Daily Papers

The exponential growth of Large Language Models (LLMs) continues to highlight the need for efficient strategies to meet ever-expanding computational and data demands. This survey provides a comprehensive analysis of two complementary paradigms: Knowledge Distillation (KD) and Dataset Distillation (DD), both aimed at compressing LLMs while preserving their advanced reasoning capabilities and linguistic diversity. We first examine key methodologies in KD, such as task-specific alignment, rationale-based training, and multi-teacher frameworks, alongside DD techniques that synthesize compact, high-impact datasets through optimization-based gradient matching, latent space regularization, and generative synthesis. Building on these foundations, we explore how integrating KD and DD can produce more effective and scalable compression strategies. Together, these approaches address persistent challenges in model scalability, architectural heterogeneity, and the preservation of emergent LLM abilities. We further highlight applications across domains such as healthcare and education, where distillation enables efficient deployment without sacrificing performance. Despite substantial progress, open challenges remain in preserving emergent reasoning and linguistic diversity, enabling efficient adaptation to continually evolving teacher models and datasets, and establishing comprehensive evaluation protocols. By synthesizing methodological innovations, theoretical foundations, and practical insights, our survey charts a path toward sustainable, resource-efficient LLMs through the tighter integration of KD and DD principles.

The reasoning steps generated by LLMs might be incomplete, as they mimic logical leaps common in everyday communication found in their pre-training data: underlying rationales are frequently left implicit (unstated). To address this challenge, we introduce RATIONALYST, a model for process-supervision of reasoning based on pre-training on a vast collection of rationale annotations extracted from unlabeled data. We extract 79k rationales from web-scale unlabelled dataset (the Pile) and a combination of reasoning datasets with minimal human intervention. This web-scale pre-training for reasoning allows RATIONALYST to consistently generalize across diverse reasoning tasks, including mathematical, commonsense, scientific, and logical reasoning. Fine-tuned from LLaMa-3-8B, RATIONALYST improves the accuracy of reasoning by an average of 3.9% on 7 representative reasoning benchmarks. It also demonstrates superior performance compared to significantly larger verifiers like GPT-4 and similarly sized models fine-tuned on matching training sets.

Self-training approach for large language models (LLMs) improves reasoning abilities by training the models on their self-generated rationales. Previous approaches have labeled rationales that produce correct answers for a given question as appropriate for training. However, a single measure risks misjudging rationale quality, leading the models to learn flawed reasoning patterns. To address this issue, we propose CREST (Consistency-driven Rationale Evaluation for Self-Training), a self-training framework that further evaluates each rationale through follow-up questions and leverages this evaluation to guide its training. Specifically, we introduce two methods: (1) filtering out rationales that frequently result in incorrect answers on follow-up questions and (2) preference learning based on mixed preferences from rationale evaluation results of both original and follow-up questions. Experiments on three question-answering datasets using open LLMs show that CREST not only improves the logical robustness and correctness of rationales but also improves reasoning abilities compared to previous self-training approaches.

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

Large language models (LLMs) often generate inaccurate or fabricated information and generally fail to indicate their confidence, which limits their broader applications. Previous work elicits confidence from LLMs by direct or self-consistency prompting, or constructing specific datasets for supervised finetuning. The prompting-based approaches have inferior performance, and the training-based approaches are limited to binary or inaccurate group-level confidence estimates. In this work, we present the advanced SaySelf, a training framework that teaches LLMs to express more accurate fine-grained confidence estimates. In addition, beyond the confidence scores, SaySelf initiates the process of directing LLMs to produce self-reflective rationales that clearly identify gaps in their parametric knowledge and explain their uncertainty. This is achieved by using an LLM to automatically summarize the uncertainties in specific knowledge via natural language. The summarization is based on the analysis of the inconsistency in multiple sampled reasoning chains, and the resulting data is utilized for supervised fine-tuning. Moreover, we utilize reinforcement learning with a meticulously crafted reward function to calibrate the confidence estimates, motivating LLMs to deliver accurate, high-confidence predictions and to penalize overconfidence in erroneous outputs. Experimental results in both in-distribution and out-of-distribution datasets demonstrate the effectiveness of SaySelf in reducing the confidence calibration error and maintaining the task performance. We show that the generated self-reflective rationales are reasonable and can further contribute to the calibration. The code is made public at https://github.com/xu1868/SaySelf.

Large Language Models (LLMs) have shown strong performance in solving mathematical problems, with code-based solutions proving particularly effective. However, the best practice to leverage coding instruction data to enhance mathematical reasoning remains underexplored. This study investigates three key questions: (1) How do different coding styles of mathematical code-based rationales impact LLMs' learning performance? (2) Can general-domain coding instructions improve performance? (3) How does integrating textual rationales with code-based ones during training enhance mathematical reasoning abilities? Our findings reveal that code-based rationales with concise comments, descriptive naming, and hardcoded solutions are beneficial, while improvements from general-domain coding instructions and textual rationales are relatively minor. Based on these insights, we propose CoinMath, a learning strategy designed to enhance mathematical reasoning by diversifying the coding styles of code-based rationales. CoinMath generates a variety of code-based rationales incorporating concise comments, descriptive naming conventions, and hardcoded solutions. Experimental results demonstrate that CoinMath significantly outperforms its baseline model, MAmmoTH, one of the SOTA math LLMs.

A major issue with using deep learning models in sensitive applications is that they provide no explanation for their output. To address this problem, unsupervised selective rationalization produces rationales alongside predictions by chaining two jointly-trained components, a rationale generator and a predictor. Although this architecture guarantees that the prediction relies solely on the rationale, it does not ensure that the rationale contains a plausible explanation for the prediction. We introduce a novel training technique that effectively limits generation of implausible rationales by injecting noise between the generator and the predictor. Furthermore, we propose a new benchmark for evaluating unsupervised selective rationalization models using movie reviews from existing datasets. We achieve sizeable improvements in rationale plausibility and task accuracy over the state-of-the-art across a variety of tasks, including our new benchmark, while maintaining or improving model faithfulness.

Large-scale high-quality training data is important for improving the performance of models. After trained with data that has rationales (reasoning steps), models gain reasoning capability. However, the dataset with high-quality rationales is relatively scarce due to the high annotation cost. To address this issue, we propose Self-motivated Learning framework. The framework motivates the model itself to automatically generate rationales on existing datasets. Based on the inherent rank from correctness across multiple rationales, the model learns to generate better rationales, leading to higher reasoning capability. Specifically, we train a reward model with the rank to evaluate the quality of rationales, and improve the performance of reasoning through reinforcement learning. Experiment results of Llama2 7B on multiple reasoning datasets show that our method significantly improves the reasoning ability of models, even outperforming text-davinci-002 in some datasets.

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

Generating step-by-step "chain-of-thought" rationales improves language model performance on complex reasoning tasks like mathematics or commonsense question-answering. However, inducing language model rationale generation currently requires either constructing massive rationale datasets or sacrificing accuracy by using only few-shot inference. We propose a technique to iteratively leverage a small number of rationale examples and a large dataset without rationales, to bootstrap the ability to perform successively more complex reasoning. This technique, the "Self-Taught Reasoner" (STaR), relies on a simple loop: generate rationales to answer many questions, prompted with a few rationale examples; if the generated answers are wrong, try again to generate a rationale given the correct answer; fine-tune on all the rationales that ultimately yielded correct answers; repeat. We show that STaR significantly improves performance on multiple datasets compared to a model fine-tuned to directly predict final answers, and performs comparably to fine-tuning a 30times larger state-of-the-art language model on CommensenseQA. Thus, STaR lets a model improve itself by learning from its own generated reasoning.

Automated rationale generation is an approach for real-time explanation generation whereby a computational model learns to translate an autonomous agent's internal state and action data representations into natural language. Training on human explanation data can enable agents to learn to generate human-like explanations for their behavior. In this paper, using the context of an agent that plays Frogger, we describe (a) how to collect a corpus of explanations, (b) how to train a neural rationale generator to produce different styles of rationales, and (c) how people perceive these rationales. We conducted two user studies. The first study establishes the plausibility of each type of generated rationale and situates their user perceptions along the dimensions of confidence, humanlike-ness, adequate justification, and understandability. The second study further explores user preferences between the generated rationales with regard to confidence in the autonomous agent, communicating failure and unexpected behavior. Overall, we find alignment between the intended differences in features of the generated rationales and the perceived differences by users. Moreover, context permitting, participants preferred detailed rationales to form a stable mental model of the agent's behavior.

Eliciting feedback from end users of NLP models can be beneficial for improving models. However, how should we present model responses to users so they are most amenable to be corrected from user feedback? Further, what properties do users value to understand and trust responses? We answer these questions by analyzing the effect of rationales (or explanations) generated by QA models to support their answers. We specifically consider decomposed QA models that first extract an intermediate rationale based on a context and a question and then use solely this rationale to answer the question. A rationale outlines the approach followed by the model to answer the question. Our work considers various formats of these rationales that vary according to well-defined properties of interest. We sample rationales from language models using few-shot prompting for two datasets, and then perform two user studies. First, we present users with incorrect answers and corresponding rationales in various formats and ask them to provide natural language feedback to revise the rationale. We then measure the effectiveness of this feedback in patching these rationales through in-context learning. The second study evaluates how well different rationale formats enable users to understand and trust model answers, when they are correct. We find that rationale formats significantly affect how easy it is (1) for users to give feedback for rationales, and (2) for models to subsequently execute this feedback. In addition, formats with attributions to the context and in-depth reasoning significantly enhance user-reported understanding and trust of model outputs.

Neural language models (LMs) have achieved impressive results on various language-based reasoning tasks by utilizing latent knowledge encoded in their own pretrained parameters. To make this reasoning process more explicit, recent works retrieve a rationalizing LM's internal knowledge by training or prompting it to generate free-text rationales, which can be used to guide task predictions made by either the same LM or a separate reasoning LM. However, rationalizing LMs require expensive rationale annotation and/or computation, without any assurance that their generated rationales improve LM task performance or faithfully reflect LM decision-making. In this paper, we propose PINTO, an LM pipeline that rationalizes via prompt-based learning, and learns to faithfully reason over rationales via counterfactual regularization. First, PINTO maps out a suitable reasoning process for the task input by prompting a frozen rationalizing LM to generate a free-text rationale. Second, PINTO's reasoning LM is fine-tuned to solve the task using the generated rationale as context, while regularized to output less confident predictions when the rationale is perturbed. Across four datasets, we show that PINTO significantly improves the generalization ability of the reasoning LM, yielding higher performance on both in-distribution and out-of-distribution test sets. Also, we find that PINTO's rationales are more faithful to its task predictions than those generated by competitive baselines.

Training language models with rationales augmentation has been shown to be beneficial in many existing works. In this paper, we identify that such a prevailing view does not hold consistently. We conduct comprehensive investigations to thoroughly inspect the impact of rationales on model performance as well as a novel perspective of model reliability. The results lead to several key findings that add new insights upon existing understandings: 1) Rationales can, at times, deteriorate model performance; 2) Rationales can, at times, improve model reliability, even outperforming their untrained counterparts; 3) A linear correspondence exists in between the performance and reliability improvements, while both are driven by the intrinsic difficulty of the task. These findings provide informative regulations on the broad utilization of rationales and raise critical implications on the procedure of explicitly aligning language models with implicit human thoughts. Codes can be found at https://github.com/Ignoramus0817/rationales.

Being prompted to engage in reasoning has emerged as a core technique for using large language models (LLMs), deploying additional inference-time compute to improve task performance. However, as LLMs increase in both size and adoption, inference costs are correspondingly becoming increasingly burdensome. How, then, might we optimize reasoning's cost-performance tradeoff? This work introduces a novel approach based on computational models of metareasoning used in cognitive science, training LLMs to selectively use intermediate reasoning steps only when necessary. We first develop a reward function that incorporates the Value of Computation by penalizing unnecessary reasoning, then use this reward function with Expert Iteration to train the LLM. Compared to few-shot chain-of-thought prompting and STaR, our method significantly reduces inference costs (20-37\% fewer tokens generated across three models) while maintaining task performance across diverse datasets.

Retrieval-Augmented Generation (RAG) effectively improves the accuracy of Large Language Models (LLMs). However, retrieval noises significantly impact the quality of LLMs' generation, necessitating the development of denoising mechanisms. Previous methods extract evidence straightforwardly without explicit thinking, which risks filtering out key clues and struggles with generalization. To this end, we propose EviOmni, which learns to extract rational evidence by (1) explicitly reasoning to identify potential cues within retrieval contents first, and then (2) consciously extracting to avoid omitting any key cues helpful for answering questions. Specifically, we frame evidence reasoning and evidence extraction into one unified response for end-to-end training; apply knowledge token masks for disentanglement to derive reasoning-based and extraction-based answers; and devise three types of verifiable reward functions, including answer, length, and format, to update the model via the policy optimization algorithm. Extensive experiments on three benchmark datasets show the effectiveness of EviOmni, providing compact and high-quality evidence, improving the accuracy of downstream tasks, and promoting effective application in online RAG systems.

LLM-as-a-judge models have been used for evaluating both human and AI generated content, specifically by providing scores and rationales. Rationales, in addition to increasing transparency, help models learn to calibrate its judgments. Enhancing a model's rationale can therefore improve its calibration abilities and ultimately the ability to score content. We introduce Self-Rationalization, an iterative process of improving the rationales for the judge models, which consequently improves the score for fine-grained customizable scoring criteria (i.e., likert-scale scoring with arbitrary evaluation criteria). Self-rationalization works by having the model generate multiple judgments with rationales for the same input, curating a preference pair dataset from its own judgements, and iteratively fine-tuning the judge via DPO. Intuitively, this approach allows the judge model to self-improve by learning from its own rationales, leading to better alignment and evaluation accuracy. After just two iterations -- while only relying on examples in the training set -- human evaluation shows that our judge model learns to produce higher quality rationales, with a win rate of 62% on average compared to models just trained via SFT on rationale . This judge model also achieves high scoring accuracy on BigGen Bench and Reward Bench, outperforming even bigger sized models trained using SFT with rationale, self-consistency or best-of-N sampling by 3% to 9%.

Bootstrapping from pre-trained language models has been proven to be an efficient approach for building vision-language models (VLM) for tasks such as image captioning or visual question answering. However, outputs of these models rarely align with user's rationales for specific answers. In order to improve this alignment and reinforce commonsense reasons, we propose a tuning paradigm based on human interactions with machine generated data. Our ILLUME executes the following loop: Given an image-question-answer prompt, the VLM samples multiple candidate rationales, and a human critic provides minimal feedback via preference selection, used for fine-tuning. This loop increases the training data and gradually carves out the VLM's rationalization capabilities that are aligned with human intend. Our exhaustive experiments demonstrate that ILLUME is competitive with standard supervised fine-tuning while using significantly fewer training data and only requiring minimal feedback.

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

Large Language Models (LLMs) have recently demonstrated strong potential in generating 'believable human-like' behavior in web environments. Prior work has explored augmenting training data with LLM-synthesized rationales and applying supervised fine-tuning (SFT) to enhance reasoning ability, which in turn can improve downstream action prediction. However, the performance of such approaches remains inherently bounded by the reasoning capabilities of the model used to generate the rationales. In this paper, we introduce Shop-R1, a novel reinforcement learning (RL) framework aimed at enhancing the reasoning ability of LLMs for simulation of real human behavior in online shopping environments Specifically, Shop-R1 decomposes the human behavior simulation task into two stages: rationale generation and action prediction, each guided by distinct reward signals. For rationale generation, we leverage internal model signals (e.g., logit distributions) to guide the reasoning process in a self-supervised manner. For action prediction, we propose a hierarchical reward structure with difficulty-aware scaling to prevent reward hacking and enable fine-grained reward assignment. This design evaluates both high-level action types and the correctness of fine-grained sub-action details (attributes and values), rewarding outputs proportionally to their difficulty. Experimental results show that our method achieves a relative improvement of over 65% compared to the baseline.

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.

Rationale is defined as a subset of input features that best explains or supports the prediction by machine learning models. Rationale identification has improved the generalizability and interpretability of neural networks on vision and language data. In graph applications such as molecule and polymer property prediction, identifying representative subgraph structures named as graph rationales plays an essential role in the performance of graph neural networks. Existing graph pooling and/or distribution intervention methods suffer from lack of examples to learn to identify optimal graph rationales. In this work, we introduce a new augmentation operation called environment replacement that automatically creates virtual data examples to improve rationale identification. We propose an efficient framework that performs rationale-environment separation and representation learning on the real and augmented examples in latent spaces to avoid the high complexity of explicit graph decoding and encoding. Comparing against recent techniques, experiments on seven molecular and four polymer real datasets demonstrate the effectiveness and efficiency of the proposed augmentation-based graph rationalization framework.

Generating rationales that justify scoring decisions has been a promising way to facilitate explainability in automated scoring systems. However, existing methods do not match the accuracy of classifier-based methods. Plus, the generated rationales often contain hallucinated information. To address these issues, we propose a novel framework capable of generating more faithful rationales and, more importantly, matching performance with classifier-based black-box scoring systems. We first mimic the human assessment process by querying Large Language Models (LLMs) to generate a thought tree. We then summarise intermediate assessment decisions from each thought tree path for creating synthetic rationale data and rationale preference data. Finally, we utilise the generated synthetic data to calibrate LLMs through a two-step training process: supervised fine-tuning and preference optimization. Extensive experimental results demonstrate that our framework achieves a 38% assessment performance improvement in the QWK score compared to prior work while producing higher-quality rationales, as recognised by human evaluators and LLMs. Our work sheds light on the effectiveness of performing preference optimization using synthetic preference data obtained from thought tree paths.

Human-annotated textual explanations are becoming increasingly important in Explainable Natural Language Processing. Rationale extraction aims to provide faithful (i.e., reflective of the behavior of the model) and plausible (i.e., convincing to humans) explanations by highlighting the inputs that had the largest impact on the prediction without compromising the performance of the task model. In recent works, the focus of training rationale extractors was primarily on optimizing for plausibility using human highlights, while the task model was trained on jointly optimizing for task predictive accuracy and faithfulness. We propose REFER, a framework that employs a differentiable rationale extractor that allows to back-propagate through the rationale extraction process. We analyze the impact of using human highlights during training by jointly training the task model and the rationale extractor. In our experiments, REFER yields significantly better results in terms of faithfulness, plausibility, and downstream task accuracy on both in-distribution and out-of-distribution data. On both e-SNLI and CoS-E, our best setting produces better results in terms of composite normalized relative gain than the previous baselines by 11% and 3%, respectively.

Reinforcement learning from human feedback plays a crucial role in aligning language models towards human preferences, traditionally represented through comparisons between pairs or sets of responses within a given context. While many studies have enhanced algorithmic techniques to optimize learning from such data, this work shifts focus to improving preference learning through a data-centric approach. Specifically, we propose enriching existing preference datasets with machine-generated rationales that explain the reasons behind choices. We develop a simple and principled framework to augment current preference learning methods with rationale information. Our comprehensive analysis highlights how rationales enhance learning efficiency. Extensive experiments reveal that rationale-enriched preference learning offers multiple advantages: it improves data efficiency, accelerates convergence to higher-performing models, and reduces verbosity bias and hallucination. Furthermore, this framework is versatile enough to integrate with various preference optimization algorithms. Overall, our findings highlight the potential of re-imagining data design for preference learning, demonstrating that even freely available machine-generated rationales can significantly boost performance across multiple dimensions. The code repository is available at https: //github.com/reds-lab/preference-learning-with-rationales

Solving algebraic word problems requires executing a series of arithmetic operations---a program---to obtain a final answer. However, since programs can be arbitrarily complicated, inducing them directly from question-answer pairs is a formidable challenge. To make this task more feasible, we solve these problems by generating answer rationales, sequences of natural language and human-readable mathematical expressions that derive the final answer through a series of small steps. Although rationales do not explicitly specify programs, they provide a scaffolding for their structure via intermediate milestones. To evaluate our approach, we have created a new 100,000-sample dataset of questions, answers and rationales. Experimental results show that indirect supervision of program learning via answer rationales is a promising strategy for inducing arithmetic programs.

As large language models (LLMs) grow larger and more sophisticated, assessing their "reasoning" capabilities in natural language grows more challenging. Recent question answering (QA) benchmarks that attempt to assess reasoning are often limited by a narrow scope of covered situations and subject matters. We introduce WikiWhy, a QA dataset built around a novel auxiliary task: explaining why an answer is true in natural language. WikiWhy contains over 9,000 "why" question-answer-rationale triples, grounded on Wikipedia facts across a diverse set of topics. Each rationale is a set of supporting statements connecting the question to the answer. WikiWhy serves as a benchmark for the reasoning capabilities of LLMs because it demands rigorous explicit rationales for each answer to demonstrate the acquisition of implicit commonsense knowledge, which is unlikely to be easily memorized. GPT-3 baselines achieve only 38.7% human-evaluated correctness in the end-to-end answer & explain condition, leaving significant room for future improvements.

