's reasoning capabilities can be improved by training on synthetic datasets of chain-of-thought (CoT) traces from more capable models, even when all of those traces lead to an incorrect final answer. Our experiments show this approach can yield better performance on reasoning tasks than training on human-annotated datasets. We hypothesize that two key factors explain this phenomenon: first, the distribution of synthetic data is inherently closer to the language model's own distribution, making it more amenable to learning. Second, these `incorrect' traces are often only partially flawed and contain valid reasoning steps from which the model can learn. To further test the first hypothesis, we use a language model to paraphrase human-annotated traces -- shifting their distribution closer to the model's own distribution -- and show that this improves performance. For the second hypothesis, we introduce increasingly flawed CoT traces and study to what extent models are tolerant to these flaws. We demonstrate our findings across various reasoning domains like math, algorithmic reasoning and code generation using MATH, GSM8K, Countdown and MBPP datasets on various language models ranging from 1.5B to 9B across Qwen, Llama, and Gemma models. Our study shows that curating datasets that are closer to the model's distribution is a critical aspect to consider. We also show that a correct final answer is not always a reliable indicator of a faithful reasoning process.

Chain-of-Thought (CoT) prompting in large language models (LLMs) has shown promising performance on mathematical reasoning tasks. Recently, Self-Consistency samples a diverse set of reasoning chains with different answers and chooses the answer by majority voting. Though effective, its performance cannot be further improved by sampling more reasoning chains. To address this problem, we propose to integrate backward reasoning into answer verification. We first mask a number in the question by {bf x}. The LLM is then asked to predict the masked number with a candidate answer A embedded in the template: ``If we know the answer to the above question is {A}, what is the value of unknown variable {bf x}?'' The LLM is expected to predict the masked number successfully if the provided candidate answer is correct. To further improve performance, we propose FOBAR (FOrward-BAckward Reasoning) to combine forward and backward reasoning for verifying candidate answers. Experiments are performed on six standard mathematical data sets and three LLMs (text-davinci-003, GPT-3.5-Turbo, GPT-4). Results show that FOBAR achieves state-of-the-art performance. In particular, FOBAR outperforms Self-Consistency which uses forward reasoning alone, demonstrating that combining forward and forward reasoning is better. It also outperforms existing verification methods, verifying the effectiveness of using the simple template in backward reasoning and the proposed combination.

Recent studies on large language model (LLM) reasoning capabilities have demonstrated promising improvements in model performance by leveraging a lengthy thinking process and additional computational resources during inference, primarily in tasks involving mathematical reasoning (Muennighoff et al., 2025). However, it remains uncertain if longer reasoning chains inherently enhance factual accuracy, particularly beyond mathematical contexts. In this work, we thoroughly examine LLM reasoning within complex open-domain question-answering (QA) scenarios. We initially distill reasoning traces from advanced, large-scale reasoning models (QwQ-32B and DeepSeek-R1-671B), then fine-tune a variety of models ranging from smaller, instruction-tuned variants to larger architectures based on Qwen2.5. To enrich reasoning traces, we introduce factual information from knowledge graphs in the form of paths into our reasoning traces. Our experimental setup includes four baseline approaches and six different instruction-tuned models evaluated across a benchmark of six datasets, encompassing over 22.6K questions. Overall, we carry out 168 experimental runs and analyze approximately 1.7 million reasoning traces. Our findings indicate that, within a single run, smaller reasoning models achieve noticeable improvements in factual accuracy compared to their original instruction-tuned counterparts. Moreover, our analysis demonstrates that adding test-time compute and token budgets factual accuracy consistently improves by 2-8%, further confirming the effectiveness of test-time scaling for enhancing performance and consequently improving reasoning accuracy in open-domain QA tasks. We release all the experimental artifacts for further research.

Recent advancements in Large Language Models (LLMs) have sparked interest in their formal reasoning capabilities, particularly in mathematics. The GSM8K benchmark is widely used to assess the mathematical reasoning of models on grade-school-level questions. While the performance of LLMs on GSM8K has significantly improved in recent years, it remains unclear whether their mathematical reasoning capabilities have genuinely advanced, raising questions about the reliability of the reported metrics. To address these concerns, we conduct a large-scale study on several SOTA open and closed models. To overcome the limitations of existing evaluations, we introduce GSM-Symbolic, an improved benchmark created from symbolic templates that allow for the generation of a diverse set of questions. GSM-Symbolic enables more controllable evaluations, providing key insights and more reliable metrics for measuring the reasoning capabilities of models.Our findings reveal that LLMs exhibit noticeable variance when responding to different instantiations of the same question. Specifically, the performance of all models declines when only the numerical values in the question are altered in the GSM-Symbolic benchmark. Furthermore, we investigate the fragility of mathematical reasoning in these models and show that their performance significantly deteriorates as the number of clauses in a question increases. We hypothesize that this decline is because current LLMs cannot perform genuine logical reasoning; they replicate reasoning steps from their training data. Adding a single clause that seems relevant to the question causes significant performance drops (up to 65%) across all state-of-the-art models, even though the clause doesn't contribute to the reasoning chain needed for the final answer. Overall, our work offers a more nuanced understanding of LLMs' capabilities and limitations in mathematical reasoning.

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.