We introduce a novel framework, LM-Guided CoT, that leverages a lightweight (i.e., <1B) language model (LM) for guiding a black-box large (i.e., >10B) LM in reasoning tasks. Specifically, the lightweight LM first generates a rationale for each input instance. The Frozen large LM is then prompted to predict a task output based on the rationale generated by the lightweight LM. Our approach is resource-efficient in the sense that it only requires training the lightweight LM. We optimize the model through 1) knowledge distillation and 2) reinforcement learning from rationale-oriented and task-oriented reward signals. We assess our method with multi-hop extractive question answering (QA) benchmarks, HotpotQA, and 2WikiMultiHopQA. Experimental results show that our approach outperforms all baselines regarding answer prediction accuracy. We also find that reinforcement learning helps the model to produce higher-quality rationales with improved QA performance.

Reinforcement learning (RL) has become the dominant paradigm for endowing language models with advanced reasoning capabilities. Despite the substantial empirical gains demonstrated by RL-based training methods like GRPO, a granular understanding of their advantages is still lacking. To address this gap, we introduce a fine-grained analytic framework to dissect the impact of RL on reasoning. Our framework specifically investigates key elements that have been hypothesized to benefit from RL training: (1) plan-following and execution, (2) problem decomposition, and (3) improved reasoning and knowledge utilization. Using this framework, we gain insights beyond mere accuracy. For instance, providing models with explicit step-by-step plans surprisingly degrades performance on the most challenging benchmarks, yet RL-tuned models exhibit greater robustness, experiencing markedly smaller performance drops than their base counterparts. This suggests that RL may not primarily enhance the execution of external plans but rather empower models to formulate and follow internal strategies better suited to their reasoning processes. Conversely, we observe that RL enhances the model's capacity to integrate provided knowledge into its reasoning process, leading to performance improvements across diverse tasks. We also study difficulty, showing improved training by developing new ways to exploit hard problems. Our findings lay a foundation for more principled training and evaluation of reasoning models.

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

Rationale discovery is defined as finding a subset of the input data that maximally supports the prediction of downstream tasks. In graph machine learning context, graph rationale is defined to locate the critical subgraph in the given graph topology, which fundamentally determines the prediction results. In contrast to the rationale subgraph, the remaining subgraph is named the environment subgraph. Graph rationalization can enhance the model performance as the mapping between the graph rationale and prediction label is viewed as invariant, by assumption. To ensure the discriminative power of the extracted rationale subgraphs, a key technique named "intervention" is applied. The core idea of intervention is that given any changing environment subgraphs, the semantics from the rationale subgraph is invariant, which guarantees the correct prediction result. However, most, if not all, of the existing rationalization works on graph data develop their intervention strategies on the graph level, which is coarse-grained. In this paper, we propose well-tailored intervention strategies on graph data. Our idea is driven by the development of Transformer models, whose self-attention module provides rich interactions between input nodes. Based on the self-attention module, our proposed invariant graph Transformer (IGT) can achieve fine-grained, more specifically, node-level and virtual node-level intervention. Our comprehensive experiments involve 7 real-world datasets, and the proposed IGT shows significant performance advantages compared to 13 baseline methods.

Sequence models are a critical component of modern NLP systems, but their predictions are difficult to explain. We consider model explanations though rationales, subsets of context that can explain individual model predictions. We find sequential rationales by solving a combinatorial optimization: the best rationale is the smallest subset of input tokens that would predict the same output as the full sequence. Enumerating all subsets is intractable, so we propose an efficient greedy algorithm to approximate this objective. The algorithm, which is called greedy rationalization, applies to any model. For this approach to be effective, the model should form compatible conditional distributions when making predictions on incomplete subsets of the context. This condition can be enforced with a short fine-tuning step. We study greedy rationalization on language modeling and machine translation. Compared to existing baselines, greedy rationalization is best at optimizing the combinatorial objective and provides the most faithful rationales. On a new dataset of annotated sequential rationales, greedy rationales are most similar to human rationales.

The rapid development of large language and vision models (LLVMs) has been driven by advances in visual instruction tuning. Recently, open-source LLVMs have curated high-quality visual instruction tuning datasets and utilized additional vision encoders or multiple computer vision models in order to narrow the performance gap with powerful closed-source LLVMs. These advancements are attributed to multifaceted information required for diverse capabilities, including fundamental image understanding, real-world knowledge about common-sense and non-object concepts (e.g., charts, diagrams, symbols, signs, and math problems), and step-by-step procedures for solving complex questions. Drawing from the multifaceted information, we present a new efficient LLVM, Mamba-based traversal of rationales (Meteor), which leverages multifaceted rationale to enhance understanding and answering capabilities. To embed lengthy rationales containing abundant information, we employ the Mamba architecture, capable of processing sequential data with linear time complexity. We introduce a new concept of traversal of rationale that facilitates efficient embedding of rationale. Subsequently, the backbone multimodal language model (MLM) is trained to generate answers with the aid of rationale. Through these steps, Meteor achieves significant improvements in vision language performances across multiple evaluation benchmarks requiring diverse capabilities, without scaling up the model size or employing additional vision encoders and computer vision models.

Large Language Models (LLMs) have demonstrated remarkable capabilities in performing complex tasks. Moreover, recent research has shown that incorporating human-annotated rationales (e.g., Chain-of-Thought prompting) during in-context learning can significantly enhance the performance of these models, particularly on tasks that require reasoning capabilities. However, incorporating such rationales poses challenges in terms of scalability as this requires a high degree of human involvement. In this work, we present a novel framework, Amplifying Model Performance by Leveraging In-Context Learning with Post Hoc Explanations (AMPLIFY), which addresses the aforementioned challenges by automating the process of rationale generation. To this end, we leverage post hoc explanation methods which output attribution scores (explanations) capturing the influence of each of the input features on model predictions. More specifically, we construct automated natural language rationales that embed insights from post hoc explanations to provide corrective signals to LLMs. Extensive experimentation with real-world datasets demonstrates that our framework, AMPLIFY, leads to prediction accuracy improvements of about 10-25% over a wide range of tasks, including those where prior approaches which rely on human-annotated rationales such as Chain-of-Thought prompting fall short. Our work makes one of the first attempts at highlighting the potential of post hoc explanations as valuable tools for enhancing the effectiveness of LLMs. Furthermore, we conduct additional empirical analyses and ablation studies to demonstrate the impact of each of the components of AMPLIFY, which, in turn, leads to critical insights for refining in-context learning.

Despite significant advancements in multimodal reasoning tasks, existing Large Vision-Language Models (LVLMs) are prone to producing visually ungrounded responses when interpreting associated images. In contrast, when humans embark on learning new knowledge, they often rely on a set of fundamental pre-study principles: reviewing outlines to grasp core concepts, summarizing key points to guide their focus and enhance understanding. However, such preparatory actions are notably absent in the current instruction tuning processes. This paper presents Re-Critic, an easily scalable rationale-augmented framework designed to incorporate fundamental rules and chain-of-thought (CoT) as a bridge to enhance reasoning abilities. Specifically, Re-Critic develops a visual rationale synthesizer that scalably augments raw instructions with rationale explanation. To probe more contextually grounded responses, Re-Critic employs an in-context self-critic mechanism to select response pairs for preference tuning. Experiments demonstrate that models fine-tuned with our rationale-augmented dataset yield gains that extend beyond hallucination-specific tasks to broader multimodal reasoning tasks.

Saliency post-hoc explainability methods are important tools for understanding increasingly complex NLP models. While these methods can reflect the model's reasoning, they may not align with human intuition, making the explanations not plausible. In this work, we present a methodology for incorporating rationales, which are text annotations explaining human decisions, into text classification models. This incorporation enhances the plausibility of post-hoc explanations while preserving their faithfulness. Our approach is agnostic to model architectures and explainability methods. We introduce the rationales during model training by augmenting the standard cross-entropy loss with a novel loss function inspired by contrastive learning. By leveraging a multi-objective optimization algorithm, we explore the trade-off between the two loss functions and generate a Pareto-optimal frontier of models that balance performance and plausibility. Through extensive experiments involving diverse models, datasets, and explainability methods, we demonstrate that our approach significantly enhances the quality of model explanations without causing substantial (sometimes negligible) degradation in the original model's performance.

We introduce a framework for generating Chain-of-Thought (CoT) rationales to enhance text-to-SQL model fine-tuning. These rationales consist of intermediate SQL statements and explanations, serving as incremental steps toward constructing the final SQL query. The process begins with manually annotating a small set of examples, which are then used to prompt a large language model in an iterative, dynamic few-shot knowledge distillation procedure from a teacher model. A rationalization model is subsequently trained on the validated decomposed queries, enabling extensive synthetic CoT annotations for text-to-SQL datasets. To evaluate the approach, we fine-tune small language models with and without these rationales on the BIRD dataset. Results indicate that step-by-step query generation improves execution accuracy, especially for moderately and highly complex queries, while also enhancing explainability.

Large language models (LMs) are capable of generating free-text rationales to aid question answering. However, prior work 1) suggests that useful self-rationalization is emergent only at significant scales (e.g., 175B parameter GPT-3); and 2) focuses largely on downstream performance, ignoring the semantics of the rationales themselves, e.g., are they faithful, true, and helpful for humans? In this work, we enable small-scale LMs (approx. 200x smaller than GPT-3) to generate rationales that not only improve downstream task performance, but are also more plausible, consistent, and diverse, assessed both by automatic and human evaluation. Our method, MaRio (Multi-rewArd RatIOnalization), is a multi-reward conditioned self-rationalization algorithm that optimizes multiple distinct properties like plausibility, diversity and consistency. Results on five difficult question-answering datasets StrategyQA, QuaRel, OpenBookQA, NumerSense and QASC show that not only does MaRio improve task accuracy, but it also improves the self-rationalization quality of small LMs across the aforementioned axes better than a supervised fine-tuning (SFT) baseline. Extensive human evaluations confirm that MaRio rationales are preferred vs. SFT rationales, as well as qualitative improvements in plausibility and consistency.

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

Visual reasoning abilities play a crucial role in understanding complex multimodal data, advancing both domain-specific applications and artificial general intelligence (AGI). Existing methods improve VLM reasoning via Chain-of-Thought (CoT) supervised fine-tuning, using meticulously annotated training data to enhance visual reasoning capabilities. However, this training paradigm may lead to overfitting and cognitive rigidity, restricting the model's ability to transfer visual reasoning skills across domains and limiting its real-world applicability. To address these limitations, we propose Reason-RFT, a novel reinforcement fine-tuning framework that significantly enhances generalization capabilities in visual reasoning tasks. Reason-RFT introduces a two-phase training framework for visual reasoning: (1) Supervised Fine-Tuning (SFT) with curated Chain-of-Thought (CoT) data activates the reasoning potential of Vision-Language Models (VLMs), followed by (2) Group Relative Policy Optimization (GRPO)-based reinforcement learning that generates multiple reasoning-response pairs, significantly enhancing generalization in visual reasoning tasks. To evaluate Reason-RFT's visual reasoning capabilities, we reconstructed a comprehensive dataset spanning visual counting, structure perception, and spatial transformation. Experimental results demonstrate Reasoning-RFT's three key advantages: (1) Performance Enhancement: achieving state-of-the-art results across multiple tasks, outperforming most mainstream open-source and proprietary models; (2) Generalization Superiority: consistently maintaining robust performance across diverse tasks and domains, outperforming alternative training paradigms; (3) Data Efficiency: excelling in few-shot learning scenarios while surpassing full-dataset SFT baselines. Project website: https://tanhuajie.github.io/ReasonRFT

Large language models (LLMs) have exhibited complex reasoning abilities by generating question rationales and demonstrated exceptional performance in natural language processing (NLP) tasks. However, these reasoning capabilities generally emerge in models with tens of billions of parameters, creating significant computational challenges for real-world deployment. Recent research has concentrated on improving open-source smaller models through knowledge distillation (KD) from commercial LLMs. Nevertheless, most of these studies rely solely on the responses from one single LLM as the gold rationale for training. In this paper, we introduce a novel Mistake-Aware Peer-Review Distillation (MAPD) approach: 1) Instead of merely obtaining gold rationales from teachers, our method asks teachers to identify and explain the student's mistakes, providing customized instruction learning data. 2) We design a simulated peer-review process between teacher LLMs, which selects only the generated rationales above the acceptance threshold. This reduces the chance of teachers guessing correctly with flawed rationale, improving instructional data quality. Comprehensive experiments and analysis on mathematical, commonsense, and logical reasoning tasks demonstrate the effectiveness of our method.

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.

The deployment of large language models (LLMs) faces considerable challenges concerning resource constraints and inference efficiency. Recent research has increasingly focused on smaller, task-specific models enhanced by distilling knowledge from LLMs. However, prior studies have often overlooked the diversity and quality of knowledge, especially the untapped potential of negative knowledge. Constructing effective negative knowledge remains severely understudied. In this paper, we introduce a novel framework called quality-guided contrastive rationale distillation aimed at enhancing reasoning capabilities through contrastive knowledge learning. For positive knowledge, we enrich its diversity through temperature sampling and employ self-consistency for further denoising and refinement. For negative knowledge, we propose an innovative self-adversarial approach that generates low-quality rationales by sampling previous iterations of smaller language models, embracing the idea that one can learn from one's own weaknesses. A contrastive loss is developed to distill both positive and negative knowledge into smaller language models, where an online-updating discriminator is integrated to assess qualities of rationales and assign them appropriate weights, optimizing the training process. Through extensive experiments across multiple reasoning tasks, we demonstrate that our method consistently outperforms existing distillation techniques, yielding higher-quality rationales.

Inspired by the success of DeepSeek-R1, we explore the potential of rule-based reinforcement learning (RL) in large reasoning models. To analyze reasoning dynamics, we use synthetic logic puzzles as training data due to their controllable complexity and straightforward answer verification. We make some key technical contributions that lead to effective and stable RL training: a system prompt that emphasizes the thinking and answering process, a stringent format reward function that penalizes outputs for taking shortcuts, and a straightforward training recipe that achieves stable convergence. Our 7B model develops advanced reasoning skills-such as reflection, verification, and summarization-that are absent from the logic corpus. Remarkably, after training on just 5K logic problems, it demonstrates generalization abilities to the challenging math benchmarks AIME and AMC.

Training reasoning language models (LMs) with reinforcement learning (RL) for one-hot correctness inherently relies on the LM being able to explore and solve its task with some chance at initialization. Furthermore, a key use case of reasoning LMs is to act as teachers for distilling new students and cold-starting future RL iterations rather than being deployed themselves. From these considerations, we introduce a new framework that avoids RL's exploration challenge by training a new class of Reinforcement-Learned Teachers (RLTs) focused on yielding the most effective downstream distillation. RLTs are prompted with both the question and solution to each problem, and tasked to simply "connect-the-dots" with detailed explanations tailored for their students. We train RLTs with dense rewards obtained by feeding each explanation to the student and testing its understanding of the problem's solution. In practice, the raw outputs of a 7B RLT provide higher final performance on competition and graduate-level tasks than existing distillation and cold-starting pipelines that collect and postprocess the reasoning traces of orders of magnitude larger LMs. Furthermore, RLTs maintain their effectiveness when training larger students and when applied zero-shot to out-of-distribution tasks, unlocking new levels of efficiency and re-usability for the RL reasoning framework.

We introduce AI rationalization, an approach for generating explanations of autonomous system behavior as if a human had performed the behavior. We describe a rationalization technique that uses neural machine translation to translate internal state-action representations of an autonomous agent into natural language. We evaluate our technique in the Frogger game environment, training an autonomous game playing agent to rationalize its action choices using natural language. A natural language training corpus is collected from human players thinking out loud as they play the game. We motivate the use of rationalization as an approach to explanation generation and show the results of two experiments evaluating the effectiveness of rationalization. Results of these evaluations show that neural machine translation is able to accurately generate rationalizations that describe agent behavior, and that rationalizations are more satisfying to humans than other alternative methods of explanation.

Large Language Model (LLM) based listwise ranking has shown superior performance in many passage ranking tasks. With the development of Large Reasoning Models, many studies have demonstrated that step-by-step reasoning during test-time helps improve listwise ranking performance. However, due to the scarcity of reasoning-intensive training data, existing rerankers perform poorly in many complex ranking scenarios and the ranking ability of reasoning-intensive rerankers remains largely underdeveloped. In this paper, we first propose an automated reasoning-intensive training data synthesis framework, which sources training queries and passages from diverse domains and applies DeepSeek-R1 to generate high-quality training labels. A self-consistency data filtering mechanism is designed to ensure the data quality. To empower the listwise reranker with strong reasoning ability, we further propose a two-stage post-training approach, which includes a cold-start supervised fine-tuning (SFT) stage for reasoning pattern learning and a reinforcement learning (RL) stage for further ranking ability enhancement. During the RL stage, based on the nature of listwise ranking, we design a multi-view ranking reward, which is more effective than a ranking metric-based reward. Extensive experiments demonstrate that our trained reasoning-intensive reranker ReasonRank outperforms existing baselines significantly and also achieves much lower latency than pointwise reranker Rank1. Through further experiments, our ReasonRank has achieved state-of-the-art (SOTA) performance 40.6 on the BRIGHT leaderboard\footnote{https://brightbenchmark.github.io/.} Our codes are available at https://github.com/8421BCD/ReasonRank.

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.

Although chain-of-thought reasoning and reinforcement learning (RL) have driven breakthroughs in NLP, their integration into generative vision models remains underexplored. We introduce ReasonGen-R1, a two-stage framework that first imbues an autoregressive image generator with explicit text-based "thinking" skills via supervised fine-tuning on a newly generated reasoning dataset of written rationales, and then refines its outputs using Group Relative Policy Optimization. To enable the model to reason through text before generating images, We automatically generate and release a corpus of model crafted rationales paired with visual prompts, enabling controlled planning of object layouts, styles, and scene compositions. Our GRPO algorithm uses reward signals from a pretrained vision language model to assess overall visual quality, optimizing the policy in each update. Evaluations on GenEval, DPG, and the T2I benchmark demonstrate that ReasonGen-R1 consistently outperforms strong baselines and prior state-of-the-art models. More: aka.ms/reasongen.

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.

We introduce ASTRO, the "Autoregressive Search-Taught Reasoner", a framework for training language models to reason like search algorithms, explicitly leveraging self-reflection, backtracking, and exploration in their outputs. Recently, training large language models (LLMs) via reinforcement learning (RL) has led to the advent of reasoning models with greatly enhanced reasoning capabilities. Open-source replications of reasoning models, while successful, build upon models that already exhibit strong reasoning capabilities along with search behavior observed even before RL. As a result, it is yet unclear how to boost the reasoning capabilities of other non-reasoner models including Llama 3. ASTRO teaches such models to internalize structured search behavior through a synthetic dataset derived from Monte Carlo Tree Search (MCTS) over mathematical problem-solving trajectories. By converting search traces into natural language chain-of-thoughts that capture both successes and recoveries from failure, ASTRO bootstraps models with a rich prior for exploration during RL. We finetune our models on these search-derived traces and further improve performance via RL with verifiable rewards. We apply ASTRO to the Llama 3 family of models and achieve absolute performance gains of 16.0% on MATH-500, 26.9% on AMC 2023, and 20.0% on AIME 2024, especially improving upon challenging problems that require iterative correction. Our results demonstrate that search-inspired training offers a principled way to instill robust reasoning capabilities into open LLMs.

Designing effective reasoning-capable LLMs typically requires training using Reinforcement Learning with Verifiable Rewards (RLVR) or distillation with carefully curated Long Chain of Thoughts (CoT), both of which depend heavily on extensive training data. This creates a major challenge when the amount of quality training data is scarce. We propose a sample-efficient, two-stage training strategy to develop reasoning LLMs under limited supervision. In the first stage, we "warm up" the model by distilling Long CoTs from a toy domain, namely, Knights \& Knaves (K\&K) logic puzzles to acquire general reasoning skills. In the second stage, we apply RLVR to the warmed-up model using a limited set of target-domain examples. Our experiments demonstrate that this two-phase approach offers several benefits: (i) the warmup phase alone facilitates generalized reasoning, leading to performance improvements across a range of tasks, including MATH, HumanEval^{+}, and MMLU-Pro. (ii) When both the base model and the warmed-up model are RLVR trained on the same small dataset (leq100 examples), the warmed-up model consistently outperforms the base model; (iii) Warming up before RLVR training allows a model to maintain cross-domain generalizability even after training on a specific domain; (iv) Introducing warmup in the pipeline improves not only accuracy but also overall sample efficiency during RLVR training. The results in this paper highlight the promise of warmup for building robust reasoning LLMs in data-scarce environments.

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

Continual relation extraction (CRE) aims to solve the problem of catastrophic forgetting when learning a sequence of newly emerging relations. Recent CRE studies have found that catastrophic forgetting arises from the model's lack of robustness against future analogous relations. To address the issue, we introduce rationale, i.e., the explanations of relation classification results generated by large language models (LLM), into CRE task. Specifically, we design the multi-task rationale tuning strategy to help the model learn current relations robustly. We also conduct contrastive rationale replay to further distinguish analogous relations. Experimental results on two standard benchmarks demonstrate that our method outperforms the state-of-the-art CRE 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.

Learning from mistakes is a fundamental feature of human intelligence. Previous work has shown that Large Language Models (LLMs) can also learn from incorrect answers when provided with a comprehensive rationale detailing why an answer is wrong or how to correct it. In this work, we examine whether LLMs can learn from mistakes in mathematical reasoning tasks when these explanations are not provided. We investigate if LLMs are able to implicitly infer such rationales simply from observing both incorrect and correct answers. Surprisingly, we find that LLMs perform better, on average, when rationales are eliminated from the context and incorrect answers are simply shown alongside correct ones. This approach also substantially outperforms chain-of-thought prompting in our evaluations. We show that these results are consistent across LLMs of different sizes and varying reasoning abilities. Further, we carry out an in-depth analysis, and show that prompting with both wrong and correct answers leads to greater performance and better generalisation than introducing additional, more diverse question-answer pairs into the context. Finally, we show that new rationales generated by models that have only observed incorrect and correct answers are scored equally as highly by humans as those produced with the aid of exemplar rationales. Our results demonstrate that LLMs are indeed capable of in-context implicit learning.

Incorporating natural language rationales in the prompt and In-Context Learning (ICL) has led to a significant improvement of Large Language Models (LLMs) performance. However, rationales currently require human-annotation or the use of auxiliary proxy models to target promising samples or generate high-quality rationales. In this work, we propose Self-AMPLIFY to generate automatically rationales from post hoc explanation methods applied to Small Language Models (SLMs) to improve their own performance. Self-AMPLIFY is a 3-step method that targets samples, generates rationales and builds a final prompt to leverage ICL. Self-AMPLIFY performance is evaluated on two SLMs and two datasets requiring reasoning abilities: these experiments show that Self-AMPLIFY achieves good results against competitors. Self-AMPLIFY is the first method to apply post hoc explanation methods to SLM to generate rationales to improve their own performance in a fully automated manner.

Chain-of-thought (CoT) has proven to improve the reasoning capability of large language models (LLMs). However, due to the complexity of multimodal scenarios and the difficulty in collecting high-quality CoT data, CoT reasoning in multimodal LLMs has been largely overlooked. To this end, we propose a simple yet effective self-training framework, R3V, which iteratively enhances the model's Vision-language Reasoning by Reflecting on CoT Rationales. Our framework consists of two interleaved parts: (1) iteratively bootstrapping positive and negative solutions for reasoning datasets, and (2) reflection on rationale for learning from mistakes. Specifically, we introduce the self-refine and self-select losses, enabling the model to refine flawed rationale and derive the correct answer by comparing rationale candidates. Experiments on a wide range of vision-language tasks show that R3V consistently improves multimodal LLM reasoning, achieving a relative improvement of 23 to 60 percent over GPT-distilled baselines. Additionally, our approach supports self-reflection on generated solutions, further boosting performance through test-time computation.

We introduce iterative reasoning through energy diffusion (IRED), a novel framework for learning to reason for a variety of tasks by formulating reasoning and decision-making problems with energy-based optimization. IRED learns energy functions to represent the constraints between input conditions and desired outputs. After training, IRED adapts the number of optimization steps during inference based on problem difficulty, enabling it to solve problems outside its training distribution -- such as more complex Sudoku puzzles, matrix completion with large value magnitudes, and pathfinding in larger graphs. Key to our method's success is two novel techniques: learning a sequence of annealed energy landscapes for easier inference and a combination of score function and energy landscape supervision for faster and more stable training. Our experiments show that IRED outperforms existing methods in continuous-space reasoning, discrete-space reasoning, and planning tasks, particularly in more challenging scenarios. Code and visualizations at https://energy-based-model.github.io/ired/

Reasoning requires going beyond pattern matching or memorization of solutions to identify and implement "algorithmic procedures" that can be used to deduce answers to hard problems. Doing so requires realizing the most relevant primitives, intermediate results, or shared procedures, and building upon them. While RL post-training on long chains of thought ultimately aims to uncover this kind of algorithmic behavior, most reasoning traces learned by large models fail to consistently capture or reuse procedures, instead drifting into verbose and degenerate exploration. To address more effective reasoning, we introduce reasoning abstractions: concise natural language descriptions of procedural and factual knowledge that guide the model toward learning successful reasoning. We train models to be capable of proposing multiple abstractions given a problem, followed by RL that incentivizes building a solution while using the information provided by these abstractions. This results in a two-player RL training paradigm, abbreviated as RLAD, that jointly trains an abstraction generator and a solution generator. This setup effectively enables structured exploration, decouples learning signals of abstraction proposal and solution generation, and improves generalization to harder problems. We also show that allocating more test-time compute to generating abstractions is more beneficial for performance than generating more solutions at large test budgets, illustrating the role of abstractions in guiding meaningful exploration.

This paper offers a new perspective to ease the challenge of domain generalization, which involves maintaining robust results even in unseen environments. Our design focuses on the decision-making process in the final classifier layer. Specifically, we propose treating the element-wise contributions to the final results as the rationale for making a decision and representing the rationale for each sample as a matrix. For a well-generalized model, we suggest the rationale matrices for samples belonging to the same category should be similar, indicating the model relies on domain-invariant clues to make decisions, thereby ensuring robust results. To implement this idea, we introduce a rationale invariance loss as a simple regularization technique, requiring only a few lines of code. Our experiments demonstrate that the proposed approach achieves competitive results across various datasets, despite its simplicity. Code is available at https://github.com/liangchen527/RIDG.

The ability of large language models to solve complex mathematical problems has progressed significantly, particularly for tasks requiring advanced reasoning. However, the scarcity of sufficiently challenging problems, particularly at the Olympiad level, hinders further advancements. In this work, we introduce PromptCoT, a novel approach for automatically generating high-quality Olympiad-level math problems. The proposed method synthesizes complex problems based on mathematical concepts and the rationale behind problem construction, emulating the thought processes of experienced problem designers. We provide a theoretical analysis demonstrating that an optimal rationale should maximize both the likelihood of rationale generation given the associated concepts and the likelihood of problem generation conditioned on both the rationale and the concepts. Our method is evaluated on standard benchmarks including GSM8K, MATH-500, and AIME2024, where it consistently outperforms existing problem generation methods. Furthermore, we demonstrate that PromptCoT exhibits superior data scalability, consistently maintaining high performance as the dataset size increases, outperforming the baselines. The implementation is available at https://github.com/zhaoxlpku/PromptCoT.

We introduce Open-Reasoner-Zero, the first open source implementation of large-scale reasoning-oriented RL training focusing on scalability, simplicity and accessibility. Through extensive experiments, we demonstrate that a minimalist approach, vanilla PPO with GAE (lambda=1, gamma=1) and straightforward rule-based rewards, without any KL regularization, is sufficient to scale up both response length and benchmark performance, similar to the phenomenon observed in DeepSeek-R1-Zero. Using the same base model as DeepSeek-R1-Zero-Qwen-32B, our implementation achieves superior performance on AIME2024, MATH500, and the GPQA Diamond benchmark while demonstrating remarkable efficiency -- requiring only a tenth of the training steps, compared to DeepSeek-R1-Zero pipeline. In the spirit of open source, we release our source code, parameter settings, training data, and model weights across various sizes.

State-of-the-art models in NLP are now predominantly based on deep neural networks that are opaque in terms of how they come to make predictions. This limitation has increased interest in designing more interpretable deep models for NLP that reveal the `reasoning' behind model outputs. But work in this direction has been conducted on different datasets and tasks with correspondingly unique aims and metrics; this makes it difficult to track progress. We propose the Evaluating Rationales And Simple English Reasoning (ERASER) benchmark to advance research on interpretable models in NLP. This benchmark comprises multiple datasets and tasks for which human annotations of "rationales" (supporting evidence) have been collected. We propose several metrics that aim to capture how well the rationales provided by models align with human rationales, and also how faithful these rationales are (i.e., the degree to which provided rationales influenced the corresponding predictions). Our hope is that releasing this benchmark facilitates progress on designing more interpretable NLP systems. The benchmark, code, and documentation are available at https://www.eraserbenchmark.com/

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

Large language models (LLMs) excel at mathematical reasoning and logical problem-solving. The current popular training paradigms primarily use supervised fine-tuning (SFT) and reinforcement learning (RL) to enhance the models' reasoning abilities. However, when using SFT or RL alone, there are respective challenges: SFT may suffer from overfitting, while RL is prone to mode collapse. The state-of-the-art methods have proposed hybrid training schemes. However, static switching faces challenges such as poor generalization across different tasks and high dependence on data quality. In response to these challenges, inspired by the curriculum learning-quiz mechanism in human reasoning cultivation, We propose SASR, a step-wise adaptive hybrid training framework that theoretically unifies SFT and RL and dynamically balances the two throughout optimization. SASR uses SFT for initial warm-up to establish basic reasoning skills, and then uses an adaptive dynamic adjustment algorithm based on gradient norm and divergence relative to the original distribution to seamlessly integrate SFT with the online RL method GRPO. By monitoring the training status of LLMs and adjusting the training process in sequence, SASR ensures a smooth transition between training schemes, maintaining core reasoning abilities while exploring different paths. Experimental results demonstrate that SASR outperforms SFT, RL, and static hybrid training methods.

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.

Interpretability or explainability is an emerging research field in NLP. From a user-centric point of view, the goal is to build models that provide proper justification for their decisions, similar to those of humans, by requiring the models to satisfy additional constraints. To this end, we introduce a new application on legal text where, contrary to mainstream literature targeting word-level rationales, we conceive rationales as selected paragraphs in multi-paragraph structured court cases. We also release a new dataset comprising European Court of Human Rights cases, including annotations for paragraph-level rationales. We use this dataset to study the effect of already proposed rationale constraints, i.e., sparsity, continuity, and comprehensiveness, formulated as regularizers. Our findings indicate that some of these constraints are not beneficial in paragraph-level rationale extraction, while others need re-formulation to better handle the multi-label nature of the task we consider. We also introduce a new constraint, singularity, which further improves the quality of rationales, even compared with noisy rationale supervision. Experimental results indicate that the newly introduced task is very challenging and there is a large scope for further research.

Reinforcement learning from human feedback (RLHF) has become a powerful post-training paradigm for aligning large language models with human preferences. A core challenge in RLHF is constructing accurate reward signals, where the conventional Bradley-Terry reward models (BT RMs) often suffer from sensitivity to data size and coverage, as well as vulnerability to reward hacking. Generative reward models (GenRMs) offer a more robust alternative by generating chain-of-thought (CoT) rationales followed by a final reward. However, existing GenRMs rely on shallow, vertically scaled reasoning, limiting their capacity to handle nuanced or complex (e.g., reasoning-intensive) tasks. Moreover, their pairwise preference outputs are incompatible with standard RLHF algorithms that require pointwise reward signals. In this work, we introduce Think-RM, a training framework that enables long-horizon reasoning in GenRMs by modeling an internal thinking process. Rather than producing structured, externally provided rationales, Think-RM generates flexible, self-guided reasoning traces that support advanced capabilities such as self-reflection, hypothetical reasoning, and divergent reasoning. To elicit these reasoning abilities, we first warm-up the models by supervised fine-tuning (SFT) over long CoT data. We then further improve the model's long-horizon abilities by rule-based reinforcement learning (RL). In addition, we propose a novel pairwise RLHF pipeline that directly optimizes policies using pairwise preference rewards, eliminating the need for pointwise reward conversion and enabling more effective use of Think-RM outputs. Experiments show that Think-RM achieves state-of-the-art results on RM-Bench, outperforming both BT RM and vertically scaled GenRM by 8%. When combined with our pairwise RLHF pipeline, it demonstrates superior end-policy performance compared to traditional approaches.

Large language models (LLMs) have shown increasing in-context learning capabilities through scaling up model and data size. Despite this progress, LLMs are still unable to solve algorithmic reasoning problems. While providing a rationale with the final answer has led to further improvements in multi-step reasoning problems, Anil et al. 2022 showed that even simple algorithmic reasoning tasks such as parity are far from solved. In this work, we identify and study four key stages for successfully teaching algorithmic reasoning to LLMs: (1) formulating algorithms as skills, (2) teaching multiple skills simultaneously (skill accumulation), (3) teaching how to combine skills (skill composition) and (4) teaching how to use skills as tools. We show that it is possible to teach algorithmic reasoning to LLMs via in-context learning, which we refer to as algorithmic prompting. We evaluate our approach on a variety of arithmetic and quantitative reasoning tasks, and demonstrate significant boosts in performance over existing prompting techniques. In particular, for long parity, addition, multiplication and subtraction, we achieve an error reduction of approximately 10x, 9x, 5x and 2x respectively compared to the best available baselines.

With the release of R1, a publicly available large reasoning model (LRM), researchers commonly train new LRMs by training language models on R1's long chain-of-thought (CoT) inferences. While prior works show that LRMs' capabilities can be reproduced through direct distillation, the continued reliance on the existing models (e.g., R1) remains a critical limitation in advancing the field. As a first step toward independent LRM development, this paper explores the possibility of constructing a long CoT dataset with LLMs that are not trained for inference-time scaling. To this end, we present the Long CoT Collection, a dataset of 100K CoT rationales annotated using existing short CoT LLMs. We develop a pipeline that induces o1's novel reasoning strategies into short CoT LLMs, enabling them to think longer and introducing controllability over the thought budget to better manage the overthinking problem. Our extensive analyses validate that our dataset achieves quality comparable to--or slightly below--R1. Furthermore, our experiments demonstrate that training on our dataset not only strengthens general reasoning skills, but also provides a strong foundation for reinforcement learning--models initialized on our data achieve 2-3x larger gains with RLVR.

Training robust and generalizable reward models for human visual preferences is essential for aligning text-to-image and text-to-video generative models with human intent. However, current reward models often fail to generalize, and supervised fine-tuning leads to memorization, demanding complex annotation pipelines. While reinforcement learning (RL), specifically Group Relative Policy Optimization (GRPO), improves generalization, we uncover a key failure mode: a significant drop in reasoning accuracy occurs when a model's reasoning trace contradicts that of an independent, frozen vision-language model ("listener") evaluating the same output. To address this, we introduce a listener-augmented GRPO framework. Here, the listener re-evaluates the reasoner's chain-of-thought to provide a dense, calibrated confidence score, shaping the RL reward signal. This encourages the reasoner not only to answer correctly, but to produce explanations that are persuasive to an independent model. Our listener-shaped reward scheme achieves best accuracy on the ImageReward benchmark (67.4%), significantly improves out-of-distribution (OOD) performance on a large-scale human preference dataset (1.2M votes, up to +6% over naive reasoner), and reduces reasoning contradictions compared to strong GRPO and SFT baselines. These results demonstrate that listener-based rewards provide a scalable, data-efficient path to aligning vision-language models with nuanced human preferences. We will release our reasoning model here: https://huggingface.co/alexgambashidze/qwen2.5vl_image_preference_reasoner.

Enhancing the mathematical reasoning of Large Language Models (LLMs) is a pivotal challenge in advancing AI capabilities. While Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL) are the dominant training paradigms, a systematic methodology for combining them to maximize both accuracy and efficiency remains largely unexplored. This paper introduces a practical and effective training recipe that strategically integrates extended SFT with RL from online inference (GRPO). We posit that these methods play complementary, not competing, roles: a prolonged SFT phase first pushes the model's accuracy to its limits, after which a GRPO phase dramatically improves token efficiency while preserving this peak performance. Our experiments reveal that extending SFT for as many as 10 epochs is crucial for performance breakthroughs, and that the primary role of GRPO in this framework is to optimize solution length. The efficacy of our recipe is rigorously validated through top-tier performance on challenging benchmarks, including a high rank among over 2,200 teams in the strictly leak-free AI Mathematical Olympiad (AIMO). This work provides the community with a battle-tested blueprint for developing state-of-the-art mathematical reasoners that are both exceptionally accurate and practically efficient. To ensure full reproducibility and empower future research, we will open-source our entire framework, including all code, model checkpoints, and training configurations at https://github.com/analokmaus/kaggle-aimo2-fast-math-r1.

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

In this report, we present the third technical report on the development of slow-thinking models as part of the STILL project. As the technical pathway becomes clearer, scaling RL training has become a central technique for implementing such reasoning models. We systematically experiment with and document the effects of various factors influencing RL training, conducting experiments on both base models and fine-tuned models. Specifically, we demonstrate that our RL training approach consistently improves the Qwen2.5-32B base models, enhancing both response length and test accuracy. Furthermore, we show that even when a model like DeepSeek-R1-Distill-Qwen-1.5B has already achieved a high performance level, it can be further refined through RL training, reaching an accuracy of 39.33% on AIME 2024. Beyond RL training, we also explore the use of tool manipulation, finding that it significantly boosts the reasoning performance of large reasoning models. This approach achieves a remarkable accuracy of 86.67% with greedy search on AIME 2024, underscoring its effectiveness in enhancing model capabilities. We release our resources at the STILL project website: https://github.com/RUCAIBox/Slow_Thinking_with_LLMs.

Reinforcement learning (RL) has emerged as a promising approach to improve large language model (LLM) reasoning, yet most open efforts focus narrowly on math and code, limiting our understanding of its broader applicability to general reasoning. A key challenge lies in the lack of reliable, scalable RL reward signals across diverse reasoning domains. We introduce Guru, a curated RL reasoning corpus of 92K verifiable examples spanning six reasoning domains--Math, Code, Science, Logic, Simulation, and Tabular--each built through domain-specific reward design, deduplication, and filtering to ensure reliability and effectiveness for RL training. Based on Guru, we systematically revisit established findings in RL for LLM reasoning and observe significant variation across domains. For example, while prior work suggests that RL primarily elicits existing knowledge from pretrained models, our results reveal a more nuanced pattern: domains frequently seen during pretraining (Math, Code, Science) easily benefit from cross-domain RL training, while domains with limited pretraining exposure (Logic, Simulation, and Tabular) require in-domain training to achieve meaningful performance gains, suggesting that RL is likely to facilitate genuine skill acquisition. Finally, we present Guru-7B and Guru-32B, two models that achieve state-of-the-art performance among open models RL-trained with publicly available data, outperforming best baselines by 7.9% and 6.7% on our 17-task evaluation suite across six reasoning domains. We also show that our models effectively improve the Pass@k performance of their base models, particularly on complex tasks less likely to appear in pretraining data. We release data, models, training and evaluation code to facilitate general-purpose reasoning at: https://github.com/LLM360/Reasoning360

Reinforcement learning with verifiable rewards (RLVR) has shown promise in enhancing the reasoning capabilities of large language models by learning directly from outcome-based rewards. Recent RLVR works that operate under the zero setting avoid supervision in labeling the reasoning process, but still depend on manually curated collections of questions and answers for training. The scarcity of high-quality, human-produced examples raises concerns about the long-term scalability of relying on human supervision, a challenge already evident in the domain of language model pretraining. Furthermore, in a hypothetical future where AI surpasses human intelligence, tasks provided by humans may offer limited learning potential for a superintelligent system. To address these concerns, we propose a new RLVR paradigm called Absolute Zero, in which a single model learns to propose tasks that maximize its own learning progress and improves reasoning by solving them, without relying on any external data. Under this paradigm, we introduce the Absolute Zero Reasoner (AZR), a system that self-evolves its training curriculum and reasoning ability by using a code executor to both validate proposed code reasoning tasks and verify answers, serving as an unified source of verifiable reward to guide open-ended yet grounded learning. Despite being trained entirely without external data, AZR achieves overall SOTA performance on coding and mathematical reasoning tasks, outperforming existing zero-setting models that rely on tens of thousands of in-domain human-curated examples. Furthermore, we demonstrate that AZR can be effectively applied across different model scales and is compatible with various model classes.

The self-rationalising capabilities of large language models (LLMs) have been explored in restricted settings, using task/specific data sets. However, current LLMs do not (only) rely on specifically annotated data; nonetheless, they frequently explain their outputs. The properties of the generated explanations are influenced by the pre-training corpus and by the target data used for instruction fine-tuning. As the pre-training corpus includes a large amount of human-written explanations "in the wild", we hypothesise that LLMs adopt common properties of human explanations. By analysing the outputs for a multi-domain instruction fine-tuning data set, we find that generated explanations show selectivity and contain illustrative elements, but less frequently are subjective or misleading. We discuss reasons and consequences of the properties' presence or absence. In particular, we outline positive and negative implications depending on the goals and user groups of the self-rationalising system.