This paper investigates the mathematical reasoning capabilities of large language models (LLMs) using 50 newly constructed high-school-level word problems. Unlike prior studies that focus solely on answer correctness, we rigorously analyze both final answers and solution steps to identify reasoning failures. Evaluating eight state-of-the-art models - including Mixtral, Llama, Gemini, GPT-4o, and OpenAI's o1 variants - we find that while newer models (e.g., o3-mini, deepseek-r1) achieve higher accuracy, all models exhibit errors in spatial reasoning, strategic planning, and arithmetic, sometimes producing correct answers through flawed logic. Common failure modes include unwarranted assumptions, over-reliance on numerical patterns, and difficulty translating physical intuition into mathematical steps. Manual analysis reveals that models struggle with problems requiring multi-step deduction or real-world knowledge, despite possessing broad mathematical knowledge. Our results underscore the importance of evaluating reasoning processes, not just answers, and caution against overestimating LLMs' problem-solving proficiency. The study highlights persistent gaps in LLMs' generalization abilities, emphasizing the need for targeted improvements in structured reasoning and constraint handling.

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 presents a significant and challenging issue for Large Language Models (LLMs). The predominant focus of research has revolved around developing diverse prompting strategies to guide and structure the reasoning processes of LLMs. However, these approaches based on decoder-only causal language models often operate the input question in a single forward pass, potentially missing the rich, back-and-forth interactions inherent in human reasoning. Scant attention has been paid to a critical dimension, i.e., the input question itself embedded within the prompts. In response, we introduce a deceptively simple yet highly effective prompting strategy, termed question "re-reading". Drawing inspiration from human learning and problem-solving, re-reading entails revisiting the question information embedded within input prompts. This approach aligns seamlessly with the cognitive principle of reinforcement, enabling LLMs to extract deeper insights, identify intricate patterns, establish more nuanced connections, and ultimately enhance their reasoning capabilities across various tasks. Experiments conducted on a series of reasoning benchmarks serve to underscore the effectiveness and generality of our method. Moreover, our findings demonstrate that our approach seamlessly integrates with various language models, though-eliciting prompting methods, and ensemble techniques, further underscoring its versatility and compatibility in the realm of LLMs.

Humans make numerous inferences in text comprehension to understand discourse. This paper aims to understand the commonalities and disparities in the inference judgments between humans and state-of-the-art Large Language Models (LLMs). Leveraging a comprehensively curated entailment verification benchmark, we evaluate both human and LLM performance across various reasoning categories. Our benchmark includes datasets from three categories (NLI, contextual QA, and rationales) that include multi-sentence premises and different knowledge types, thereby evaluating the inference capabilities in complex reasoning instances. Notably, our findings reveal LLMs' superiority in multi-hop reasoning across extended contexts, while humans excel in tasks necessitating simple deductive reasoning. Leveraging these insights, we introduce a fine-tuned Flan-T5 model that outperforms GPT-3.5 and rivals with GPT-4, offering a robust open-source solution for entailment verification. As a practical application, we showcase the efficacy of our finetuned model in enhancing self-consistency in model-generated explanations, resulting in a 6% performance boost on average across three multiple-choice question-answering datasets.

In recent years, large pre-trained language models (LLMs) have demonstrated the ability to follow instructions and perform novel tasks from a few examples. The possibility to parameterise an LLM through such in-context examples widens their capability at a much lower cost than finetuning. We extend this line of reasoning and present a method which further expands the capabilities of an LLM by embedding it within an algorithm or program. To demonstrate the benefits of this approach, we present an illustrative example of evidence-supported question-answering. We obtain a 6.4\% improvement over the chain of thought baseline through a more algorithmic approach without any finetuning. Furthermore, we highlight recent work from this perspective and discuss the advantages and disadvantages in comparison to the standard approaches.

Large Reasoning Models (LRMs) embed private or copyrighted information not only in their final answers but also throughout multi-step chain-of-thought (CoT) traces, making reliable unlearning far more demanding than in standard LLMs. We introduce Reasoning-TOFU (R-TOFU), the first benchmark tailored to this setting. R-TOFU augments existing unlearning tasks with realistic CoT annotations and provides step-wise metrics that expose residual knowledge invisible to answer-level checks. Using R-TOFU, we carry out a comprehensive comparison of gradient-based and preference-optimization baselines and show that conventional answer-only objectives leave substantial forget traces in reasoning. We further propose Reasoned IDK, a preference-optimization variant that preserves coherent yet inconclusive reasoning, achieving a stronger balance between forgetting efficacy and model utility than earlier refusal styles. Finally, we identify a failure mode: decoding variants such as ZeroThink and LessThink can still reveal forgotten content despite seemingly successful unlearning, emphasizing the need to evaluate models under diverse decoding settings. Together, the benchmark, analysis, and new baseline establish a systematic foundation for studying and improving unlearning in LRMs while preserving their reasoning capabilities.

Current evaluation of mathematical reasoning in language models relies primarily on answer accuracy, potentially masking fundamental failures in logical computation. We introduce a diagnostic framework that distinguishes genuine mathematical reasoning from superficial pattern matching through four complementary axes: forward-backward consistency, transitivity coverage, counterfactual sensitivity, and perturbation robustness. Through a case study applying this framework to Qwen3-0.6B on the MenatQA dataset, we reveal a striking disconnect between surface performance and reasoning fidelity. While the model achieves reasonable answer accuracy (70%+), it demonstrates poor backward consistency (15%), limited transitivity coverage (32.2%), and brittle sensitivity to perturbations. Our diagnostics expose reasoning failures invisible to traditional accuracy metrics, suggesting that this small model relies heavily on pattern matching rather than genuine logical computation. While our empirical findings are based on a single 600M-parameter model, the diagnostic framework itself is model-agnostic and generalizable. We release our evaluation protocols to enable the research community to assess reasoning fidelity across different model scales and architectures, moving beyond surface-level accuracy toward verifiable mathematical reasoning.

Large language models (LLMs) showcase impressive reasoning capabilities when coupled with Chain-of-Thought (CoT) prompting. However, the robustness of this approach warrants further investigation. In this paper, we introduce a novel scenario termed preemptive answers, where the LLM obtains an answer before engaging in reasoning. This situation can arise inadvertently or induced by malicious users by prompt injection attacks. Experiments reveal that preemptive answers significantly impair the model's reasoning capability across various CoT methods and a broad spectrum of datasets. To bolster the robustness of reasoning, we propose two measures aimed at mitigating this issue to some extent.

Reasoning large language models (LLMs) heavily rely on scaling test-time compute to perform complex reasoning tasks by generating extensive "thinking" chains. While demonstrating impressive results, this approach incurs significant computational costs and inference time. In this work, we challenge the assumption that long thinking chains results in better reasoning capabilities. We first demonstrate that shorter reasoning chains within individual questions are significantly more likely to yield correct answers - up to 34.5% more accurate than the longest chain sampled for the same question. Based on these results, we suggest short-m@k, a novel reasoning LLM inference method. Our method executes k independent generations in parallel and halts computation once the first m thinking processes are done. The final answer is chosen using majority voting among these m chains. Basic short-1@k demonstrates similar or even superior performance over standard majority voting in low-compute settings - using up to 40% fewer thinking tokens. short-3@k, while slightly less efficient than short-1@k, consistently surpasses majority voting across all compute budgets, while still being substantially faster (up to 33% wall time reduction). Inspired by our results, we finetune an LLM using short, long, and randomly selected reasoning chains. We then observe that training on the shorter ones leads to better performance. Our findings suggest rethinking current methods of test-time compute in reasoning LLMs, emphasizing that longer "thinking" does not necessarily translate to improved performance and can, counter-intuitively, lead to degraded results.

Logical reasoning, i.e., deductively inferring the truth value of a conclusion from a set of premises, is an important task for artificial intelligence with wide potential impacts on science, mathematics, and society. While many prompting-based strategies have been proposed to enable Large Language Models (LLMs) to do such reasoning more effectively, they still appear unsatisfactory, often failing in subtle and unpredictable ways. In this work, we investigate the validity of instead reformulating such tasks as modular neurosymbolic programming, which we call LINC: Logical Inference via Neurosymbolic Computation. In LINC, the LLM acts as a semantic parser, translating premises and conclusions from natural language to expressions in first-order logic. These expressions are then offloaded to an external theorem prover, which symbolically performs deductive inference. Leveraging this approach, we observe significant performance gains on FOLIO and a balanced subset of ProofWriter for three different models in nearly all experimental conditions we evaluate. On ProofWriter, augmenting the comparatively small open-source StarCoder+ (15.5B parameters) with LINC even outperforms GPT-3.5 and GPT-4 with Chain-of-Thought (CoT) prompting by an absolute 38% and 10%, respectively. When used with GPT-4, LINC scores 26% higher than CoT on ProofWriter while performing comparatively on FOLIO. Further analysis reveals that although both methods on average succeed roughly equally often on this dataset, they exhibit distinct and complementary failure modes. We thus provide promising evidence for how logical reasoning over natural language can be tackled through jointly leveraging LLMs alongside symbolic provers. All corresponding code is publicly available at https://github.com/benlipkin/linc

There is a growing literature on reasoning by large language models (LLMs), but the discussion on the uncertainty in their responses is still lacking. Our aim is to assess the extent of confidence that LLMs have in their answers and how it correlates with accuracy. Confidence is measured (i) qualitatively in terms of persistence in keeping their answer when prompted to reconsider, and (ii) quantitatively in terms of self-reported confidence score. We investigate the performance of three LLMs -- GPT4o, GPT4-turbo and Mistral -- on two benchmark sets of questions on causal judgement and formal fallacies and a set of probability and statistical puzzles and paradoxes. Although the LLMs show significantly better performance than random guessing, there is a wide variability in their tendency to change their initial answers. There is a positive correlation between qualitative confidence and accuracy, but the overall accuracy for the second answer is often worse than for the first answer. There is a strong tendency to overstate the self-reported confidence score. Confidence is only partially explained by the underlying token-level probability. The material effects of prompting on qualitative confidence and the strong tendency for overconfidence indicate that current LLMs do not have any internally coherent sense of confidence.

Logical reasoning is a fundamental aspect of human intelligence and a key component of tasks like problem-solving and decision-making. Recent advancements have enabled Large Language Models (LLMs) to potentially exhibit reasoning capabilities, but complex logical reasoning remains a challenge. The state-of-the-art, solver-augmented language models, use LLMs to parse natural language logical questions into symbolic representations first and then adopt external logical solvers to take in the symbolic representations and output the answers. Despite their impressive performance, any parsing errors will inevitably result in the failure of the execution of the external logical solver and no answer to the logical questions. In this paper, we introduce LoGiPT, a novel language model that directly emulates the reasoning processes of logical solvers and bypasses the parsing errors by learning to strict adherence to solver syntax and grammar. LoGiPT is fine-tuned on a newly constructed instruction-tuning dataset derived from revealing and refining the invisible reasoning process of deductive solvers. Experimental results on two public deductive reasoning datasets demonstrate that LoGiPT outperforms state-of-the-art solver-augmented LMs and few-shot prompting methods on competitive LLMs like ChatGPT or GPT-4.

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.

Language models (LMs) are said to be exhibiting reasoning, but what does this entail? We assess definitions of reasoning and how key papers in the field of natural language processing (NLP) use the notion and argue that the definitions provided are not consistent with how LMs are trained, process information, and generate new tokens. To illustrate this incommensurability we assume the view that transformer-based LMs implement an implicit finite-order Markov kernel mapping contexts to conditional token distributions. In this view, reasoning-like outputs correspond to statistical regularities and approximate statistical invariances in the learned kernel rather than the implementation of explicit logical mechanisms. This view is illustrative of the claim that LMs are "statistical pattern matchers"" and not genuine reasoners and provides a perspective that clarifies why reasoning-like outputs arise in LMs without any guarantees of logical consistency. This distinction is fundamental to how epistemic uncertainty is evaluated in LMs. We invite a discussion on the importance of how the computational processes of the systems we build and analyze in NLP research are described.