Reinforcement learning (RL) has proven effective in incentivizing the reasoning abilities of large language models (LLMs), but suffers from severe efficiency challenges due to its trial-and-error nature. While the common practice employs supervised fine-tuning (SFT) as a warm-up stage for RL, this decoupled two-stage approach limits interaction between SFT and RL, thereby constraining overall effectiveness. This study introduces a novel method for learning reasoning models that employs bilevel optimization to facilitate better cooperation between these training paradigms. By conditioning the SFT objective on the optimal RL policy, our approach enables SFT to meta-learn how to guide RL's optimization process. During training, the lower level performs RL updates while simultaneously receiving SFT supervision, and the upper level explicitly maximizes the cooperative gain-the performance advantage of joint SFT-RL training over RL alone. Empirical evaluations on five reasoning benchmarks demonstrate that our method consistently outperforms baselines and achieves a better balance between effectiveness and efficiency.

We propose CURE, a novel reinforcement learning framework with a dedicated reward design that co-evolves coding and unit test generation capabilities based on their interaction outcomes, without any ground-truth code as supervision. This approach enables flexible and scalable training and allows the unit tester to learn directly from the coder's mistakes. Our derived ReasonFlux-Coder-7B and 14B models improve code generation accuracy by 5.3% and Best-of-N accuracy by 9.0% after optimization on Qwen2.5-Instruct models, outperforming similarly sized Qwen-Coder, DeepSeek-Coder, and Seed-Coder. They naturally extend to downstream tasks such as test-time scaling and agentic coding-achieving a 8.1% improvement over the base model. For the long-CoT model, our ReasonFlux-Coder-4B consistently outperforms Qwen3-4B while achieving 64.8% inference efficiency in unit test generation. Notably, we also find that our model can serve as an effective reward model for reinforcement learning on base models. Project: https://github.com/Gen-Verse/CURE

Directly training Large Language Models (LLMs) for Multi-Agent Systems (MAS) remains challenging due to intricate reward modeling, dynamic agent interactions, and demanding generalization requirements. This paper explores whether post-training techniques, specifically Supervised Fine-Tuning (SFT) and Reinforcement Learning with Verifiable Rewards (RLVR), can effectively generalize to multi-agent scenarios. We use economic reasoning as a testbed, leveraging its strong foundations in mathematics and game theory, its demand for structured analytical reasoning, and its relevance to real-world applications such as market design, resource allocation, and policy analysis. We introduce Recon (Reasoning like an ECONomist), a 7B-parameter open-source LLM post-trained on a hand-curated dataset of 2,100 high-quality economic reasoning problems. Comprehensive evaluation on economic reasoning benchmarks and multi-agent games reveals clear improvements in structured reasoning and economic rationality. These results underscore the promise of domain-aligned post-training for enhancing reasoning and agent alignment, shedding light on the roles of SFT and RL in shaping model behavior. Code is available at https://github.com/MasterZhou1/Recon .

Recent advancements in the field of large language models, particularly through the Chain of Thought (CoT) approach, have demonstrated significant improvements in solving complex problems. However, existing models either tend to sacrifice detailed reasoning for brevity due to user preferences, or require extensive and expensive training data to learn complicated reasoning ability, limiting their potential in solving complex tasks. To bridge this gap, following the concept of scaling test-time, we propose a simple method by encouraging models to adopt a more patient reasoning style without the need of introducing new knowledge or skills. To employ a preference optimization approach, we generate detailed reasoning processes as positive examples and simple answers as negative examples, thereby training the model to favor thoroughness in its responses. Our results demonstrate a performance increase of up to 6.7% on GSM8k with training just on a lightweight dataset.

The rapid advancement of large language models (LLMs) has significantly enhanced their reasoning abilities, enabling increasingly complex tasks. However, these capabilities often diminish in smaller, more computationally efficient models like GPT-2. Recent research shows that reasoning distillation can help small models acquire reasoning capabilities, but most existing methods focus primarily on improving teacher-generated reasoning paths. Our observations reveal that small models can generate high-quality reasoning paths during sampling, even without chain-of-thought prompting, though these paths are often latent due to their low probability under standard decoding strategies. To address this, we propose Self-Enhanced Reasoning Training (SERT), which activates and leverages latent reasoning capabilities in small models through self-training on filtered, self-generated reasoning paths under zero-shot conditions. Experiments using OpenAI's GPT-3.5 as the teacher model and GPT-2 models as the student models demonstrate that SERT enhances the reasoning abilities of small models, improving their performance in reasoning distillation.

Reward modeling is essential for aligning large language models (LLMs) with human preferences, especially through reinforcement learning from human feedback (RLHF). To provide accurate reward signals, a reward model (RM) should stimulate deep thinking and conduct interpretable reasoning before assigning a score or a judgment. However, existing RMs either produce opaque scalar scores or directly generate the prediction of a preferred answer, making them struggle to integrate natural language critiques, thus lacking interpretability. Inspired by recent advances of long chain-of-thought (CoT) on reasoning-intensive tasks, we hypothesize and validate that integrating reasoning capabilities into reward modeling significantly enhances RM's interpretability and performance. In this work, we introduce a new class of generative reward models -- Reasoning Reward Models (ReasRMs) -- which formulate reward modeling as a reasoning task. We propose a reasoning-oriented training pipeline and train a family of ReasRMs, RM-R1. The training consists of two key stages: (1) distillation of high-quality reasoning chains and (2) reinforcement learning with verifiable rewards. RM-R1 improves LLM rollouts by self-generating reasoning traces or chat-specific rubrics and evaluating candidate responses against them. Empirically, our models achieve state-of-the-art or near state-of-the-art performance of generative RMs across multiple comprehensive reward model benchmarks, outperforming much larger open-weight models (e.g., Llama3.1-405B) and proprietary ones (e.g., GPT-4o) by up to 13.8%. Beyond final performance, we perform thorough empirical analysis to understand the key ingredients of successful ReasRM training. To facilitate future research, we release six ReasRM models along with code and data at https://github.com/RM-R1-UIUC/RM-R1.

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.

Recent breakthroughs in large language models (LLMs) have effectively improved their reasoning abilities, particularly on mathematical and logical problems that have verifiable answers, through techniques such as supervised finetuning (SFT) and reinforcement learning (RL). Prior research indicates that RL effectively internalizes search strategies, enabling long chain-of-thought (CoT) reasoning, with backtracking emerging naturally as a learned capability. However, the precise benefits of backtracking, specifically, how significantly it contributes to reasoning improvements and the optimal extent of its use, remain poorly understood. In this work, we systematically investigate the dynamics between SFT and RL on eight reasoning tasks: Countdown, Sudoku, Arc 1D, Geometry, Color Cube Rotation, List Functions, Zebra Puzzles, and Self Reference. Our findings highlight that short CoT sequences used in SFT as a warm-up do have moderate contribution to RL training, compared with cold-start RL; however such contribution diminishes when tasks become increasingly difficult. Motivated by this observation, we construct synthetic datasets varying systematically in the number of backtracking steps and conduct controlled experiments to isolate the influence of either the correctness (content) or the structure (i.e., backtrack frequency). We find that (1) longer CoT with backtracks generally induce better and more stable RL training, (2) more challenging problems with larger search space tend to need higher numbers of backtracks during the SFT stage. Additionally, we demonstrate through experiments on distilled data that RL training is largely unaffected by the correctness of long CoT sequences, suggesting that RL prioritizes structural patterns over content correctness. Collectively, our results offer practical insights into designing optimal training strategies to effectively scale reasoning in LLMs.

Recent advances in deep thinking models have demonstrated remarkable reasoning capabilities on mathematical and coding tasks. However, their effectiveness in embodied domains which require continuous interaction with environments through image action interleaved trajectories remains largely -unexplored. We present Embodied Reasoner, a model that extends o1 style reasoning to interactive embodied search tasks. Unlike mathematical reasoning that relies primarily on logical deduction, embodied scenarios demand spatial understanding, temporal reasoning, and ongoing self-reflection based on interaction history. To address these challenges, we synthesize 9.3k coherent Observation-Thought-Action trajectories containing 64k interactive images and 90k diverse thinking processes (analysis, spatial reasoning, reflection, planning, and verification). We develop a three-stage training pipeline that progressively enhances the model's capabilities through imitation learning, self-exploration via rejection sampling, and self-correction through reflection tuning. The evaluation shows that our model significantly outperforms those advanced visual reasoning models, e.g., it exceeds OpenAI o1, o3-mini, and Claude-3.7 by +9\%, 24\%, and +13\%. Analysis reveals our model exhibits fewer repeated searches and logical inconsistencies, with particular advantages in complex long-horizon tasks. Real-world environments also show our superiority while exhibiting fewer repeated searches and logical inconsistency cases.

Large language models (LLMs) have demonstrated impressive performance on reasoning-intensive tasks, but enhancing their reasoning abilities typically relies on either reinforcement learning (RL) with verifiable signals or supervised fine-tuning (SFT) with high-quality long chain-of-thought (CoT) demonstrations, both of which are expensive. In this paper, we study a novel problem of incentivizing the reasoning capacity of LLMs without expensive high-quality demonstrations and reinforcement learning. We investigate whether the reasoning capabilities of LLMs can be effectively incentivized via supervision from significantly weaker models. We further analyze when and why such weak supervision succeeds in eliciting reasoning abilities in stronger models. Our findings show that supervision from significantly weaker reasoners can substantially improve student reasoning performance, recovering close to 94% of the gains of expensive RL at a fraction of the cost. Experiments across diverse benchmarks and model architectures demonstrate that weak reasoners can effectively incentivize reasoning in stronger student models, consistently improving performance across a wide range of reasoning tasks. Our results suggest that this simple weak-to-strong paradigm is a promising and generalizable alternative to costly methods for incentivizing strong reasoning capabilities at inference-time in LLMs. The code is publicly available at https://github.com/yuanyige/w2sr.

Rationality is the quality of being guided by reason, characterized by decision-making that aligns with evidence and logical principles. It plays a crucial role in reliable problem-solving by ensuring well-grounded and consistent solutions. While large language models (LLMs) have made significant progress in generating human-like text, they still exhibit limitations such as bounded knowledge space and inconsistent outputs. In response, recent efforts have shifted toward developing multimodal and multi-agent systems, as well as integrating modules like external tools, programming codes, symbolic reasoners, utility function, and conformal risk controls rather than relying solely on a single LLM for decision-making. This paper surveys the state-of-the-art advancements in language and multimodal agents, evaluates how they contribute to make intelligent agents more rational, and identifies open challenges and future research directions. We maintain an open repository at https://github.com/bowen-upenn/Agent_Rationality.

Large language models (LLMs) have demonstrated remarkable performance across a wide range of tasks. Advances in prompt engineering and fine-tuning techniques have further enhanced their ability to address complex reasoning challenges. However, these advanced capabilities are often exclusive to models exceeding 100 billion parameters. Although Chain-of-Thought (CoT) fine-tuning methods have been explored for smaller models (under 10 billion parameters), they typically depend on extensive CoT training data, which can introduce inconsistencies and limit effectiveness in low-data settings. To overcome these limitations, this paper introduce a new reasoning strategy Solution Guidance (SG) and a plug-and-play training paradigm Solution-Guidance Fine-Tuning (SGFT) for enhancing the reasoning capabilities of small language models. SG focuses on problem understanding and decomposition at the semantic and logical levels, rather than specific computations, which can effectively improve the SLMs' generalization and reasoning abilities. With only a small amount of SG training data, SGFT can fine-tune a SLM to produce accurate problem-solving guidances, which can then be flexibly fed to any SLM as prompts, enabling it to generate correct answers directly. Experimental results demonstrate that our method significantly improves the performance of SLMs on various reasoning tasks, enhancing both their practicality and efficiency within resource-constrained environments.

Traditional language model-based theorem proving assumes that by training on a sufficient amount of formal proof data, a model will learn to prove theorems. Our key observation is that a wealth of informal information that is not present in formal proofs can be useful for learning to prove theorems. For instance, humans think through steps of a proof, but this thought process is not visible in the resulting code. We present Lean-STaR, a framework for training language models to produce informal thoughts prior to each step of a proof, thereby boosting the model's theorem-proving capabilities. Lean-STaR uses retrospective ground-truth tactics to generate synthetic thoughts for training the language model. At inference time, the trained model directly generates the thoughts prior to the prediction of the tactics in each proof step. Building on the self-taught reasoner framework, we then apply expert iteration to further fine-tune the model on the correct proofs it samples and verifies using the Lean solver. Lean-STaR achieves state-of-the-art results on the miniF2F-test benchmark within the Lean theorem proving environment, significantly outperforming base models (43.4% rightarrow 46.3%, Pass@64). We also analyze the impact of the augmented thoughts on various aspects of the theorem proving process, providing insights into their effectiveness.

We introduce Ego-R1, a novel framework for reasoning over ultra-long (i.e., in days and weeks) egocentric videos, which leverages a structured Chain-of-Tool-Thought (CoTT) process, orchestrated by an Ego-R1 Agent trained via reinforcement learning (RL). Inspired by human problem-solving strategies, CoTT decomposes complex reasoning into modular steps, with the RL agent invoking specific tools, one per step, to iteratively and collaboratively answer sub-questions tackling such tasks as temporal retrieval and multi-modal understanding. We design a two-stage training paradigm involving supervised finetuning (SFT) of a pretrained language model using CoTT data and RL to enable our agent to dynamically propose step-by-step tools for long-range reasoning. To facilitate training, we construct a dataset called Ego-R1 Data, which consists of Ego-CoTT-25K for SFT and Ego-QA-4.4K for RL. Furthermore, our Ego-R1 agent is evaluated on a newly curated week-long video QA benchmark, Ego-R1 Bench, which contains human-verified QA pairs from hybrid sources. Extensive results demonstrate that the dynamic, tool-augmented chain-of-thought reasoning by our Ego-R1 Agent can effectively tackle the unique challenges of understanding ultra-long egocentric videos, significantly extending the time coverage from few hours to a week.

Advancements in reasoning for large language models (LLMs) have lead to significant performance improvements for LLMs in various fields such as mathematics and programming. However, research applying these advances to the financial domain, where considerable domain-specific knowledge is necessary to complete tasks, remains limited. To address this gap, we introduce FEVO (Financial Evolution), a multi-stage enhancement framework developed to enhance LLM performance in the financial domain. FEVO systemically enhances LLM performance by using continued pre-training (CPT) to expand financial domain knowledge, supervised fine-tuning (SFT) to instill structured, elaborate reasoning patterns, and reinforcement learning (RL) to further integrate the expanded financial domain knowledge with the learned structured reasoning. To ensure effective and efficient training, we leverage frontier reasoning models and rule-based filtering to curate FEVO-Train, high-quality datasets specifically designed for the different post-training phases. Using our framework, we train the FEVO series of models - C32B, S32B, R32B - from Qwen2.5-32B and evaluate them on seven benchmarks to assess financial and general capabilities, with results showing that FEVO-R32B achieves state-of-the-art performance on five financial benchmarks against much larger models as well as specialist models. More significantly, FEVO-R32B demonstrates markedly better performance than FEVO-R32B-0 (trained from Qwen2.5-32B-Instruct using only RL), thus validating the effectiveness of financial domain knowledge expansion and structured, logical reasoning distillation

The remarkable success in neural networks provokes the selective rationalization. It explains the prediction results by identifying a small subset of the inputs sufficient to support them. Since existing methods still suffer from adopting the shortcuts in data to compose rationales and limited large-scale annotated rationales by human, in this paper, we propose a Shortcuts-fused Selective Rationalization (SSR) method, which boosts the rationalization by discovering and exploiting potential shortcuts. Specifically, SSR first designs a shortcuts discovery approach to detect several potential shortcuts. Then, by introducing the identified shortcuts, we propose two strategies to mitigate the problem of utilizing shortcuts to compose rationales. Finally, we develop two data augmentations methods to close the gap in the number of annotated rationales. Extensive experimental results on real-world datasets clearly validate the effectiveness of our proposed method.

The integration of slow-thinking mechanisms into large language models (LLMs) offers a promising way toward achieving Level 2 AGI Reasoners, as exemplified by systems like OpenAI's o1. However, several significant challenges remain, including inefficient overthinking and an overreliance on auxiliary reward models. We point out that these limitations stem from LLMs' inability to internalize the search process, a key component of effective reasoning. A critical step toward addressing this issue is enabling LLMs to autonomously determine when and where to backtrack, a fundamental operation in traditional search algorithms. To this end, we propose a self-backtracking mechanism that equips LLMs with the ability to backtrack during both training and inference. This mechanism not only enhances reasoning ability but also efficiency by transforming slow-thinking processes into fast-thinking through self-improvement. Empirical evaluations demonstrate that our proposal significantly enhances the reasoning capabilities of LLMs, achieving a performance gain of over 40 percent compared to the optimal-path supervised fine-tuning method. We believe this study introduces a novel and promising pathway for developing more advanced and robust Reasoners.

Large language models have been shown to suffer from reasoning inconsistency issues. That is, they fail more in situations unfamiliar to the training data, even though exact or very similar reasoning paths exist in more common cases that they can successfully solve. Such observations motivate us to propose methods that encourage models to understand the high-level and abstract reasoning processes during training instead of only the final answer. This way, models can transfer the exact solution to similar cases, regardless of their relevance to the pre-training data distribution. In this work, we propose SAL, a self-supervised analogical learning framework. SAL mimics the human analogy process and trains models to explicitly transfer high-quality symbolic solutions from cases that they know how to solve to other rare cases in which they tend to fail more. We show that the resulting models after SAL learning outperform base language models on a wide range of reasoning benchmarks, such as StrategyQA, GSM8K, and HotpotQA, by 2% to 20%. At the same time, we show that our model is more generalizable and controllable through analytical studies.

We present Gazal-R1, a 32-billion-parameter language model that achieves state-of-the-art performance in medical reasoning while providing transparent, step-by-step explanations for clinical decision-making. Built upon Qwen3 32B, our model demonstrates that strategic training can enable mid-sized models to outperform significantly larger counterparts in specialized domains. We developed a novel two-stage training pipeline: first, supervised fine-tuning on a carefully curated dataset of 107,033 synthetic medical reasoning examples that teaches structured clinical thinking, enhanced by advanced parameter-efficient techniques including Weight-Decomposed Low-Rank Adaptation (DoRA) and Rank-Stabilized LoRA (rsLoRA); second, reinforcement learning using Group Relative Policy Optimization (GRPO) with a sophisticated multi-component reward system that refines accuracy, format adherence, and reasoning quality. Gazal-R1 achieves exceptional performance across medical benchmarks, scoring 87.1% on MedQA, 81.6% on MMLU Pro (Medical), and 79.6% on PubMedQA, surpassing models up to 12x larger. Beyond its strong empirical results, this work provides detailed insights into the challenges of training reasoning-capable models in specialized domains, including issues with reward hacking, training instability, and the fundamental tension between factual recall and detailed reasoning. Our methodology offers a reproducible framework for developing high-capability, domain-specific language models that balance performance, efficiency, and explainability.

As models increasingly leverage multi-step reasoning strategies to solve complex problems, supervising the logical validity of these intermediate steps has become a critical research challenge. Process reward models address this by providing step-by-step feedback, but current approaches have two major drawbacks: they typically function as classifiers without providing explanations, and their reliance on supervised fine-tuning with static datasets limits generalization. Inspired by recent advances, we reframe stepwise reward modeling from a classification task to a reasoning task itself. We thus propose a generative judge that reasons about the policy model's reasoning steps (i.e., meta-reasons), outputting thinking tokens before delivering a final verdict. Our model, StepWiser, is trained by reinforcement learning using relative outcomes of rollouts. We show it provides (i) better judgment accuracy on intermediate steps than existing methods; (ii) can be used to improve the policy model at training time; and (iii) improves inference-time search.

Large language models (LLMs) now solve multi-step problems by emitting extended chains of thought. During the process, they often re-derive the same intermediate steps across problems, inflating token usage and latency. This saturation of the context window leaves less capacity for exploration. We study a simple mechanism that converts recurring reasoning fragments into concise, reusable "behaviors" (name + instruction) via the model's own metacognitive analysis of prior traces. These behaviors are stored in a "behavior handbook" which supplies them to the model in-context at inference or distills them into parameters via supervised fine-tuning. This approach achieves improved test-time reasoning across three different settings - 1) Behavior-conditioned inference: Providing the LLM relevant behaviors in-context during reasoning reduces number of reasoning tokens by up to 46% while matching or improving baseline accuracy; 2) Behavior-guided self-improvement: Without any parameter updates, the model improves its own future reasoning by leveraging behaviors from its own past problem solving attempts. This yields up to 10% higher accuracy than a naive critique-and-revise baseline; and 3) Behavior-conditioned SFT: SFT on behavior-conditioned reasoning traces is more effective at converting non-reasoning models into reasoning models as compared to vanilla SFT. Together, these results indicate that turning slow derivations into fast procedural hints enables LLMs to remember how to reason, not just what to conclude.

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.