Recently, there have been notable advancements in large language models (LLMs), demonstrating their growing abilities in complex reasoning. However, existing research largely overlooks a thorough and systematic comparison of these models' reasoning processes and outputs, particularly regarding their self-reflection pattern (also termed "Aha moment") and the interconnections across diverse domains. This paper proposes a novel framework for analyzing the reasoning characteristics of four cutting-edge large reasoning models (GPT-o1, DeepSeek-R1, Kimi-k1.5, and Grok-3) using keywords statistic and LLM-as-a-judge paradigm. Our approach connects their internal thinking processes with their final outputs. A diverse dataset consists of real-world scenario-based questions covering logical deduction, causal inference, and multi-step problem-solving. Additionally, a set of metrics is put forward to assess both the coherence of reasoning and the accuracy of the outputs. The research results uncover various patterns of how these models balance exploration and exploitation, deal with problems, and reach conclusions during the reasoning process. Through quantitative and qualitative comparisons, disparities among these models are identified in aspects such as the depth of reasoning, the reliance on intermediate steps, and the degree of similarity between their thinking processes and output patterns and those of GPT-o1. This work offers valuable insights into the trade-off between computational efficiency and reasoning robustness and provides practical recommendations for enhancing model design and evaluation in practical applications. We publicly release our project at: https://github.com/ChangWenhan/FromThinking2Output

Logical reasoning is a key task for artificial intelligence due to it's role in major downstream tasks such as Question Answering, Summarization. Recent methods in improving the reasoning ability of LLMs fall short in correctly converting a natural language reasoning problem to an equivalent logical formulation, which hinders the framework's overall ability to reason. Towards this, we propose to use finetuning on a preference optimization dataset to learn to parse and represent a natural language problem as a whole to a consistent logical program by 1) introducing a new supervised and preference optimization dataset LogicPO, and 2) adopting popular techniques such as Direct Preference Optimization (DPO), Kahneman-Tversky optimization (KTO) to finetune open-source LLMs. Our best model with Phi-3.5 consistently outperforms GPT-3.5-turbo's (8-shot) by producing 10% more logically correct and with 14% less syntax errors. Through the framework and our improved evaluation metrics, we offer a promising direction in improving the logical reasoning of LLMs by better representing them in their logical formulations.

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

We introduce Phi-4-reasoning, a 14-billion parameter reasoning model that achieves strong performance on complex reasoning tasks. Trained via supervised fine-tuning of Phi-4 on carefully curated set of "teachable" prompts-selected for the right level of complexity and diversity-and reasoning demonstrations generated using o3-mini, Phi-4-reasoning generates detailed reasoning chains that effectively leverage inference-time compute. We further develop Phi-4-reasoning-plus, a variant enhanced through a short phase of outcome-based reinforcement learning that offers higher performance by generating longer reasoning traces. Across a wide range of reasoning tasks, both models outperform significantly larger open-weight models such as DeepSeek-R1-Distill-Llama-70B model and approach the performance levels of full DeepSeek-R1 model. Our comprehensive evaluations span benchmarks in math and scientific reasoning, coding, algorithmic problem solving, planning, and spatial understanding. Interestingly, we observe a non-trivial transfer of improvements to general-purpose benchmarks as well. In this report, we provide insights into our training data, our training methodologies, and our evaluations. We show that the benefit of careful data curation for supervised fine-tuning (SFT) extends to reasoning language models, and can be further amplified by reinforcement learning (RL). Finally, our evaluation points to opportunities for improving how we assess the performance and robustness of reasoning models.

Scaling the test-time compute of large language models has demonstrated impressive performance on reasoning benchmarks. However, existing evaluations of test-time scaling make the strong assumption that a reasoning system should always give an answer to any question provided. This overlooks concerns about whether a model is confident in its answer, and whether it is appropriate to always provide a response. To address these concerns, we extract confidence scores during reasoning for thresholding model responses. We find that increasing compute budget at inference time not only helps models answer more questions correctly, but also increases confidence in correct responses. We then extend the current paradigm of zero-risk responses during evaluation by considering settings with non-zero levels of response risk, and suggest a recipe for reporting evaluations under these settings.

Large language models (LLMs) have a substantial capacity for high-level analogical reasoning: reproducing patterns in linear text that occur in their training data (zero-shot evaluation) or in the provided context (few-shot in-context learning). However, recent studies show that even the more advanced LLMs fail in scenarios that require reasoning over multiple objects or facts and making sequences of logical deductions. We propose a two-stage probabilistic inference paradigm, ThinkSum, which reasons over sets of objects or facts in a structured manner. In the first stage (Think - retrieval of associations), a LLM is queried in parallel over a set of phrases extracted from the prompt or an auxiliary model call. In the second stage (Sum - probabilistic inference or reasoning), the results of these queries are aggregated to make the final prediction. We demonstrate the possibilities and advantages of ThinkSum on the BIG-bench suite of LLM evaluation tasks, achieving improvements over the state of the art using GPT-family models on thirteen difficult tasks, often with far smaller model variants. We also compare and contrast ThinkSum with other proposed modifications to direct prompting of LLMs, such as variants of chain-of-thought prompting. Our results suggest that because the probabilistic inference in ThinkSum is performed outside of calls to the LLM, ThinkSum is less sensitive to prompt design, yields more interpretable predictions, and can be flexibly combined with latent variable models to extract structured knowledge from LLMs. Overall, our proposed paradigm represents a promising approach for enhancing the reasoning capabilities of LLMs.

We introduce the Probabilistic Worldbuilding Model (PWM), a new fully-symbolic Bayesian model of semantic parsing and reasoning, as a first step in a research program toward more domain- and task-general NLU and AI. Humans create internal mental models of their observations which greatly aid in their ability to understand and reason about a large variety of problems. In PWM, the meanings of sentences, acquired facts about the world, and intermediate steps in reasoning are all expressed in a human-readable formal language, with the design goal of interpretability. PWM is Bayesian, designed specifically to be able to generalize to new domains and new tasks. We derive and implement an inference algorithm that reads sentences by parsing and abducing updates to its latent world model that capture the semantics of those sentences, and evaluate it on two out-of-domain question-answering datasets: (1) ProofWriter and (2) a new dataset we call FictionalGeoQA, designed to be more representative of real language but still simple enough to focus on evaluating reasoning ability, while being robust against heuristics. Our method outperforms baselines on both, thereby demonstrating its value as a proof-of-concept.

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.

Recent years have witnessed significant progress in large language models' (LLMs) reasoning, which is largely due to the chain-of-thought (CoT) approaches, allowing models to generate intermediate reasoning steps before reaching the final answer. Building on these advances, state-of-the-art LLMs are instruction-tuned to provide long and detailed CoT pathways when responding to reasoning-related questions. However, human beings are naturally cognitive misers and will prompt language models to give rather short responses, thus raising a significant conflict with CoT reasoning. In this paper, we delve into how LLMs' reasoning performance changes when users provide short-path prompts. The results and analysis reveal that language models can reason effectively and robustly without explicit CoT prompts, while under short-path prompting, LLMs' reasoning ability drops significantly and becomes unstable, even on grade-school problems. To address this issue, we propose two approaches: an instruction-guided approach and a fine-tuning approach, both designed to effectively manage the conflict. Experimental results show that both methods achieve high accuracy, providing insights into the trade-off between instruction adherence and reasoning accuracy in current models.

The paradigm shift in large language models (LLMs) from instinctive responses to chain-of-thought (CoT) reasoning has fueled two prevailing assumptions: (1) reasoning capabilities only emerge in sufficiently large models, and (2) such capabilities require training on massive datasets. While the first assumption has already been challenged by recent sub-billion-parameter reasoning models such as Qwen3-0.6B and DeepSeek distilled variants, the second remains largely unquestioned. In this work, we revisit the necessity of scaling to extremely large corpora (>10T tokens) for reasoning emergence. By carefully curating and resampling open-source datasets that we identify as beneficial under our designed metrics, we demonstrate that strong reasoning abilities can emerge with far less data. Specifically, we show that only ~2T tokens of high-quality data are sufficient, and pre-training with 4.2T tokens on the dataset resampled from these ~2T tokens, followed by a established post-training procedure, enables the development of MobileLLM-R1, a series of sub-billion-parameter reasoning models that substantially outperform prior models trained on fully open-sourced data. For example, MobileLLM-R1-950M achieves an AIME score of 15.5, compared to just 0.6 for OLMo-2-1.48B and 0.3 for SmolLM-2-1.7B. Remarkably, despite being trained on only 11.7% of the tokens compared to Qwen3's proprietary 36T-token corpus for pretraining, MobileLLM-R1-950M matches or surpasses Qwen3-0.6B across multiple reasoning benchmarks. To facilitate further research in this direction, we have released the complete training recipe, data sources, data mixing ratio, and model checkpoints, together with the key insights obtained throughout this study.

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

Recent advances in reasoning-centric models promise improved robustness through mechanisms such as chain-of-thought prompting and test-time scaling. However, their ability to withstand misleading user input remains underexplored. In this paper, we conduct a systematic evaluation of three state-of-the-art reasoning models, i.e., OpenAI's o4-mini, Claude-3.7-Sonnet and Gemini-2.5-Flash, across three multimodal benchmarks: MMMU, MathVista, and CharXiv. Our evaluation reveals significant accuracy drops (25-29% on average) following gaslighting negation prompts, indicating that even top-tier reasoning models struggle to preserve correct answers under manipulative user feedback. Built upon the insights of the evaluation and to further probe this vulnerability, we introduce GaslightingBench-R, a new diagnostic benchmark specifically designed to evaluate reasoning models' susceptibility to defend their belief under gaslighting negation prompt. Constructed by filtering and curating 1,025 challenging samples from the existing benchmarks, GaslightingBench-R induces even more dramatic failures, with accuracy drops exceeding 53% on average. Our findings reveal fundamental limitations in the robustness of reasoning models, highlighting the gap between step-by-step reasoning and belief persistence.

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).

A key limitation in current datasets for multi-hop reasoning is that the required steps for answering the question are mentioned in it explicitly. In this work, we introduce StrategyQA, a question answering (QA) benchmark where the required reasoning steps are implicit in the question, and should be inferred using a strategy. A fundamental challenge in this setup is how to elicit such creative questions from crowdsourcing workers, while covering a broad range of potential strategies. We propose a data collection procedure that combines term-based priming to inspire annotators, careful control over the annotator population, and adversarial filtering for eliminating reasoning shortcuts. Moreover, we annotate each question with (1) a decomposition into reasoning steps for answering it, and (2) Wikipedia paragraphs that contain the answers to each step. Overall, StrategyQA includes 2,780 examples, each consisting of a strategy question, its decomposition, and evidence paragraphs. Analysis shows that questions in StrategyQA are short, topic-diverse, and cover a wide range of strategies. Empirically, we show that humans perform well (87%) on this task, while our best baseline reaches an accuracy of sim66%.