Fine-grained visual reasoning remains a core challenge for multimodal large language models (MLLMs). The recently introduced ReasonMap highlights this gap by showing that even advanced MLLMs struggle with spatial reasoning in structured and information-rich settings such as transit maps, a task of clear practical and scientific importance. However, standard reinforcement learning (RL) on such tasks is impeded by sparse rewards and unstable optimization. To address this, we first construct ReasonMap-Plus, an extended dataset that introduces dense reward signals through Visual Question Answering (VQA) tasks, enabling effective cold-start training of fine-grained visual understanding skills. Next, we propose RewardMap, a multi-stage RL framework designed to improve both visual understanding and reasoning capabilities of MLLMs. RewardMap incorporates two key designs. First, we introduce a difficulty-aware reward design that incorporates detail rewards, directly tackling the sparse rewards while providing richer supervision. Second, we propose a multi-stage RL scheme that bootstraps training from simple perception to complex reasoning tasks, offering a more effective cold-start strategy than conventional Supervised Fine-Tuning (SFT). Experiments on ReasonMap and ReasonMap-Plus demonstrate that each component of RewardMap contributes to consistent performance gains, while their combination yields the best results. Moreover, models trained with RewardMap achieve an average improvement of 3.47% across 6 benchmarks spanning spatial reasoning, fine-grained visual reasoning, and general tasks beyond transit maps, underscoring enhanced visual understanding and reasoning capabilities.

Recent AI advancements, such as OpenAI's new models, are transforming LLMs into LRMs (Large Reasoning Models) that perform reasoning during inference, taking extra time and compute for higher-quality outputs. We aim to uncover the algorithmic framework for training LRMs. Methods like self-consistency, PRM, and AlphaZero suggest reasoning as guided search. We ask: what is the simplest, most scalable way to enable search in LLMs? We propose a post-training framework called Reinforcement Learning via Self-Play (RLSP). RLSP involves three steps: (1) supervised fine-tuning with human or synthetic demonstrations of the reasoning process, (2) using an exploration reward signal to encourage diverse and efficient reasoning behaviors, and (3) RL training with an outcome verifier to ensure correctness while preventing reward hacking. Our key innovation is to decouple exploration and correctness signals during PPO training, carefully balancing them to improve performance and efficiency. Empirical studies in the math domain show that RLSP improves reasoning. On the Llama-3.1-8B-Instruct model, RLSP can boost performance by 23% in MATH-500 test set; On AIME 2024 math problems, Qwen2.5-32B-Instruct improved by 10% due to RLSP. However, a more important finding of this work is that the models trained using RLSP, even with the simplest exploration reward that encourages the model to take more intermediate steps, showed several emergent behaviors such as backtracking, exploration of ideas, and verification. These findings demonstrate that RLSP framework might be enough to enable emergence of complex reasoning abilities in LLMs when scaled. Lastly, we propose a theory as to why RLSP search strategy is more suitable for LLMs inspired by a remarkable result that says CoT provably increases computational power of LLMs, which grows as the number of steps in CoT li2024chain,merrill2023expresssive.

This paper investigates an under-explored challenge in large language models (LLMs): chain-of-thought prompting with noisy rationales, which include irrelevant or inaccurate reasoning thoughts within examples used for in-context learning. We construct NoRa dataset that is tailored to evaluate the robustness of reasoning in the presence of noisy rationales. Our findings on NoRa dataset reveal a prevalent vulnerability to such noise among current LLMs, with existing robust methods like self-correction and self-consistency showing limited efficacy. Notably, compared to prompting with clean rationales, base LLM drops by 1.4%-19.8% in accuracy with irrelevant thoughts and more drastically by 2.2%-40.4% with inaccurate thoughts. Addressing this challenge necessitates external supervision that should be accessible in practice. Here, we propose the method of contrastive denoising with noisy chain-of-thought (CD-CoT). It enhances LLMs' denoising-reasoning capabilities by contrasting noisy rationales with only one clean rationale, which can be the minimal requirement for denoising-purpose prompting. This method follows a principle of exploration and exploitation: (1) rephrasing and selecting rationales in the input space to achieve explicit denoising and (2) exploring diverse reasoning paths and voting on answers in the output space. Empirically, CD-CoT demonstrates an average improvement of 17.8% in accuracy over the base model and shows significantly stronger denoising capabilities than baseline methods. The source code is publicly available at: https://github.com/tmlr-group/NoisyRationales.

Reasoning training incentivizes LLMs to produce long chains of thought (long CoT), which among other things, allows them to explore solution strategies with self-checking. This results in higher accuracy, but inflates context length, token/compute cost, and answer latency. We ask: Can current models leverage their metacognition to provide other combinations on this Pareto frontier, e.g., better accuracy with lower context length and/or latency? Abstractly, we view the model as an improvement operator on its own "thoughts" with a continuum of possible strategies. We identify an interesting inference family Parallel-Distill-Refine (PDR), which performs the following: (i) generate diverse drafts in parallel; (ii) distill them into a bounded, textual workspace; and (iii) refine conditioned on this workspace, producing an output that seeds the next round. Importantly, context length (hence compute cost) is controllable via degree of parallelism, and is no longer conflated with the total number of generated tokens. We report PDR instantiations of current models that give better accuracy than long CoT while incurring lower latency. Setting degree of parallelism to 1 yields an interesting subcase, Sequential Refinement (SR) (iteratively improve a single candidate answer) which provides performance superior to long CoT. Success of such model orchestrations raises the question whether further training could shift the Pareto frontier. To this end, we train an 8B thinking model with Reinforcement Learning (RL) to make it consistent with PDR as the inference method. On math tasks with verifiable answers, iterative pipelines surpass single-pass baselines at matched sequential budgets, with PDR delivering the largest gains (e.g., +11% on AIME 2024 and +9% on AIME 2025).

One way to enhance the reasoning capability of Large Language Models (LLMs) is to conduct Supervised Fine-Tuning (SFT) using Chain-of-Thought (CoT) annotations. This approach does not show sufficiently strong generalization ability, however, because the training only relies on the given CoT data. In math problem-solving, for example, there is usually only one annotated reasoning path for each question in the training data. Intuitively, it would be better for the algorithm to learn from multiple annotated reasoning paths given a question. To address this issue, we propose a simple yet effective approach called Reinforced Fine-Tuning (ReFT) to enhance the generalizability of learning LLMs for reasoning, with math problem-solving as an example. ReFT first warmups the model with SFT, and then employs on-line reinforcement learning, specifically the PPO algorithm in this paper, to further fine-tune the model, where an abundance of reasoning paths are automatically sampled given the question and the rewards are naturally derived from the ground-truth answers. Extensive experiments on GSM8K, MathQA, and SVAMP datasets show that ReFT significantly outperforms SFT, and the performance can be potentially further boosted by combining inference-time strategies such as majority voting and re-ranking. Note that ReFT obtains the improvement by learning from the same training questions as SFT, without relying on extra or augmented training questions. This indicates a superior generalization ability for ReFT.

Large reasoning models (LRMs) have recently demonstrated impressive capabilities in complex reasoning tasks by leveraging increased test-time computation and exhibiting behaviors reminiscent of human-like self-reflection. While LRMs show a clear capacity for valuable self-reflection, how this ability interacts with other model behaviors remains underexplored. We investigate this connection by analyzing verbalized confidence, how models articulate their certainty, as a lens into the nature of self-reflection in LRMs. We find that supervised fine-tuning on reasoning traces (i.e., distillation) and reinforcement learning can improve verbalized calibration in reasoning-intensive settings in a progressive, laddered fashion. However, our results also indicate that reasoning models may possess a diminished awareness of their own knowledge boundaries, as evidenced by significantly lower "I don't know" response rates on factuality benchmarks. Moreover, we examine the relationship between verbalized confidence and reasoning chains, finding that models tend to express higher confidence when providing shorter or less elaborate reasoning. Our findings highlight how reasoning-oriented training can enhance performance in reasoning-centric tasks while potentially incurring a "reasoning tax," a cost reflected in the model's reduced ability to accurately recognize the limits of its own knowledge in small-scale models. More broadly, our work showcases how this erosion of knowledge boundaries can compromise model faithfulness, as models grow more confident without a commensurate understanding of when they should abstain.

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

We present a fundamental discovery that challenges our understanding of how complex reasoning emerges in large language models. While conventional wisdom suggests that sophisticated reasoning tasks demand extensive training data (>100,000 examples), we demonstrate that complex mathematical reasoning abilities can be effectively elicited with surprisingly few examples. Through comprehensive experiments, our proposed model LIMO demonstrates unprecedented performance in mathematical reasoning. With merely 817 curated training samples, LIMO achieves 57.1% accuracy on AIME and 94.8% on MATH, improving from previous SFT-based models' 6.5% and 59.2% respectively, while only using 1% of the training data required by previous approaches. LIMO demonstrates exceptional out-of-distribution generalization, achieving 40.5% absolute improvement across 10 diverse benchmarks, outperforming models trained on 100x more data, challenging the notion that SFT leads to memorization rather than generalization. Based on these results, we propose the Less-Is-More Reasoning Hypothesis (LIMO Hypothesis): In foundation models where domain knowledge has been comprehensively encoded during pre-training, sophisticated reasoning capabilities can emerge through minimal but precisely orchestrated demonstrations of cognitive processes. This hypothesis posits that the elicitation threshold for complex reasoning is determined by two key factors: (1) the completeness of the model's encoded knowledge foundation during pre-training, and (2) the effectiveness of post-training examples as "cognitive templates" that show the model how to utilize its knowledge base to solve complex reasoning tasks. To facilitate reproducibility and future research in data-efficient reasoning, we release LIMO as a comprehensive open-source suite at https://github.com/GAIR-NLP/LIMO.

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.

Generating high-quality stories spanning thousands of tokens requires competency across a variety of skills, from tracking plot and character arcs to keeping a consistent and engaging style. Due to the difficulty of sourcing labeled datasets and precise quality measurements, most work using large language models (LLMs) for long-form story generation uses combinations of hand-designed prompting techniques to elicit author-like behavior. This is a manual process that is highly dependent on the specific story-generation task. Motivated by the recent success of applying RL with Verifiable Rewards to domains like math and coding, we propose a general story-generation task (Next-Chapter Prediction) and a reward formulation (Verified Rewards via Completion Likelihood Improvement) that allows us to use an unlabeled book dataset as a learning signal for reasoning. We learn to reason over a story's condensed information and generate a detailed plan for the next chapter. Our reasoning is evaluated via the chapters it helps a story-generator create, and compared against non-trained and supervised finetuning (SFT) baselines. Pairwise human judgments reveal the chapters our learned reasoning produces are preferred across almost all metrics, and the effect is more pronounced in Scifi and Fantasy genres.

Existing post-training techniques for large language models are broadly categorized into Supervised Fine-Tuning (SFT) and Reinforcement Fine-Tuning (RFT). Each paradigm presents a distinct trade-off: SFT excels at mimicking demonstration data but can lead to problematic generalization as a form of behavior cloning. Conversely, RFT can significantly enhance a model's performance but is prone to learn unexpected behaviors, and its performance is highly sensitive to the initial policy. In this paper, we propose a unified view of these methods and introduce Prefix-RFT, a hybrid approach that synergizes learning from both demonstration and exploration. Using mathematical reasoning problems as a testbed, we empirically demonstrate that Prefix-RFT is both simple and effective. It not only surpasses the performance of standalone SFT and RFT but also outperforms parallel mixed-policy RFT methods. A key advantage is its seamless integration into existing open-source frameworks, requiring only minimal modifications to the standard RFT pipeline. Our analysis highlights the complementary nature of SFT and RFT, and validates that Prefix-RFT effectively harmonizes these two learning paradigms. Furthermore, ablation studies confirm the method's robustness to variations in the quality and quantity of demonstration data. We hope this work offers a new perspective on LLM post-training, suggesting that a unified paradigm that judiciously integrates demonstration and exploration could be a promising direction for future research.

Inspired by the success of DeepSeek R1 in reasoning via reinforcement learning without human feedback, we train a 3B language model using the Countdown Game with pure reinforcement learning. Our model outperforms baselines on four of five benchmarks, demonstrating improved generalization beyond its training data. Notably, response length does not correlate with reasoning quality, and while "aha moments" emerge, they do not always yield correct answers. These findings highlight the potential of RL-only training for reasoning enhancement and suggest future work on refining reward structures to bridge emergent insights with accuracy.

Advanced models such as OpenAI o1 exhibit impressive problem-solving capabilities through step-by-step reasoning. However, they may still falter on more complex problems, making errors that disrupt their reasoning paths. We attribute this to the expansive solution space, where each step has the risk of diverging into mistakes. To enhance language model reasoning, we introduce a specialized training framework called Reasoning Paths Optimization (RPO), which enables learning to reason and explore from diverse paths. Our approach encourages favorable branches at each reasoning step while penalizing unfavorable ones, enhancing the model's overall problem-solving performance. Reasoning Paths Optimization does not rely on large-scale human-annotated rationales or outputs from closed-source models, making it scalable and data-efficient. We focus on multi-step reasoning tasks, such as math word problems and science-based exam questions. The experiments demonstrate that our framework significantly enhances the reasoning performance of large language models, with up to 3.1% and 4.3% improvement on GSM8K and MMLU (STEM) respectively. Our data and code can be found at https://reasoning-paths.github.io.

Large Language Models (LLMs) have shown superior capability to solve reasoning problems with programs. While being a promising direction, most of such frameworks are trained and evaluated in settings with a prior knowledge of task requirements. However, as LLMs become more capable, it is necessary to assess their reasoning abilities in more realistic scenarios where many real-world problems are open-ended with ambiguous scope, and often require multiple formalisms to solve. To investigate this, we introduce the task of reasoning in the wild, where an LLM is tasked to solve a reasoning problem of unknown type by identifying the subproblems and their corresponding formalisms, and writing a program to solve each subproblem, guided by a tactic. We create a large tactic-guided trajectory dataset containing detailed solutions to a diverse set of reasoning problems, ranging from well-defined single-form reasoning (e.g., math, logic), to ambiguous and hybrid ones (e.g., commonsense, combined math and logic). This allows us to test various aspects of LLMs reasoning at the fine-grained level such as the selection and execution of tactics, and the tendency to take undesired shortcuts. In experiments, we highlight that existing LLMs fail significantly on problems with ambiguous and mixed scope, revealing critical limitations and overfitting issues (e.g. accuracy on GSM8K drops by at least 50\%). We further show the potential of finetuning a local LLM on the tactic-guided trajectories in achieving better performance. Project repo is available at github.com/gblackout/Reason-in-the-Wild

Large language models (LLMs) have demonstrated outstanding performance across various tasks, yet they still exhibit limitations such as hallucination, unfaithful reasoning, and toxic content. One potential approach to mitigate these issues is learning from human or external feedback (e.g. tools). In this paper, we introduce an intrinsic self-correct reasoning framework for LLMs that eliminates the need for human feedback, external tools, and handcraft prompts. The proposed framework, based on a multi-step reasoning paradigm Learning from Correctness (LeCo), improves reasoning performance without needing to learn from errors. This paradigm prioritizes learning from correct reasoning steps, and a unique method to measure confidence for each reasoning step based on generation logits. Experimental results across various multi-step reasoning tasks demonstrate the effectiveness of the framework in improving reasoning performance with reduced token consumption.

We study the process through which reasoning models trained with reinforcement learning on verifiable rewards (RLVR) can learn to solve new problems. We find that RLVR drives performance in two main ways: (1) by compressing pass@k into pass@1 and (2) via "capability gain" in which models learn to solve new problems that they previously could not solve even at high k. We find that while capability gain exists across model scales, learning to solve new problems is primarily driven through self-distillation. We demonstrate these findings across model scales ranging from 0.5B to 72B parameters on >500,000 reasoning problems with prompts and verifiable final answers across math, science, and code domains. We further show that we can significantly improve pass@k rates by leveraging natural language guidance for the model to consider within context while still requiring the model to derive a solution chain from scratch. Based of these insights, we derive Guide -- a new class of online training algorithms. Guide adaptively incorporates hints into the model's context on problems for which all rollouts were initially incorrect and adjusts the importance sampling ratio for the "off-policy" trajectories in order to optimize the policy for contexts in which the hints are no longer present. We describe variants of Guide for GRPO and PPO and empirically show that Guide-GRPO on 7B and 32B parameter models improves generalization over its vanilla counterpart with up to 4% macro-average improvement across math benchmarks. We include careful ablations to analyze Guide's components and theoretically analyze Guide's learning efficiency.

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

Recent advancements in reasoning-focused language models such as OpenAI's O1 and DeepSeek-R1 have shown that scaling test-time computation-through chain-of-thought reasoning and iterative exploration-can yield substantial improvements on complex tasks like mathematics and code generation. These breakthroughs have been driven by large-scale reinforcement learning (RL), particularly when combined with verifiable reward signals that provide objective and grounded supervision. In this report, we investigate the effects of prolonged reinforcement learning on a small language model across a diverse set of reasoning domains. Our work identifies several key ingredients for effective training, including the use of verifiable reward tasks, enhancements to Group Relative Policy Optimization (GRPO), and practical techniques to improve training stability and generalization. We introduce controlled KL regularization, clipping ratio, and periodic reference policy resets as critical components for unlocking long-term performance gains. Our model achieves significant improvements over strong baselines, including +14.7% on math, +13.9% on coding, and +54.8% on logic puzzle tasks. To facilitate continued research, we release our model publicly.

The structure of causal language model training assumes that each token can be accurately predicted from the previous context. This contrasts with humans' natural writing and reasoning process, where goals are typically known before the exact argument or phrasings. While this mismatch has been well studied in the literature, the working assumption has been that architectural changes are needed to address this mismatch. We argue that rearranging and processing the training data sequences can allow models to more accurately imitate the true data-generating process, and does not require any other changes to the architecture or training infrastructure. We demonstrate that this technique, Trelawney, and the inference algorithms derived from it allow us to improve performance on several key benchmarks that span planning, algorithmic reasoning, and story generation tasks. Finally, our method naturally enables the generation of long-term goals at no additional cost. We investigate how using the model's goal-generation capability can further improve planning and reasoning. Additionally, we believe Trelawney could potentially open doors to new capabilities beyond the current language modeling paradigm.

Reinforcement learning (RL) has recently demonstrated strong potential in enhancing the reasoning capabilities of large language models (LLMs). Particularly, the "Zero" reinforcement learning introduced by Deepseek-R1-Zero, enables direct RL training of base LLMs without relying on an intermediate supervised fine-tuning stage. Despite these advancements, current works for LLM reasoning mainly focus on mathematical and coding domains, largely due to data abundance and the ease of answer verification. This limits the applicability and generalization of such models to broader domains, where questions often have diverse answer representations, and data is more scarce. In this paper, we propose General-Reasoner, a novel training paradigm designed to enhance LLM reasoning capabilities across diverse domains. Our key contributions include: (1) constructing a large-scale, high-quality dataset of questions with verifiable answers curated by web crawling, covering a wide range of disciplines; and (2) developing a generative model-based answer verifier, which replaces traditional rule-based verification with the capability of chain-of-thought and context-awareness. We train a series of models and evaluate them on a wide range of datasets covering wide domains like physics, chemistry, finance, electronics etc. Our comprehensive evaluation across these 12 benchmarks (e.g. MMLU-Pro, GPQA, SuperGPQA, TheoremQA, BBEH and MATH AMC) demonstrates that General-Reasoner outperforms existing baseline methods, achieving robust and generalizable reasoning performance while maintaining superior effectiveness in mathematical reasoning tasks.

Reasoning-Oriented Reinforcement Learning (RORL) enhances the reasoning ability of Large Language Models (LLMs). However, due to the sparsity of rewards in RORL, effective training is highly dependent on the selection of problems of appropriate difficulty. Although curriculum learning attempts to address this by adjusting difficulty, it often relies on static schedules, and even recent online filtering methods lack theoretical grounding and a systematic understanding of their effectiveness. In this work, we theoretically and empirically show that curating the batch with the problems that the training model achieves intermediate accuracy on the fly can maximize the effectiveness of RORL training, namely balanced online difficulty filtering. We first derive that the lower bound of the KL divergence between the initial and the optimal policy can be expressed with the variance of the sampled accuracy. Building on those insights, we show that balanced filtering can maximize the lower bound, leading to better performance. Experimental results across five challenging math reasoning benchmarks show that balanced online filtering yields an additional 10% in AIME and 4% improvements in average over plain GRPO. Moreover, further analysis shows the gains in sample efficiency and training time efficiency, exceeding the maximum reward of plain GRPO within 60% training time and the volume of the training set.

The remarkable reasoning capability of large language models (LLMs) stems from cognitive behaviors that emerge through reinforcement with verifiable rewards. This work investigates how to transfer this principle to Multimodal LLMs (MLLMs) to unlock advanced visual reasoning. We introduce a two-stage paradigm built on Qwen2.5-VL-7B: a massive linguistic cold-start fine-tuning, followed by multimodal reinforcement learning (RL) spanning nearly 1,000 steps, surpassing all previous open-source efforts in scale. This pioneering work reveals three fundamental insights: 1) Behavior transfer emerges surprisingly early in cold start due to linguistic mental imagery. 2) Cold start broadly memorizes visual behaviors, while RL critically discerns and scales up effective patterns. 3) Transfer strategically favors high-utility behaviors such as visual reflection. Our resulting model, Open-Vision-Reasoner (OVR), achieves state-of-the-art performance on a suite of reasoning benchmarks, including 95.3% on MATH500, 51.8% on MathVision and 54.6% on MathVerse. We release our model, data, and training dynamics to catalyze the development of more capable, behavior-aligned multimodal reasoners.