With the help of Chain-of-Thought (CoT) prompting, Large Language Models (LLMs) have achieved remarkable performance on various reasoning tasks. However, most of them have been evaluated under noise-free context and the dilemma for LLMs to produce inaccurate results under the noisy context has not been fully investigated. Existing studies utilize trigger sentences to encourage LLMs to concentrate on the relevant information but the trigger has limited effect on final answer prediction. Inspired by interactive CoT method, where intermediate reasoning steps are promoted by multiple rounds of interaction between users and LLMs, we propose a novel prompting method, namely R^3 prompting, for CoT reasoning under noisy context. Specifically, R^3 prompting interacts with LLMs to perform key sentence extraction, variable declaration and answer prediction, which corresponds to a thought process of reviewing, rephrasing and resolving. The responses generated at the last interaction will perform as hints to guide toward the responses of the next interaction. Our experiments show that R^3 prompting significantly outperforms existing CoT prompting methods on five reasoning tasks under noisy context. With GPT-3.5-turbo, we observe 3.7% accuracy improvement on average on the reasoning tasks under noisy context compared to the most competitive prompting baseline. More analyses and ablation studies show the robustness and generalization of R^3 prompting method in solving reasoning tasks in LLMs under noisy context.

Large Language Models (LLMs) are extensively used today across various sectors, including academia, research, business, and finance, for tasks such as text generation, summarization, and translation. Despite their widespread adoption, these models often produce incorrect and misleading information, exhibiting a tendency to hallucinate. This behavior can be attributed to several factors, with consistency and reasoning capabilities being significant contributors. LLMs frequently lack the ability to generate explanations and engage in coherent reasoning, leading to inaccurate responses. Moreover, they exhibit inconsistencies in their outputs. This paper aims to evaluate and compare the consistency and reasoning capabilities of both public and proprietary LLMs. The experiments utilize the Boolq dataset as the ground truth, comprising questions, answers, and corresponding explanations. Queries from the dataset are presented as prompts to the LLMs, and the generated responses are evaluated against the ground truth answers. Additionally, explanations are generated to assess the models' reasoning abilities. Consistency is evaluated by repeatedly presenting the same query to the models and observing for variations in their responses. For measuring reasoning capabilities, the generated explanations are compared to the ground truth explanations using metrics such as BERT, BLEU, and F-1 scores. The findings reveal that proprietary models generally outperform public models in terms of both consistency and reasoning capabilities. However, even when presented with basic general knowledge questions, none of the models achieved a score of 90\% in both consistency and reasoning. This study underscores the direct correlation between consistency and reasoning abilities in LLMs and highlights the inherent reasoning challenges present in current language models.

Large language models (LLMs) have demonstrated impressive performance in various natural language processing tasks, yet their ability to perform multi-step logical reasoning remains an open challenge. Although Chain-of-Thought prompting has improved logical reasoning by enabling models to generate intermediate steps, it lacks mechanisms to assess the coherence of these logical transitions. In this paper, we propose a novel, lightweight evaluation strategy for logical reasoning that uses query-key alignments inside transformer attention heads. By computing a single forward pass and extracting a "QK-score" from carefully chosen heads, our method reveals latent representations that reliably separate valid from invalid inferences, offering a scalable alternative to traditional ablation-based techniques. We also provide an empirical validation on multiple logical reasoning benchmarks, demonstrating improved robustness of our evaluation method against distractors and increased reasoning depth. The experiments were conducted on a diverse set of models, ranging from 1.5B to 70B parameters.

Composing knowledge from multiple pieces of texts is a key challenge in multi-hop question answering. We present a multi-hop reasoning dataset, Question Answering via Sentence Composition(QASC), that requires retrieving facts from a large corpus and composing them to answer a multiple-choice question. QASC is the first dataset to offer two desirable properties: (a) the facts to be composed are annotated in a large corpus, and (b) the decomposition into these facts is not evident from the question itself. The latter makes retrieval challenging as the system must introduce new concepts or relations in order to discover potential decompositions. Further, the reasoning model must then learn to identify valid compositions of these retrieved facts using common-sense reasoning. To help address these challenges, we provide annotation for supporting facts as well as their composition. Guided by these annotations, we present a two-step approach to mitigate the retrieval challenges. We use other multiple-choice datasets as additional training data to strengthen the reasoning model. Our proposed approach improves over current state-of-the-art language models by 11% (absolute). The reasoning and retrieval problems, however, remain unsolved as this model still lags by 20% behind human performance.

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

Large Language Models (LLMs) have demonstrated remarkable capabilities in complex tasks. Recent advancements in Large Reasoning Models (LRMs), such as OpenAI o1 and DeepSeek-R1, have further improved performance in System-2 reasoning domains like mathematics and programming by harnessing supervised fine-tuning (SFT) and reinforcement learning (RL) techniques to enhance the Chain-of-Thought (CoT) reasoning. However, while longer CoT reasoning sequences improve performance, they also introduce significant computational overhead due to verbose and redundant outputs, known as the "overthinking phenomenon". In this paper, we provide the first structured survey to systematically investigate and explore the current progress toward achieving efficient reasoning in LLMs. Overall, relying on the inherent mechanism of LLMs, we categorize existing works into several key directions: (1) model-based efficient reasoning, which considers optimizing full-length reasoning models into more concise reasoning models or directly training efficient reasoning models; (2) reasoning output-based efficient reasoning, which aims to dynamically reduce reasoning steps and length during inference; (3) input prompts-based efficient reasoning, which seeks to enhance reasoning efficiency based on input prompt properties such as difficulty or length control. Additionally, we introduce the use of efficient data for training reasoning models, explore the reasoning capabilities of small language models, and discuss evaluation methods and benchmarking.