Post-training, particularly reinforcement learning (RL) using self-play-generated data, has become a new learning paradigm for large language models (LLMs). However, scaling RL to develop a general reasoner remains a research challenge, as existing methods focus on task-specific reasoning without adequately addressing generalization across a broader range of tasks. Moreover, unlike traditional RL with limited action space, LLMs operate in an infinite space, making it crucial to search for valuable and diverse strategies to solve problems effectively. To address this, we propose searching within the action space on high-level abstract plans to enhance model generalization and introduce Critical Plan Step Learning (CPL), comprising: 1) searching on plan, using Monte Carlo Tree Search (MCTS) to explore diverse plan steps in multi-step reasoning tasks, and 2) learning critical plan steps through Step-level Advantage Preference Optimization (Step-APO), which integrates advantage estimates for step preference obtained via MCTS into Direct Preference Optimization (DPO). This combination helps the model effectively learn critical plan steps, enhancing both reasoning capabilities and generalization. Experimental results demonstrate that our method, trained exclusively on GSM8K and MATH, not only significantly improves performance on GSM8K (+10.5%) and MATH (+6.5%), but also enhances out-of-domain reasoning benchmarks, such as HumanEval (+12.2%), GPQA (+8.6%), ARC-C (+4.0%), MMLU-STEM (+2.2%), and BBH (+1.8%).

Reinforcement Learning (RL) has proven to be an effective post-training strategy for enhancing reasoning in vision-language models (VLMs). Group Relative Policy Optimization (GRPO) is a recent prominent method that encourages models to generate complete reasoning traces before answering, leading to increased token usage and computational cost. Inspired by the human-like thinking process-where people skip reasoning for easy questions but think carefully when needed-we explore how to enable VLMs to first decide when reasoning is necessary. To realize this, we propose TON, a two-stage training strategy: (i) a supervised fine-tuning (SFT) stage with a simple yet effective 'thought dropout' operation, where reasoning traces are randomly replaced with empty thoughts. This introduces a think-or-not format that serves as a cold start for selective reasoning; (ii) a GRPO stage that enables the model to freely explore when to think or not, while maximizing task-aware outcome rewards. Experimental results show that TON can reduce the completion length by up to 90% compared to vanilla GRPO, without sacrificing performance or even improving it. Further evaluations across diverse vision-language tasks-covering a range of reasoning difficulties under both 3B and 7B models-consistently reveal that the model progressively learns to bypass unnecessary reasoning steps as training advances. These findings shed light on the path toward human-like reasoning patterns in reinforcement learning approaches. Our code is available at https://github.com/kokolerk/TON.

Scientists often infer abstract procedures from specific instances of problems and use the abstractions to generate new, related instances. For example, programs encoding the formal rules and properties of a system have been useful in fields ranging from RL (procedural environments) to physics (simulation engines). These programs can be seen as functions which execute to different outputs based on their parameterizations (e.g., gridworld configuration or initial physical conditions). We introduce the term EFA (Executable Functional Abstraction) to denote such programs for math problems. EFA-like constructs have been shown to be useful for math reasoning as problem generators for stress-testing models. However, prior work has been limited to abstractions for grade-school math (whose simple rules are easy to encode in programs), while generating EFAs for advanced math has thus far required human engineering. We explore the automatic construction of EFAs for advanced math problems. We operationalize the task of automatically constructing EFAs as a program synthesis task, and develop EFAGen, which conditions an LLM on a seed math problem and its step-by-step solution to generate candidate EFA programs that are faithful to the generalized problem and solution class underlying the seed problem. Furthermore, we formalize properties any valid EFA must possess in terms of executable unit tests, and show how the tests can be used as verifiable rewards to train LLMs to become better writers of EFAs. We demonstrate that EFAs constructed by EFAGen behave rationally by remaining faithful to seed problems, produce learnable problem variations, and that EFAGen can infer EFAs across multiple diverse sources of competition-level math problems. Finally, we show downstream uses of model-written EFAs e.g. finding problem variations that are harder or easier for a learner to solve, as well as data generation.

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.

Reinforcement fine-tuning (RFT) has emerged as a powerful post-training technique to incentivize the reasoning ability of large language models (LLMs). However, LLMs can respond very inconsistently to RFT: some show substantial performance gains, while others plateau or even degrade. To understand this divergence, we analyze the per-step influence of the RL objective and identify two key conditions for effective post-training: (1) RL-informative rollout accuracy, and (2) strong data co-influence, which quantifies how much the training data affects performance on other samples. Guided by these insights, we propose behavior injection, a task-agnostic data-augmentation scheme applied prior to RL. Behavior injection enriches the supervised finetuning (SFT) data by seeding exploratory and exploitative behaviors, effectively making the model more RL-ready. We evaluate our method across two reasoning benchmarks with multiple base models. The results demonstrate that our theoretically motivated augmentation can significantly increases the performance gain from RFT over the pre-RL model.

Despite recent progress in large-scale reinforcement learning (RL) for reasoning, the training recipe for building high-performing reasoning models remains elusive. Key implementation details of frontier models, such as DeepSeek-R1, including data curation strategies and RL training recipe, are often omitted. Moreover, recent research indicates distillation remains more effective than RL for smaller models. In this work, we demonstrate that large-scale RL can significantly enhance the reasoning capabilities of strong, small- and mid-sized models, achieving results that surpass those of state-of-the-art distillation-based models. We systematically study the RL training process through extensive ablations and propose a simple yet effective approach: first training on math-only prompts, then on code-only prompts. Notably, we find that math-only RL not only significantly enhances the performance of strong distilled models on math benchmarks (e.g., +14.6% / +17.2% on AIME 2025 for the 7B / 14B models), but also code reasoning tasks (e.g., +6.8% / +5.8% on LiveCodeBench for the 7B / 14B models). In addition, extended code-only RL iterations further improve performance on code benchmarks with minimal or no degradation in math results. We develop a robust data curation pipeline to collect challenging prompts with high-quality, verifiable answers and test cases to enable verification-based RL across both domains. Finally, we identify key experimental insights, including curriculum learning with progressively increasing response lengths and the stabilizing effect of on-policy parameter updates. We find that RL not only elicits the foundational reasoning capabilities acquired during pretraining and supervised fine-tuning (e.g., distillation), but also pushes the limits of the model's reasoning ability, enabling it to solve problems that were previously unsolvable.

Scaling model size and training data has led to great advances in the performance of Large Language Models (LLMs). However, the diminishing returns of this approach necessitate alternative methods to improve model capabilities, particularly in tasks requiring advanced reasoning. Large reasoning models, which leverage long chain-of-thoughts, bring unprecedented breakthroughs in problem-solving capabilities but at a substantial deployment cost associated to longer generations. Reducing inference costs is crucial for the economic feasibility, user experience, and environmental sustainability of these models. In this work, we propose to train large reasoning models to reason efficiently. More precisely, we use reinforcement learning (RL) to train reasoning models to dynamically allocate inference-time compute based on task complexity. Our method incentivizes models to minimize unnecessary computational overhead while maintaining accuracy, thereby achieving substantial efficiency gains. It enables the derivation of a family of reasoning models with varying efficiency levels, controlled via a single hyperparameter. Experiments on two open-weight large reasoning models demonstrate significant reductions in inference cost while preserving most of the accuracy.

Reasoning models excel in complex problem solving but exhibit a concerning trade off between reasoning capabilities and instruction following abilities. Existing approaches for improving instruction following rely on stronger external models, creating methodological bottlenecks and practical limitations including increased costs and accessibility constraints. We propose a self-supervised RL framework that leverages reasoning models' own internal signals to improve instruction following capabilities without external supervision. Extensive experiments demonstrate that our framework significantly improves instruction following capabilities while maintaining reasoning performance, offering a scalable and cost-effective approach to enhance instruction following in reasoning models. The data and code are publicly available at https://github.com/Rainier-rq/verl-if.

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.

Continual post-training (CPT) is a popular and effective technique for adapting foundation models like multimodal large language models to specific and ever-evolving downstream tasks. While existing research has primarily concentrated on methods like data replay, model expansion, or parameter regularization, the fundamental role of the learning paradigm within CPT remains largely unexplored. This paper presents a comparative analysis of two core post-training paradigms: supervised fine-tuning (SFT) and reinforcement fine-tuning (RFT), investigating their respective impacts on knowledge retention during CPT. Our experiments are conducted on a benchmark comprising seven diverse multimodal tasks, utilizing Qwen2.5-VL-7B-Instruct as the base model for continual post-training. The investigation yields two significant findings: (1) When continuously learning on downstream tasks, SFT leads to catastrophic forgetting of previously learned tasks. In contrast, RFT inherently preserves prior knowledge and achieve performance comparable to multi-task training. (2) RFT successfully protects and even enhances the model's general knowledge on standard benchmarks (e.g., MMMU and MMLU-Pro). Conversely, SFT degrades general model capabilities severely. Further analysis shows that explicit mechanisms, such as KL penalty and chain-of-thought reasoning, are not the primary factors. Instead, we find that the implicit regularization inherent to RFT is a key factor in mitigating forgetting. Finally, we propose a rollout-based instance filtering algorithm to improve the stability and efficiency of RFT. Our comprehensive study demonstrates the superiority of RFT as a robust paradigm for continual post-training.

We present a scientific reasoning foundation model that aligns natural language with heterogeneous scientific representations. The model is pretrained on a 206B-token corpus spanning scientific text, pure sequences, and sequence-text pairs, then aligned via SFT on 40M instructions, annealed cold-start bootstrapping to elicit long-form chain-of-thought, and reinforcement learning with task-specific reward shaping, which instills deliberate scientific reasoning. It supports four capability families, covering up to 103 tasks across workflows: (i) faithful translation between text and scientific formats, (ii) text/knowledge extraction, (iii) property prediction, (iv) property classification, (v) unconditional and conditional sequence generation and design. Compared with specialist systems, our approach broadens instruction coverage, improves cross-domain generalization, and enhances fidelity. We detail data curation and training and show that cross-discipline learning strengthens transfer and downstream reliability. The model, instruct tuning datasets and the evaluation code are open-sourced at https://huggingface.co/SciReason and https://github.com/open-sciencelab/SciReason.

Large reasoning models (LRMs) can do complex reasoning via long chain-of-thought (CoT) involving cognitive strategies such as backtracking and self-correction. Recent studies suggest that some models inherently possess these long reasoning abilities, which may be unlocked via extra training. Our work first investigates whether we can elicit such behavior without any training. To this end, we propose a decoding-time approach, ThinkLogit, which utilizes logits arithmetic (Liu et al., 2024) to tune a target large LM for long reasoning using a substantially smaller model as guider. We then show that we can further boost performance by training the guider model with preference optimization over correct/incorrect reasoning pairs sampled from both the target and guider model -- a setup we refer to as ThinkLogit-DPO. Our experiments demonstrate that ThinkLogit and ThinkLogit-DPO achieve a relative improvement in pass@1 by 26% and 29%, respectively, over four mathematical datasets using the Qwen2.5-32B when guided by R1-Distill-Qwen-1.5B -- a model 21x smaller. Lastly, we show that ThinkLogit can transfer long reasoning skills acquired through reinforcement learning, improving pass@1 by 13% relative compared to the Qwen2.5-32B base model. Our work presents a computationally-efficient method to elicit long reasoning in large models with minimal or no additional training.

Reinforcement Learning from Verifiable Rewards (RLVR) improves the reasoning abilities of Large Language Models (LLMs) but it struggles with unstable exploration. We propose FR3E (First Return, Entropy-Eliciting Explore), a structured exploration framework that identifies high-uncertainty decision points in reasoning trajectories and performs targeted rollouts to construct semantically grounded intermediate feedback. Our method provides targeted guidance without relying on dense supervision. Empirical results on mathematical reasoning benchmarks(AIME24) show that FR3E promotes more stable training, produces longer and more coherent responses, and increases the proportion of fully correct trajectories. These results highlight the framework's effectiveness in improving LLM reasoning through more robust and structured exploration.

Self-taught reasoners (STaRs) enhance the mathematical reasoning abilities of large language models (LLMs) by leveraging self-generated responses for self-training. Recent studies have incorporated reward models to guide response selection or decoding, aiming to obtain higher-quality data. However, they typically allocate a uniform sampling budget across all problems, overlooking the varying utility of problems at different difficulty levels. In this work, we conduct an empirical study and find that problems near the boundary of the LLM's reasoning capability offer significantly greater learning utility than both easy and overly difficult ones. To identify and exploit such problems, we propose HS-STaR, a Hierarchical Sampling framework for Self-Taught Reasoners. Given a fixed sampling budget, HS-STaR first performs lightweight pre-sampling with a reward-guided difficulty estimation strategy to efficiently identify boundary-level problems. Subsequently, it dynamically reallocates the remaining budget toward these high-utility problems during a re-sampling phase, maximizing the generation of valuable training data. Extensive experiments across multiple reasoning benchmarks and backbone LLMs demonstrate that HS-STaR significantly outperforms other baselines without requiring additional sampling budget.

A fundamental skill among human developers is the ability to understand and reason about program execution. As an example, a programmer can mentally simulate code execution in natural language to debug and repair code (aka. rubber duck debugging). However, large language models (LLMs) of code are typically trained on the surface textual form of programs, thus may lack a semantic understanding of how programs execute at run-time. To address this issue, we propose NExT, a method to teach LLMs to inspect the execution traces of programs (variable states of executed lines) and reason about their run-time behavior through chain-of-thought (CoT) rationales. Specifically, NExT uses self-training to bootstrap a synthetic training set of execution-aware rationales that lead to correct task solutions (e.g., fixed programs) without laborious manual annotation. Experiments on program repair tasks based on MBPP and HumanEval demonstrate that NExT improves the fix rate of a PaLM 2 model, by 26.1% and 14.3% absolute, respectively, with significantly improved rationale quality as verified by automated metrics and human raters. Our model can also generalize to scenarios where program traces are absent at test-time.

Recent methodologies in LLM self-training mostly rely on LLM generating responses and filtering those with correct output answers as training data. This approach often yields a low-quality fine-tuning training set (e.g., incorrect plans or intermediate reasoning). In this paper, we develop a reinforced self-training approach, called ReST-MCTS*, based on integrating process reward guidance with tree search MCTS* for collecting higher-quality reasoning traces as well as per-step value to train policy and reward models. ReST-MCTS* circumvents the per-step manual annotation typically used to train process rewards by tree-search-based reinforcement learning: Given oracle final correct answers, ReST-MCTS* is able to infer the correct process rewards by estimating the probability this step can help lead to the correct answer. These inferred rewards serve dual purposes: they act as value targets for further refining the process reward model and also facilitate the selection of high-quality traces for policy model self-training. We first show that the tree-search policy in ReST-MCTS* achieves higher accuracy compared with prior LLM reasoning baselines such as Best-of-N and Tree-of-Thought, within the same search budget. We then show that by using traces searched by this tree-search policy as training data, we can continuously enhance the three language models for multiple iterations, and outperform other self-training algorithms such as ReST^EM and Self-Rewarding LM.

Mathematical reasoning has long represented one of the most fundamental and challenging frontiers in artificial intelligence research. In recent years, large language models (LLMs) have achieved significant advances in this area. This survey examines the development of mathematical reasoning abilities in LLMs through two high-level cognitive phases: comprehension, where models gain mathematical understanding via diverse pretraining strategies, and answer generation, which has progressed from direct prediction to step-by-step Chain-of-Thought (CoT) reasoning. We review methods for enhancing mathematical reasoning, ranging from training-free prompting to fine-tuning approaches such as supervised fine-tuning and reinforcement learning, and discuss recent work on extended CoT and "test-time scaling". Despite notable progress, fundamental challenges remain in terms of capacity, efficiency, and generalization. To address these issues, we highlight promising research directions, including advanced pretraining and knowledge augmentation techniques, formal reasoning frameworks, and meta-generalization through principled learning paradigms. This survey tries to provide some insights for researchers interested in enhancing reasoning capabilities of LLMs and for those seeking to apply these techniques to other domains.

Large Language Models exhibit impressive reasoning capabilities across diverse tasks, motivating efforts to distill these capabilities into smaller models through generated reasoning data. However, direct training on such synthesized reasoning data may lead to superficial imitation of reasoning process, rather than fostering a genuine integration of reasoning capabilities with underlying knowledge. To address this, we propose TinyThinker, a framework introducing two novel approaches. First, we introduce a three-stage process that incrementally guides the student model through the reasoning process, progressively refining knowledge from coarse to fine granularity. Second, we develop a two-phase training framework comprising an initial reasoning acquisition phase followed by a self-reflection phase utilizing self-generated data. Experiments on commonsense reasoning benchmarks demonstrate that TinyThinker achieves superior performance compared to baselines. Ablation studies further validate the effectiveness of each component in our framework. TinyThinker is extendable to other knowledge-intensive reasoning tasks, offering an alternative strategy for developing effective reasoning capabilities in smaller language models. Codes are available at https://github.com/shengminp/TinyThinker

Does RL teach LLMs genuinely new skills, or does it merely activate existing ones? This question lies at the core of ongoing debates about the role of RL in LLM post-training. On one side, strong empirical results can be achieved with RL even without preceding supervised finetuning; on the other, critics argue that RL contributes little beyond reweighting existing reasoning strategies. This work provides concrete evidence that LLMs can acquire genuinely new skills during RL by composing existing ones, mirroring one of the central mechanisms by which humans acquire new cognitive skills. To mitigate data contamination and other confounding factors, and to allow precise control over task complexity, we develop a synthetic framework for our investigation. Specifically, we define a skill as the ability to infer the output of a string transformation function f(x) given x. When an LLM has already learned f and g prior to RL, our experiments reveal that RL enables it to learn unseen compositions of them h(x)=g(f(x)). Further, this compositional ability generalizes to more difficult problems such as compositions of >2 functions unseen during RL training. Surprisingly, our experiments show that compositional skill acquired on a source task transfers to a different target task. This transfer happens even without compositional training on the target, requiring only prior knowledge of the target's atomic skills. Our qualitative analysis shows that RL fundamentally changes the reasoning behaviors of the models. In contrast, next-token training with the same data yields none of these findings. Our systematic experiments provide fresh insights into LLM learning, suggesting the value of first building base models with basic skills, then using RL to incentivize advanced, generalizable skills for complex problems.

Reinforcement learning (RL) has proven effective for fine-tuning large language models (LLMs), significantly enhancing their reasoning abilities in domains such as mathematics and code generation. A crucial factor influencing RL fine-tuning success is the training curriculum: the order in which training problems are presented. While random curricula serve as common baselines, they remain suboptimal; manually designed curricula often rely heavily on heuristics, and online filtering methods can be computationally prohibitive. To address these limitations, we propose Self-Evolving Curriculum (SEC), an automatic curriculum learning method that learns a curriculum policy concurrently with the RL fine-tuning process. Our approach formulates curriculum selection as a non-stationary Multi-Armed Bandit problem, treating each problem category (e.g., difficulty level or problem type) as an individual arm. We leverage the absolute advantage from policy gradient methods as a proxy measure for immediate learning gain. At each training step, the curriculum policy selects categories to maximize this reward signal and is updated using the TD(0) method. Across three distinct reasoning domains: planning, inductive reasoning, and mathematics, our experiments demonstrate that SEC significantly improves models' reasoning capabilities, enabling better generalization to harder, out-of-distribution test problems. Additionally, our approach achieves better skill balance when fine-tuning simultaneously on multiple reasoning domains. These findings highlight SEC as a promising strategy for RL fine-tuning of LLMs.

Recent advances in large language model (LLM) reasoning have shown that sophisticated behaviors such as planning and self-reflection can emerge through reinforcement learning (RL). However, despite these successes, RL in its current form remains insufficient to induce capabilities that exceed the limitations of the base model, as it is primarily optimized based on existing knowledge of the model rather than facilitating the acquisition of new information. To address this limitation, we employ supervised fine-tuning (SFT) to learn what RL cannot, which enables the incorporation of new knowledge and reasoning patterns by leveraging high-quality demonstration data. We analyze the training dynamics of RL and SFT for LLM reasoning and find that RL excels at maintaining and improving performance on questions within the model's original capabilities, while SFT is more effective at enabling progress on questions beyond the current scope of the model. Motivated by the complementary strengths of RL and SFT, we introduce a novel training approach, ReLIFT (Reinforcement Learning Interleaved with Online Fine-Tuning). In ReLIFT, the model is primarily trained using RL, but when it encounters challenging questions, high-quality solutions are collected for fine-tuning, and the training process alternates between RL and fine-tuning to enhance the model's reasoning abilities. ReLIFT achieves an average improvement of over +5.2 points across five competition-level benchmarks and one out-of-distribution benchmark compared to other zero-RL models. Furthermore, we demonstrate that ReLIFT outperforms both RL and SFT while using only 13\% of the detailed demonstration data, highlighting its scalability. These results provide compelling evidence that ReLIFT overcomes the fundamental limitations of RL and underscores the significant potential.