Large Language Models (LLMs) have demonstrated significant potential in handling complex reasoning tasks through step-by-step rationale generation. However, recent studies have raised concerns regarding the hallucination and flaws in their reasoning process. Substantial efforts are being made to improve the reliability and faithfulness of the generated rationales. Some approaches model reasoning as planning, while others focus on annotating for process supervision. Nevertheless, the planning-based search process often results in high latency due to the frequent assessment of intermediate reasoning states and the extensive exploration space. Additionally, supervising the reasoning process with human annotation is costly and challenging to scale for LLM training. To address these issues, in this paper, we propose a framework to learn planning-based reasoning through direct preference optimization (DPO) on collected trajectories, which are ranked according to synthesized process rewards. Our results on challenging logical reasoning benchmarks demonstrate the effectiveness of our learning framework, showing that our 7B model can surpass the strong counterparts like GPT-3.5-Turbo.

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.

Recent studies on transformer-based language models show that they can answer questions by reasoning over knowledge provided as part of the context (i.e., in-context reasoning). However, since the available knowledge is often not filtered for a particular question, in-context reasoning can be sensitive to distractor facts, additional content that is irrelevant to a question but that may be relevant for a different question (i.e., not necessarily random noise). In these situations, the model fails to distinguish the knowledge that is necessary to answer the question, leading to spurious reasoning and degraded performance. This reasoning failure contrasts with the model's apparent ability to distinguish its contextual knowledge from all the knowledge it has memorized during pre-training. Following this observation, we propose teaching the model to reason more robustly by folding the provided contextual knowledge into the model's parameters before presenting it with a question. Our method, RECKONING, is a bi-level learning algorithm that teaches language models to reason by updating their parametric knowledge through back-propagation, allowing them to then answer questions using the updated parameters. During training, the inner loop rapidly adapts a copy of the model weights to encode contextual knowledge into its parameters. In the outer loop, the model learns to use the updated weights to reproduce and answer reasoning questions about the memorized knowledge. Our experiments on two multi-hop reasoning datasets show that RECKONING's performance improves over the in-context reasoning baseline (by up to 4.5%). We also find that compared to in-context reasoning, RECKONING generalizes better to longer reasoning chains unseen during training, is more robust to distractors in the context, and is more computationally efficient when multiple questions are asked about the same knowledge.

Retrieval-Augmented Generation (RAG) effectively enhances Large Language Models (LLMs) by incorporating retrieved external knowledge into the generation process. Reasoning models improve LLM performance in multi-hop QA tasks, which require integrating and reasoning over multiple pieces of evidence across different documents to answer a complex question. However, they often introduce substantial computational costs, including increased token consumption and inference latency. To better understand and mitigate this trade-off, we conduct a comprehensive study of reasoning strategies for reasoning models in RAG multi-hop QA tasks. Our findings reveal that reasoning models adopt structured strategies to integrate retrieved and internal knowledge, primarily following two modes: Context-Grounded Reasoning, which relies directly on retrieved content, and Knowledge-Reconciled Reasoning, which resolves conflicts or gaps using internal knowledge. To this end, we propose a novel Lightweight Rerank Reasoning Strategy Framework for RAG (LiR^3AG) to enable non-reasoning models to transfer reasoning strategies by restructuring retrieved evidence into coherent reasoning chains. LiR^3AG significantly reduce the average 98% output tokens overhead and 58.6% inferencing time while improving 8B non-reasoning model's F1 performance ranging from 6.2% to 22.5% to surpass the performance of 32B reasoning model in RAG, offering a practical and efficient path forward for RAG systems.

Recent Large Reasoning Models (LRMs), such as DeepSeek-R1 and OpenAI o1, have demonstrated strong performance gains by scaling up the length of Chain-of-Thought (CoT) reasoning during inference. However, a growing concern lies in their tendency to produce excessively long reasoning traces, which are often filled with redundant content (e.g., repeated definitions), over-analysis of simple problems, and superficial exploration of multiple reasoning paths for harder tasks. This inefficiency introduces significant challenges for training, inference, and real-world deployment (e.g., in agent-based systems), where token economy is critical. In this survey, we provide a comprehensive overview of recent efforts aimed at improving reasoning efficiency in LRMs, with a particular focus on the unique challenges that arise in this new paradigm. We identify common patterns of inefficiency, examine methods proposed across the LRM lifecycle, i.e., from pretraining to inference, and discuss promising future directions for research. To support ongoing development, we also maintain a real-time GitHub repository tracking recent progress in the field. We hope this survey serves as a foundation for further exploration and inspires innovation in this rapidly evolving area.

The context window of large language models (LLMs) has been extended significantly in recent years. However, while the context length that the LLM can process has grown, the capability of the model to accurately reason over that context degrades noticeably. This occurs because modern LLMs often become overwhelmed by the vast amount of information in the context; when answering questions, the model must identify and reason over relevant evidence sparsely distributed throughout the text. To alleviate the challenge of long-context reasoning, we develop a retrieve-then-reason framework, enabling LLMs to reason over relevant evidence collected during an intermediate retrieval step. We find that modern LLMs struggle to accurately retrieve relevant facts and instead, often hallucinate "retrieved facts", resulting in flawed reasoning and the production of incorrect answers. To address these issues, we introduce ALR^2, a method that augments the long-context reasoning capability of LLMs via an explicit two-stage procedure, i.e., aligning LLMs with the objectives of both retrieval and reasoning. We demonstrate the efficacy of ALR^2 for mitigating performance degradation in long-context reasoning tasks. Through extensive experiments on long-context QA benchmarks, we find our method to outperform competitive baselines by large margins, achieving at least 8.4 and 7.9 EM gains on the long-context versions of HotpotQA and SQuAD datasets, respectively.