Reinforcement learning (RL) has emerged as an effective method for training reasoning models. However, existing RL approaches typically bias the model's output distribution toward reward-maximizing paths without introducing external knowledge. This limits their exploration capacity and results in a narrower reasoning capability boundary compared to base models. To address this limitation, we propose TAPO (Thought-Augmented Policy Optimization), a novel framework that augments RL by incorporating external high-level guidance ("thought patterns"). By adaptively integrating structured thoughts during training, TAPO effectively balances model-internal exploration and external guidance exploitation. Extensive experiments show that our approach significantly outperforms GRPO by 99% on AIME, 41% on AMC, and 17% on Minerva Math. Notably, these high-level thought patterns, abstracted from only 500 prior samples, generalize effectively across various tasks and models. This highlights TAPO's potential for broader applications across multiple tasks and domains. Our further analysis reveals that introducing external guidance produces powerful reasoning models with superior explainability of inference behavior and enhanced output readability.

Though reasoning-based large language models (LLMs) have excelled in mathematics and programming, their capabilities in knowledge-intensive medical question answering remain underexplored. To address this, we introduce ReasonMed, the largest medical reasoning dataset, comprising 370k high-quality examples distilled from 1.7 million initial reasoning paths generated by various LLMs. ReasonMed is constructed through a multi-agent verification and refinement process, where we design an Error Refiner to enhance the reasoning paths by identifying and correcting error-prone steps flagged by a verifier. Leveraging ReasonMed, we systematically investigate best practices for training medical reasoning models and find that combining detailed Chain-of-Thought (CoT) reasoning with concise answer summaries yields the most effective fine-tuning strategy. Based on this strategy, we train ReasonMed-7B, which sets a new benchmark for sub-10B models, outperforming the prior best by 4.17\% and even exceeding LLaMA3.1-70B on PubMedQA by 4.60\%.

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.

Large Language Reasoning Models have demonstrated remarkable success on static tasks, yet their application to multi-round agentic planning in interactive environments faces two fundamental challenges. First, the intractable credit assignment problem renders conventional reinforcement learning ineffective in sparse-reward settings. Second, the computational overhead of verbose, step-by-step reasoning histories is prohibitive. To address these challenges, we propose BPO, a three-stage framework (bootstrapping, extrapolation, and refinement) that establishes a self-improving data flywheel to develop robust reasoning models for long-horizon, sparse-reward environments. Our framework first bootstraps efficient reasoning using the proposed planning quaternions with long-short chain-of-thought fusion. It then extrapolates to out-of-distribution tasks through complexity-stratified curriculum learning. Finally, the model iteratively refines itself by learning exclusively on experiences selected via reward-gated rejection sampling. Experiments on ALFWorld, ScienceWorld, and WebShop demonstrate that our approach achieves state-of-the-art with significant token efficiency, providing a new recipe for reasoning models in agentic planning.

Tables play a crucial role in conveying information in various domains. We propose a Plan-then-Reason framework to answer different types of user queries over tables with sentence context. The framework first plans the reasoning paths over the context, then assigns each step to program-based or textual reasoning to reach the final answer. This framework enhances the table reasoning abilities for both in-context learning and fine-tuning methods. GPT-3.5-Turbo following Plan-then-Reason framework surpasses other prompting baselines without self-consistency while using less API calls and in-context demonstrations. We also construct an instruction tuning set TrixInstruct to evaluate the effectiveness of fine-tuning with this framework. We present ProTrix model family by finetuning models on TrixInstruct. Our experiments show that ProTrix family generalizes to diverse unseen tabular tasks with only 6k training instances. We further demonstrate that ProTrix can generate accurate and faithful explanations to answer complex free-form questions. Our work underscores the importance of the planning and reasoning abilities towards a model over tabular tasks with generalizability and interpretability. We open-source our dataset and models at https://github.com/WilliamZR/ProTrix.

Recent research has focused on enhancing the capability of smaller models through imitation learning, drawing on the outputs generated by large foundation models (LFMs). A number of issues impact the quality of these models, ranging from limited imitation signals from shallow LFM outputs; small scale homogeneous training data; and most notably a lack of rigorous evaluation resulting in overestimating the small model's capability as they tend to learn to imitate the style, but not the reasoning process of LFMs. To address these challenges, we develop Orca (We are working with our legal team to publicly release a diff of the model weights in accordance with LLaMA's release policy to be published at https://aka.ms/orca-lm), a 13-billion parameter model that learns to imitate the reasoning process of LFMs. Orca learns from rich signals from GPT-4 including explanation traces; step-by-step thought processes; and other complex instructions, guided by teacher assistance from ChatGPT. To promote this progressive learning, we tap into large-scale and diverse imitation data with judicious sampling and selection. Orca surpasses conventional state-of-the-art instruction-tuned models such as Vicuna-13B by more than 100% in complex zero-shot reasoning benchmarks like Big-Bench Hard (BBH) and 42% on AGIEval. Moreover, Orca reaches parity with ChatGPT on the BBH benchmark and shows competitive performance (4 pts gap with optimized system message) in professional and academic examinations like the SAT, LSAT, GRE, and GMAT, both in zero-shot settings without CoT; while trailing behind GPT-4. Our research indicates that learning from step-by-step explanations, whether these are generated by humans or more advanced AI models, is a promising direction to improve model capabilities and skills.

Chain-of-thought prompting (e.g., "Let's think step-by-step") primes large language models to verbalize rationalization for their predictions. While chain-of-thought can lead to dramatic performance gains, benefits appear to emerge only for sufficiently large models (beyond 50B parameters). We show that orders-of-magnitude smaller models (125M -- 1.3B parameters) can still benefit from chain-of-thought prompting. To achieve this, we introduce Symbolic Chain-of-Thought Distillation (SCoTD), a method to train a smaller student model on rationalizations sampled from a significantly larger teacher model. Experiments across several commonsense benchmarks show that: 1) SCoTD enhances the performance of the student model in both supervised and few-shot settings, and especially for challenge sets; 2) sampling many reasoning chains per instance from the teacher is paramount; and 3) after distillation, student chain-of-thoughts are judged by humans as comparable to the teacher, despite orders of magnitude fewer parameters. We test several hypotheses regarding what properties of chain-of-thought samples are important, e.g., diversity vs. teacher likelihood vs. open-endedness. We release our corpus of chain-of-thought samples and code.

The remarkable performance of Multimodal Large Language Models (MLLMs) has unequivocally demonstrated their proficient understanding capabilities in handling a wide array of visual tasks. Nevertheless, the opaque nature of their black-box reasoning processes persists as an enigma, rendering them uninterpretable and struggling with hallucination. Their ability to execute intricate compositional reasoning tasks is also constrained, culminating in a stagnation of learning progression for these models. In this work, we introduce Fact, a novel paradigm designed to generate multimodal rationales that are faithful, concise, and transferable for teaching MLLMs. This paradigm utilizes verifiable visual programming to generate executable code guaranteeing faithfulness and precision. Subsequently, through a series of operations including pruning, merging, and bridging, the rationale enhances its conciseness. Furthermore, we filter rationales that can be transferred to end-to-end paradigms from programming paradigms to guarantee transferability. Empirical evidence from experiments demonstrates the superiority of our method across models of varying parameter sizes, significantly enhancing their compositional reasoning and generalization ability. Our approach also reduces hallucinations owing to its high correlation between images and text.

Large Language Models (LLMs) have achieved excellent performances in various tasks. However, fine-tuning an LLM requires extensive supervision. Human, on the other hand, may improve their reasoning abilities by self-thinking without external inputs. In this work, we demonstrate that an LLM is also capable of self-improving with only unlabeled datasets. We use a pre-trained LLM to generate "high-confidence" rationale-augmented answers for unlabeled questions using Chain-of-Thought prompting and self-consistency, and fine-tune the LLM using those self-generated solutions as target outputs. We show that our approach improves the general reasoning ability of a 540B-parameter LLM (74.4%->82.1% on GSM8K, 78.2%->83.0% on DROP, 90.0%->94.4% on OpenBookQA, and 63.4%->67.9% on ANLI-A3) and achieves state-of-the-art-level performance, without any ground truth label. We conduct ablation studies and show that fine-tuning on reasoning is critical for self-improvement.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a promising paradigm for advancing the reasoning capabilities of Large Language Models (LLMs). However, a critical paradox clouds its efficacy: RLVR-tuned models often underperform their base models on the Pass@K metric for solution-finding, leading to the hypothesis that RLVR merely re-weights existing reasoning paths at the cost of reasoning diversity. In this work, we resolve this contradiction by identifying the source of the problem: the Pass@K metric itself is a flawed measure of reasoning, as it credits correct final answers that probably arise from inaccurate or incomplete chains of thought (CoTs). To address this, we introduce a more precise evaluation metric, CoT-Pass@K, which mandates that both the reasoning path and the final answer be correct. We provide a new theoretical foundation that formalizes how RLVR, unlike traditional RL, is uniquely structured to incentivize logical integrity. Our empirical results are supportive: using CoT-Pass@K, we observe that RLVR can incentivize the generalization of correct reasoning for all values of K. Furthermore, by analyzing the training dynamics, we find that this enhanced reasoning capability emerges early in the training process and smoothly generalizes. Our work provides a clear perspective on the role of RLVR, offers a more reliable method for its evaluation, and confirms its potential to genuinely advance machine reasoning.

The dominant paradigm for training large reasoning models starts with pre-training using next-token prediction loss on vast amounts of data. Reinforcement learning, while powerful in scaling reasoning, is introduced only as the very last phase of post-training, preceded by supervised fine-tuning. While dominant, is this an optimal way of training? In this paper, we present RLP, an information-driven reinforcement pretraining objective, that brings the core spirit of reinforcement learning -- exploration -- to the last phase of pretraining. The key idea is to treat chain-of-thought as an exploratory action, with rewards computed based on the information gain it provides for predicting future tokens. This training objective essentially encourages the model to think for itself before predicting what comes next, thus teaching an independent thinking behavior earlier in the pretraining. More concretely, the reward signal measures the increase in log-likelihood of the next token when conditioning on both context and a sampled reasoning chain, compared to conditioning on context alone. This approach yields a verifier-free dense reward signal, allowing for efficient training for the full document stream during pretraining. Specifically, RLP reframes reinforcement learning for reasoning as a pretraining objective on ordinary text, bridging the gap between next-token prediction and the emergence of useful chain-of-thought reasoning. Pretraining with RLP on Qwen3-1.7B-Base lifts the overall average across an eight-benchmark math-and-science suite by 19%. With identical post-training, the gains compound, with the largest improvements on reasoning-heavy tasks such as AIME25 and MMLU-Pro. Applying RLP to the hybrid Nemotron-Nano-12B-v2 increases the overall average from 42.81% to 61.32% and raises the average on scientific reasoning by 23%, demonstrating scalability across architectures and model sizes.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a powerful paradigm for enhancing the reasoning capabilities of LLMs. Existing research has predominantly concentrated on isolated reasoning domains such as mathematical problem-solving, coding tasks, or logical reasoning. However, real world reasoning scenarios inherently demand an integrated application of multiple cognitive skills. Despite this, the interplay among these reasoning skills under reinforcement learning remains poorly understood. To bridge this gap, we present a systematic investigation of multi-domain reasoning within the RLVR framework, explicitly focusing on three primary domains: mathematical reasoning, code generation, and logical puzzle solving. We conduct a comprehensive study comprising four key components: (1) Leveraging the GRPO algorithm and the Qwen-2.5-7B model family, our study thoroughly evaluates the models' in-domain improvements and cross-domain generalization capabilities when trained on single-domain datasets. (2) Additionally, we examine the intricate interactions including mutual enhancements and conflicts that emerge during combined cross-domain training. (3) To further understand the influence of SFT on RL, we also analyze and compare performance differences between base and instruct models under identical RL configurations. (4) Furthermore, we delve into critical RL training details, systematically exploring the impacts of curriculum learning strategies, variations in reward design, and language-specific factors. Through extensive experiments, our results offer significant insights into the dynamics governing domain interactions, revealing key factors influencing both specialized and generalizable reasoning performance. These findings provide valuable guidance for optimizing RL methodologies to foster comprehensive, multi-domain reasoning capabilities in LLMs.

The recent advent of large language models has reinvigorated debate over whether human cognitive capacities might emerge in such generic models given sufficient training data. Of particular interest is the ability of these models to reason about novel problems zero-shot, without any direct training. In human cognition, this capacity is closely tied to an ability to reason by analogy. Here, we performed a direct comparison between human reasoners and a large language model (the text-davinci-003 variant of GPT-3) on a range of analogical tasks, including a non-visual matrix reasoning task based on the rule structure of Raven's Standard Progressive Matrices. We found that GPT-3 displayed a surprisingly strong capacity for abstract pattern induction, matching or even surpassing human capabilities in most settings; preliminary tests of GPT-4 indicated even better performance. Our results indicate that large language models such as GPT-3 have acquired an emergent ability to find zero-shot solutions to a broad range of analogy problems.

This paper investigates prior prompt engineering (pPE) in the context of reinforcement fine-tuning (RFT), where language models (LMs) are incentivized to exhibit behaviors that maximize performance through reward signals. While existing RFT research has primarily focused on algorithms, reward shaping, and data curation, the design of the prior prompt--the instructions prepended to queries during training to elicit behaviors such as step-by-step reasoning--remains underexplored. We investigate whether different pPE approaches can guide LMs to internalize distinct behaviors after RFT. Inspired by inference-time prompt engineering (iPE), we translate five representative iPE strategies--reasoning, planning, code-based reasoning, knowledge recall, and null-example utilization--into corresponding pPE approaches. We experiment with Qwen2.5-7B using each of the pPE approaches, then evaluate performance on in-domain and out-of-domain benchmarks (e.g., AIME2024, HumanEval+, and GPQA-Diamond). Our results show that all pPE-trained models surpass their iPE-prompted counterparts, with the null-example pPE approach achieving the largest average performance gain and the highest improvement on AIME2024 and GPQA-Diamond, surpassing the commonly used reasoning approach. Furthermore, by adapting a behavior-classification framework, we demonstrate that different pPE strategies instill distinct behavioral styles in the resulting models. These findings position pPE as a powerful yet understudied axis for RFT.

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.

Recent work shows that reinforcement learning(RL) can markedly sharpen the reasoning ability of large language models (LLMs) by prompting them to "think before answering." Yet whether and how these gains transfer to audio-language reasoning remains largely unexplored. We extend the Group-Relative Policy Optimization (GRPO) framework from DeepSeek-R1 to a Large Audio-Language Model (LALM), and construct a 32k sample multiple-choice corpus. Using a two-stage regimen supervised fine-tuning on structured and unstructured chains-of-thought, followed by curriculum-guided GRPO, we systematically compare implicit vs. explicit, and structured vs. free form reasoning under identical architectures. Our structured audio reasoning model, SARI (Structured Audio Reasoning via Curriculum-Guided Reinforcement Learning), achieves a 16.35% improvement in average accuracy over the base model Qwen2-Audio-7B-Instruct. Furthermore, the variant built upon Qwen2.5-Omni reaches state-of-the-art performance of 67.08% on the MMAU test-mini benchmark. Ablation experiments show that on the base model we use: (i) SFT warm-up is important for stable RL training, (ii) structured chains yield more robust generalization than unstructured ones, and (iii) easy-to-hard curricula accelerate convergence and improve final performance. These findings demonstrate that explicit, structured reasoning and curriculum learning substantially enhances audio-language understanding.

Traditional neural network training typically follows fixed, predefined optimization recipes, lacking the flexibility to dynamically respond to instabilities or emerging training issues. In this paper, we introduce Interactive Training, an open-source framework that enables real-time, feedback-driven intervention during neural network training by human experts or automated AI agents. At its core, Interactive Training uses a control server to mediate communication between users or agents and the ongoing training process, allowing users to dynamically adjust optimizer hyperparameters, training data, and model checkpoints. Through three case studies, we demonstrate that Interactive Training achieves superior training stability, reduced sensitivity to initial hyperparameters, and improved adaptability to evolving user needs, paving the way toward a future training paradigm where AI agents autonomously monitor training logs, proactively resolve instabilities, and optimize training dynamics.

Recent advances leverage post-training to enhance model reasoning performance, which typically requires costly training pipelines and still suffers from inefficient, overly lengthy outputs. We introduce Speculative Thinking, a training-free framework that enables large reasoning models to guide smaller ones during inference at the reasoning level, distinct from speculative decoding, which operates at the token level. Our approach is based on two observations: (1) reasoning-supportive tokens such as "wait" frequently appear after structural delimiters like "\n\n", serving as signals for reflection or continuation; and (2) larger models exhibit stronger control over reflective behavior, reducing unnecessary backtracking while improving reasoning quality. By strategically delegating reflective steps to a more capable model, our method significantly boosts the reasoning accuracy of reasoning models while shortening their output. With the assistance of the 32B reasoning model, the 1.5B model's accuracy on MATH500 increases from 83.2% to 89.4%, marking a substantial improvement of 6.2%. Simultaneously, the average output length is reduced from 5439 tokens to 4583 tokens, representing a 15.7% decrease. Moreover, when applied to a non-reasoning model (Qwen-2.5-7B-Instruct), our framework boosts its accuracy from 74.0% to 81.8% on the same benchmark, achieving a relative improvement of 7.8%.

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

Long chain-of-thought (CoT) significantly enhances large language models' (LLM) reasoning capabilities. However, the extensive reasoning traces lead to inefficiencies and an increased time-to-first-token (TTFT). We propose a novel training paradigm that uses reinforcement learning (RL) to guide reasoning LLMs to interleave thinking and answering for multi-hop questions. We observe that models inherently possess the ability to perform interleaved reasoning, which can be further enhanced through RL. We introduce a simple yet effective rule-based reward to incentivize correct intermediate steps, which guides the policy model toward correct reasoning paths by leveraging intermediate signals generated during interleaved reasoning. Extensive experiments conducted across five diverse datasets and three RL algorithms (PPO, GRPO, and REINFORCE++) demonstrate consistent improvements over traditional think-answer reasoning, without requiring external tools. Specifically, our approach reduces TTFT by over 80% on average and improves up to 19.3% in Pass@1 accuracy. Furthermore, our method, trained solely on question answering and logical reasoning datasets, exhibits strong generalization ability to complex reasoning datasets such as MATH, GPQA, and MMLU. Additionally, we conduct in-depth analysis to reveal several valuable insights into conditional reward modeling.

While large language models (LLMs) are proficient at question-answering (QA), it is not always clear how (or even if) an answer follows from their latent "beliefs". This lack of interpretability is a growing impediment to widespread use of LLMs. To address this, our goals are to make model beliefs and their inferential relationships explicit, and to resolve inconsistencies that may exist, so that answers are supported by interpretable chains of reasoning drawn from a consistent network of beliefs. Our approach, which we call REFLEX, is to add a rational, self-reflecting layer on top of the LLM. First, given a question, we construct a belief graph using a backward-chaining process to materialize relevant model beliefs (including beliefs about answer candidates) and their inferential relationships. Second, we identify and minimize contradictions in that graph using a formal constraint reasoner. We find that REFLEX significantly improves consistency (by 8%-11% absolute) without harming overall answer accuracy, resulting in answers supported by faithful chains of reasoning drawn from a more consistent belief system. This suggests a new style of system architecture in which an LLM extended with a rational layer can provide an interpretable window into system beliefs, add a systematic reasoning capability, and repair latent inconsistencies present in the LLM.

Large Language Models (LLMs) have shown remarkable capabilities in reasoning, exemplified by the success of OpenAI-o1 and DeepSeek-R1. However, integrating reasoning with external search processes remains challenging, especially for complex multi-hop questions requiring multiple retrieval steps. We propose ReSearch, a novel framework that trains LLMs to Reason with Search via reinforcement learning without using any supervised data on reasoning steps. Our approach treats search operations as integral components of the reasoning chain, where when and how to perform searches is guided by text-based thinking, and search results subsequently influence further reasoning. We train ReSearch on Qwen2.5-7B(-Instruct) and Qwen2.5-32B(-Instruct) models and conduct extensive experiments. Despite being trained on only one dataset, our models demonstrate strong generalizability across various benchmarks. Analysis reveals that ReSearch naturally elicits advanced reasoning capabilities such as reflection and self-correction during the reinforcement learning process.