Chain-of-thought (CoT) reasoning in vision language models (VLMs) is crucial for improving interpretability and trustworthiness. However, current training recipes lack robust CoT reasoning data, relying on datasets dominated by short annotations with minimal rationales. In this work, we show that training VLM on short answers does not generalize well to reasoning tasks that require more detailed responses. To address this, we propose a two-fold approach. First, we distill rationales from GPT-4o model to enrich the training data and fine-tune VLMs, boosting their CoT performance. Second, we apply reinforcement learning to further calibrate reasoning quality. Specifically, we construct positive (correct) and negative (incorrect) pairs of model-generated reasoning chains, by comparing their predictions with annotated short answers. Using this pairwise data, we apply the Direct Preference Optimization algorithm to refine the model's reasoning abilities. Our experiments demonstrate significant improvements in CoT reasoning on benchmark datasets and better generalization to direct answer prediction as well. This work emphasizes the importance of incorporating detailed rationales in training and leveraging reinforcement learning to strengthen the reasoning capabilities of VLMs.

Language models are known to absorb biases from their training data, leading to predictions driven by statistical regularities rather than semantic relevance. We investigate the impact of these biases on answer choice preferences in the Massive Multi-Task Language Understanding (MMLU) task. Our findings reveal that differences in learned regularities across answer options are predictive of model preferences and mirror human test-taking strategies. To address this issue, we introduce two novel methods: Counterfactual Prompting with Chain of Thought (CoT) and Counterfactual Prompting with Agnostically Primed CoT (APriCoT). We demonstrate that while Counterfactual Prompting with CoT alone is insufficient to mitigate bias, our novel Primed Counterfactual Prompting with CoT approach effectively reduces the influence of base-rate probabilities while improving overall accuracy. Our results suggest that mitigating bias requires a "System-2" like process and that CoT reasoning is susceptible to confirmation bias under some prompting methodologies. Our contributions offer practical solutions for developing more robust and fair language models.

Large language models (LLMs) have been shown to perform better when asked to reason step-by-step before answering a question. However, it is unclear to what degree the model's final answer is faithful to the stated reasoning steps. In this paper, we perform a causal mediation analysis on twelve LLMs to examine how intermediate reasoning steps generated by the LLM influence the final outcome and find that LLMs do not reliably use their intermediate reasoning steps when generating an answer. To address this issue, we introduce FRODO, a framework to tailor small-sized LMs to generate correct reasoning steps and robustly reason over these steps. FRODO consists of an inference module that learns to generate correct reasoning steps using an implicit causal reward function and a reasoning module that learns to faithfully reason over these intermediate inferences using a counterfactual and causal preference objective. Our experiments show that FRODO significantly outperforms four competitive baselines. Furthermore, FRODO improves the robustness and generalization ability of the reasoning LM, yielding higher performance on out-of-distribution test sets. Finally, we find that FRODO's rationales are more faithful to its final answer predictions than standard supervised fine-tuning.

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.

Large language models (LLMs) have shown impressive performance in various reasoning benchmarks with the emergence of Chain-of-Thought (CoT) and its derivative methods, particularly in tasks involving multi-choice questions (MCQs). However, current works all process data uniformly without considering the problem-solving difficulty, which means an excessive focus on simple questions while insufficient to intricate ones. To address this challenge, we inspired by humans using heuristic strategies to categorize tasks and handle them individually, propose to apply the Divide and Conquer to LLMs reasoning. First, we divide questions into different subsets based on the statistical confidence score (CS), then fix nearly resolved sets and conquer demanding nuanced process ones with elaborately designed methods, including Prior Knowledge based Reasoning (PKR) and Filter Choices based Reasoning (FCR), as well as their integration variants. Our experiments demonstrate that this proposed strategy significantly boosts the models' reasoning abilities across nine datasets involving arithmetic, commonsense, and logic tasks. For instance, compared to baseline, we make a striking improvement on low confidence subsets of 8.72\% for AQuA, 15.07\% for ARC Challenge and 7.71\% for RiddleSense. In addition, through extensive analysis on length of rationale and number of options, we verify that longer reasoning paths in PKR could prevent models from referring infer-harmful shortcuts, and also find that removing irrelevant choices in FCR would substantially avoid models' confusion. The code is at https://github.com/AiMijie/Divide-and-Conquer

Reasoning is a fundamental component for achieving language understanding. Among the multiple types of reasoning, conditional reasoning, the ability to draw different conclusions depending on some condition, has been understudied in large language models (LLMs). Recent prompting methods, such as chain of thought, have significantly improved LLMs on reasoning tasks. Nevertheless, there is still little understanding of what triggers reasoning abilities in LLMs. We hypothesize that code prompts can trigger conditional reasoning in LLMs trained on text and code. We propose a chain of prompts that transforms a natural language problem into code and prompts the LLM with the generated code. Our experiments find that code prompts exhibit a performance boost between 2.6 and 7.7 points on GPT 3.5 across multiple datasets requiring conditional reasoning. We then conduct experiments to discover how code prompts elicit conditional reasoning abilities and through which features. We observe that prompts need to contain natural language text accompanied by high-quality code that closely represents the semantics of the instance text. Furthermore, we show that code prompts are more efficient, requiring fewer demonstrations, and that they trigger superior state tracking of variables or key entities.

Large Language Models (LLMs) have demonstrated good performance in many reasoning tasks, but they still struggle with some complicated reasoning tasks including logical reasoning. One non-negligible reason for LLMs' suboptimal performance on logical reasoning is their overlooking of understanding logical fallacies correctly. To evaluate LLMs' capability of logical fallacy understanding (LFU), we propose five concrete tasks from three cognitive dimensions of WHAT, WHY, and HOW in this paper. Towards these LFU tasks, we have successfully constructed a new dataset LFUD based on GPT-4 accompanied by a little human effort. Our extensive experiments justify that our LFUD can be used not only to evaluate LLMs' LFU capability, but also to fine-tune LLMs to obtain significantly enhanced performance on logical reasoning.