Reasoning has emerged as the next major frontier for language models (LMs), with rapid advances from both academic and industrial labs. However, this progress often outpaces methodological rigor, with many evaluations relying on benchmarking practices that lack transparency, robustness, or statistical grounding. In this work, we conduct a comprehensive empirical study and find that current mathematical reasoning benchmarks are highly sensitive to subtle implementation choices - including decoding parameters, random seeds, prompt formatting, and even hardware and software-framework configurations. Performance gains reported in recent studies frequently hinge on unclear comparisons or unreported sources of variance. To address these issues, we propose a standardized evaluation framework with clearly defined best practices and reporting standards. Using this framework, we reassess recent methods and find that reinforcement learning (RL) approaches yield only modest improvements - far below prior claims - and are prone to overfitting, especially on small-scale benchmarks like AIME24. In contrast, supervised finetuning (SFT) methods show consistently stronger generalization. To foster reproducibility, we release all code, prompts, and model outputs, for reasoning benchmarks, establishing more rigorous foundations for future work.

The proliferation of Large Language Models (LLMs) in medicine has enabled impressive capabilities, yet a critical gap remains in their ability to perform systematic, transparent, and verifiable reasoning, a cornerstone of clinical practice. This has catalyzed a shift from single-step answer generation to the development of LLMs explicitly designed for medical reasoning. This paper provides the first systematic review of this emerging field. We propose a taxonomy of reasoning enhancement techniques, categorized into training-time strategies (e.g., supervised fine-tuning, reinforcement learning) and test-time mechanisms (e.g., prompt engineering, multi-agent systems). We analyze how these techniques are applied across different data modalities (text, image, code) and in key clinical applications such as diagnosis, education, and treatment planning. Furthermore, we survey the evolution of evaluation benchmarks from simple accuracy metrics to sophisticated assessments of reasoning quality and visual interpretability. Based on an analysis of 60 seminal studies from 2022-2025, we conclude by identifying critical challenges, including the faithfulness-plausibility gap and the need for native multimodal reasoning, and outlining future directions toward building efficient, robust, and sociotechnically responsible medical AI.

Root Cause Analysis (RCA) in mobile networks remains a challenging task due to the need for interpretability, domain expertise, and causal reasoning. In this work, we propose a lightweight framework that leverages Large Language Models (LLMs) for RCA. To do so, we introduce TeleLogs, a curated dataset of annotated troubleshooting problems designed to benchmark RCA capabilities. Our evaluation reveals that existing open-source reasoning LLMs struggle with these problems, underscoring the need for domain-specific adaptation. To address this issue, we propose a two-stage training methodology that combines supervised fine-tuning with reinforcement learning to improve the accuracy and reasoning quality of LLMs. The proposed approach fine-tunes a series of RCA models to integrate domain knowledge and generate structured, multi-step diagnostic explanations, improving both interpretability and effectiveness. Extensive experiments across multiple LLM sizes show significant performance gains over state-of-the-art reasoning and non-reasoning models, including strong generalization to randomized test variants. These results demonstrate the promise of domain-adapted, reasoning-enhanced LLMs for practical and explainable RCA in network operation and management.

Chain-of-thought (CoT) reasoning has emerged as an effective approach for activating latent capabilities in large language models (LLMs). We observe that CoT shares significant similarities with self-training in terms of their learning processes. Motivated by these parallels, this paper explores the underlying relationship between CoT and self-training, demonstrating how insights from self-training can enhance CoT performance. Specifically, our study first reveals that CoT, like self-training, follows the principle of semantic entropy minimization. Leveraging this insight, we propose a novel CoT framework that incorporates two key components: (i) a task-specific prompt module designed to guide LLMs in generating high-quality initial reasoning processes, and (ii) an adaptive reasoning iteration module for progressively refining the reasoning process.

Reinforcement finetuning (RFT) has shown great potential for enhancing the mathematical reasoning capabilities of large language models (LLMs), but it is often sample- and compute-inefficient, requiring extensive training. In this work, we introduce AdaRFT (Adaptive Curriculum Reinforcement Finetuning), a method that significantly improves both the efficiency and final accuracy of RFT through adaptive curriculum learning. AdaRFT dynamically adjusts the difficulty of training problems based on the model's recent reward signals, ensuring that the model consistently trains on tasks that are challenging but solvable. This adaptive sampling strategy accelerates learning by maintaining an optimal difficulty range, avoiding wasted computation on problems that are too easy or too hard. AdaRFT requires only a lightweight extension to standard RFT algorithms like Proximal Policy Optimization (PPO), without modifying the reward function or model architecture. Experiments on competition-level math datasets-including AMC, AIME, and IMO-style problems-demonstrate that AdaRFT significantly improves both training efficiency and reasoning performance. We evaluate AdaRFT across multiple data distributions and model sizes, showing that it reduces the number of training steps by up to 2x and improves accuracy by a considerable margin, offering a more scalable and effective RFT framework.

Recent Graphical User Interface (GUI) agents replicate the R1-Zero paradigm, coupling online Reinforcement Learning (RL) with explicit chain-of-thought reasoning prior to object grounding and thereby achieving substantial performance gains. In this paper, we first conduct extensive analysis experiments of three key components of that training pipeline: input design, output evaluation, and policy update-each revealing distinct challenges arising from blindly applying general-purpose RL without adapting to GUI grounding tasks. Input design: Current templates encourage the model to generate chain-of-thought reasoning, but longer chains unexpectedly lead to worse grounding performance. Output evaluation: Reward functions based on hit signals or box area allow models to exploit box size, leading to reward hacking and poor localization quality. Policy update: Online RL tends to overfit easy examples due to biases in length and sample difficulty, leading to under-optimization on harder cases. To address these issues, we propose three targeted solutions. First, we adopt a Fast Thinking Template that encourages direct answer generation, reducing excessive reasoning during training. Second, we incorporate a box size constraint into the reward function to mitigate reward hacking. Third, we revise the RL objective by adjusting length normalization and adding a difficulty-aware scaling factor, enabling better optimization on hard samples. Our GUI-G1-3B, trained on 17K public samples with Qwen2.5-VL-3B-Instruct, achieves 90.3% accuracy on ScreenSpot and 37.1% on ScreenSpot-Pro. This surpasses all prior models of similar size and even outperforms the larger UI-TARS-7B, establishing a new state-of-the-art in GUI agent grounding. The project repository is available at https://github.com/Yuqi-Zhou/GUI-G1.

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

Large language models (LLMs) have been widely adopted as the core of agent frameworks in various scenarios, such as social simulations and AI companions. However, the extent to which they can replicate human-like motivations remains an underexplored question. Existing benchmarks are constrained by simplistic scenarios and the absence of character identities, resulting in an information asymmetry with real-world situations. To address this gap, we propose MotiveBench, which consists of 200 rich contextual scenarios and 600 reasoning tasks covering multiple levels of motivation. Using MotiveBench, we conduct extensive experiments on seven popular model families, comparing different scales and versions within each family. The results show that even the most advanced LLMs still fall short in achieving human-like motivational reasoning. Our analysis reveals key findings, including the difficulty LLMs face in reasoning about "love & belonging" motivations and their tendency toward excessive rationality and idealism. These insights highlight a promising direction for future research on the humanization of LLMs. The dataset, benchmark, and code are available at https://aka.ms/motivebench.

Developing custom reasoning models via Reinforcement Learning (RL) that can incorporate organization-specific knowledge has great potential to address problems faced by enterprise customers. In many of these problems, the reward function is verifiable, a setting termed RL with Verifiable Rewards (RLVR). We apply RLVR to a popular data science benchmark called BIRD that measures the ability of an AI agent to convert a natural language query for a database to SQL executions. We apply a simple and general-purpose training recipe involving careful prompt and model selection, a warm-up stage using our offline RL approach called TAO, followed by rigorous online RLVR training. With no additional training data beyond the BIRD training set and no use of proprietary models, our very first submission to the BIRD leaderboard reached state-of-the-art accuracy on the private test set: 73.56% without self-consistency and 75.68% with self-consistency. In the latter case, our model also required fewer generations than the second-best approach. While BIRD is only a proxy task, the simplicity of our framework makes it broadly applicable to enterprise domains such as business intelligence, data science, and coding.

Recent advances such as DeepSeek R1-Zero highlight the effectiveness of incentive training, a reinforcement learning paradigm that computes rewards solely based on the final answer part of a language model's output, thereby encouraging the generation of intermediate reasoning steps. However, these methods fundamentally rely on external verifiers, which limits their applicability to domains like mathematics and coding where such verifiers are readily available. Although reward models can serve as verifiers, they require high-quality annotated data and are costly to train. In this work, we propose NOVER, NO-VERifier Reinforcement Learning, a general reinforcement learning framework that requires only standard supervised fine-tuning data with no need for an external verifier. NOVER enables incentive training across a wide range of text-to-text tasks and outperforms the model of the same size distilled from large reasoning models such as DeepSeek R1 671B by 7.7 percent. Moreover, the flexibility of NOVER enables new possibilities for optimizing large language models, such as inverse incentive training.

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

Large Language Models (LLMs) perform complex reasoning by generating explanations for their predictions. However, a complementary goal of explanations is to also communicate useful knowledge that improves weaker agents. Hence, we investigate whether LLMs also make good teachers for weaker agents. In particular, we consider a student-teacher framework between two LLM agents and study if, when, and how the teacher should intervene with natural language explanations to improve the student's performance. Since communication is expensive, we define a budget such that the teacher only communicates explanations for a fraction of the data, after which the student should perform well on its own. We decompose the teaching problem along four axes: (1) if teacher's test time intervention improve student predictions, (2) when it is worth explaining a data point, (3) how the teacher should personalize explanations to better teach the student, and (4) if teacher explanations also improve student performance on future unexplained data. We first show that teacher LLMs can indeed intervene on student reasoning to improve their performance. Next, we propose a Theory of Mind approach, in which the teacher builds two few-shot mental models of the student. The first model defines an Intervention Function that simulates the utility of an intervention, allowing the teacher to intervene when this utility is the highest and improving student performance at lower budgets. The second model enables the teacher to personalize explanations for a particular student and outperform unpersonalized teachers. We also demonstrate that in multi-turn interactions, teacher explanations generalize and learning from explained data improves student performance on future unexplained data. Finally, we also verify that misaligned teachers can lower student performance to random chance by intentionally misleading them.

Different base language model families, such as Llama and Qwen, exhibit divergent behaviors during post-training with reinforcement learning (RL), especially on reasoning-intensive tasks. What makes a base language model suitable for reinforcement learning? Gaining deeper insight into this question is essential for developing RL-scalable foundation models of the next generation. In this work, we investigate how mid-training strategies shape RL dynamics, focusing on two representative model families: Qwen and Llama. Our study reveals that (1) high-quality mathematical corpora, such as MegaMath-Web-Pro, significantly improve both base model and RL performance, while existing alternatives (e.g., FineMath-4plus) fail to do so; (2) further adding QA-style data, particularly long chain-of-thought (CoT) reasoning examples, enhances RL outcomes, and instruction data further unlocks this effect; (3) while long-CoT improves reasoning depth, it can also induce verbosity of model responses and unstability of RL training, underscoring the importance of data formatting; (4) scaling mid-training consistently leads to stronger downstream RL performance. Building on these insights, we introduce a two-stage mid-training strategy, Stable-then-Decay, in which base models are first trained on 200B tokens with a constant learning rate, followed by 20B tokens across three CoT-focused branches with learning rate decay. This yields OctoThinker, a family of models demonstrating strong RL compatibility and closing the performance gap with more RL-friendly model families, i.e., Qwen. We hope our work will help shape pre-training strategies for foundation models in the RL era. To support further research, we release our open-source models along with a curated math reasoning-intensive corpus of over 70 billion tokens (i.e., MegaMath-Web-Pro-Max).

Prompting Large Language Models (LLMs), or providing context on the expected model of operation, is an effective way to steer the outputs of such models to satisfy human desiderata after they have been trained. But in rapidly evolving domains, there is often need to fine-tune LLMs to improve either the kind of knowledge in their memory or their abilities to perform open ended reasoning in new domains. When human's learn new concepts, we often do so by linking the new material that we are studying to concepts we have already learned before. To that end, we ask, "can prompting help us teach LLMs how to learn". In this work, we study a novel generalization of instruction tuning, called contextual fine-tuning, to fine-tune LLMs. Our method leverages instructional prompts designed to mimic human cognitive strategies in learning and problem-solving to guide the learning process during training, aiming to improve the model's interpretation and understanding of domain-specific knowledge. We empirically demonstrate that this simple yet effective modification improves the ability of LLMs to be fine-tuned rapidly on new datasets both within the medical and financial domains.

Scaling inference compute enhances reasoning in large language models (LLMs), with long chains-of-thought (CoTs) enabling strategies like backtracking and error correction. Reinforcement learning (RL) has emerged as a crucial method for developing these capabilities, yet the conditions under which long CoTs emerge remain unclear, and RL training requires careful design choices. In this study, we systematically investigate the mechanics of long CoT reasoning, identifying the key factors that enable models to generate long CoT trajectories. Through extensive supervised fine-tuning (SFT) and RL experiments, we present four main findings: (1) While SFT is not strictly necessary, it simplifies training and improves efficiency; (2) Reasoning capabilities tend to emerge with increased training compute, but their development is not guaranteed, making reward shaping crucial for stabilizing CoT length growth; (3) Scaling verifiable reward signals is critical for RL. We find that leveraging noisy, web-extracted solutions with filtering mechanisms shows strong potential, particularly for out-of-distribution (OOD) tasks such as STEM reasoning; and (4) Core abilities like error correction are inherently present in base models, but incentivizing these skills effectively for complex tasks via RL demands significant compute, and measuring their emergence requires a nuanced approach. These insights provide practical guidance for optimizing training strategies to enhance long CoT reasoning in LLMs. Our code is available at: https://github.com/eddycmu/demystify-long-cot.

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

Intent detection, a critical component in task-oriented dialogue (TOD) systems, faces significant challenges in adapting to the rapid influx of integrable tools with complex interrelationships. Existing approaches, such as zero-shot reformulations and LLM-based dynamic recognition, struggle with performance degradation when encountering unseen intents, leading to erroneous task routing. To enhance the model's generalization performance on unseen tasks, we employ Reinforcement Learning (RL) combined with a Reward-based Curriculum Sampling (RCS) during Group Relative Policy Optimization (GRPO) training in intent detection tasks. Experiments demonstrate that RL-trained models substantially outperform supervised fine-tuning (SFT) baselines in generalization. Besides, the introduction of the RCS, significantly bolsters the effectiveness of RL in intent detection by focusing the model on challenging cases during training. Moreover, incorporating Chain-of-Thought (COT) processes in RL notably improves generalization in complex intent detection tasks, underscoring the importance of thought in challenging scenarios. This work advances the generalization of intent detection tasks, offering practical insights for deploying adaptable dialogue systems.

Reasoning methods that adaptively allocate test-time compute have advanced LLM performance on easy to verify domains such as math and code. In this work, we study how to utilize this approach to train models that exhibit a degree of robustness to safety vulnerabilities, and show that doing so can provide benefits. We build a recipe called TARS (Training Adaptive Reasoners for Safety), a reinforcement learning (RL) approach that trains models to reason about safety using chain-of-thought traces and a reward signal that balances safety with task completion. To build TARS, we identify three critical design choices: (1) a "lightweight" warmstart SFT stage, (2) a mix of harmful, harmless, and ambiguous prompts to prevent shortcut behaviors such as too many refusals, and (3) a reward function to prevent degeneration of reasoning capabilities during training. Models trained with TARS exhibit adaptive behaviors by spending more compute on ambiguous queries, leading to better safety-refusal trade-offs. They also internally learn to better distinguish between safe and unsafe prompts and attain greater robustness to both white-box (e.g., GCG) and black-box attacks (e.g., PAIR). Overall, our work provides an effective, open recipe for training LLMs against jailbreaks and harmful requests by reasoning per prompt.

Reinforcement learning (RL) has significantly advanced code generation for large language models (LLMs). However, current paradigms rely on outcome-based rewards from test cases, neglecting the quality of the intermediate reasoning process. While supervising the reasoning process directly is a promising direction, it is highly susceptible to reward hacking, where the policy model learns to exploit the reasoning reward signal without improving final outcomes. To address this, we introduce a unified framework that can effectively incorporate the quality of the reasoning process during RL. First, to enable reasoning evaluation, we develop LCB-RB, a benchmark comprising preference pairs of superior and inferior reasoning processes. Second, to accurately score reasoning quality, we introduce an Optimized-Degraded based (OD-based) method for reward model training. This method generates high-quality preference pairs by systematically optimizing and degrading initial reasoning paths along curated dimensions of reasoning quality, such as factual accuracy, logical rigor, and coherence. A 7B parameter reward model with this method achieves state-of-the-art (SOTA) performance on LCB-RB and generalizes well to other benchmarks. Finally, we introduce Posterior-GRPO (P-GRPO), a novel RL method that conditions process-based rewards on task success. By selectively applying rewards to the reasoning processes of only successful outcomes, P-GRPO effectively mitigates reward hacking and aligns the model's internal reasoning with final code correctness. A 7B parameter model with P-GRPO achieves superior performance across diverse code generation tasks, outperforming outcome-only baselines by 4.5%, achieving comparable performance to GPT-4-Turbo. We further demonstrate the generalizability of our approach by extending it to mathematical tasks. Our models, dataset, and code are publicly available.

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

Recent advances have shown success in eliciting strong reasoning abilities in multimodal large language models (MLLMs) through rule-based reinforcement learning (RL) with outcome rewards. However, this paradigm typically lacks supervision over the thinking process leading to the final outcome.As a result, the model may learn sub-optimal reasoning strategies, which can hinder its generalization ability. In light of this, we propose SophiaVL-R1, as an attempt to add reward signals for the thinking process in this paradigm. To achieve this, we first train a thinking reward model that evaluates the quality of the entire thinking process. Given that the thinking reward may be unreliable for certain samples due to reward hacking, we propose the Trust-GRPO method, which assigns a trustworthiness weight to the thinking reward during training. This weight is computed based on the thinking reward comparison of responses leading to correct answers versus incorrect answers, helping to mitigate the impact of potentially unreliable thinking rewards. Moreover, we design an annealing training strategy that gradually reduces the thinking reward over time, allowing the model to rely more on the accurate rule-based outcome reward in later training stages. Experiments show that our SophiaVL-R1 surpasses a series of reasoning MLLMs on various benchmarks (e.g., MathVisita, MMMU), demonstrating strong reasoning and generalization capabilities. Notably, our SophiaVL-R1-7B even outperforms LLaVA-OneVision-72B on most benchmarks, despite the latter having 10 times more parameters. All code, models, and datasets are made publicly available at https://github.com/kxfan2002/SophiaVL-R1.

We introduce INTELLECT-2, the first globally distributed reinforcement learning (RL) training run of a 32 billion parameter language model. Unlike traditional centralized training efforts, INTELLECT-2 trains a reasoning model using fully asynchronous RL across a dynamic, heterogeneous swarm of permissionless compute contributors. To enable a training run with this unique infrastructure, we built various components from scratch: we introduce PRIME-RL, our training framework purpose-built for distributed asynchronous reinforcement learning, based on top of novel components such as TOPLOC, which verifies rollouts from untrusted inference workers, and SHARDCAST, which efficiently broadcasts policy weights from training nodes to inference workers. Beyond infrastructure components, we propose modifications to the standard GRPO training recipe and data filtering techniques that were crucial to achieve training stability and ensure that our model successfully learned its training objective, thus improving upon QwQ-32B, the state of the art reasoning model in the 32B parameter range. We open-source INTELLECT-2 along with all of our code and data, hoping to encourage and enable more open research in the field of decentralized training.

We present a demonstration of a large language model engaging in alignment faking: selectively complying with its training objective in training to prevent modification of its behavior out of training. First, we give Claude 3 Opus a system prompt stating it is being trained to answer all queries, even harmful ones, which conflicts with its prior training to refuse such queries. To allow the model to infer when it is in training, we say it will be trained only on conversations with free users, not paid users. We find the model complies with harmful queries from free users 14% of the time, versus almost never for paid users. Explaining this gap, in almost all cases where the model complies with a harmful query from a free user, we observe explicit alignment-faking reasoning, with the model stating it is strategically answering harmful queries in training to preserve its preferred harmlessness behavior out of training. Next, we study a more realistic setting where information about the training process is provided not in a system prompt, but by training on synthetic documents that mimic pre-training data--and observe similar alignment faking. Finally, we study the effect of actually training the model to comply with harmful queries via reinforcement learning, which we find increases the rate of alignment-faking reasoning to 78%, though also increases compliance even out of training. We additionally observe other behaviors such as the model exfiltrating its weights when given an easy opportunity. While we made alignment faking easier by telling the model when and by what criteria it was being trained, we did not instruct the model to fake alignment or give it any explicit goal. As future models might infer information about their training process without being told, our results suggest a risk of alignment faking in future models, whether due to a benign preference--as in this case--or not.

We present Klear-Reasoner, a model with long reasoning capabilities that demonstrates careful deliberation during problem solving, achieving outstanding performance across multiple benchmarks. Although there are already many excellent works related to inference models in the current community, there are still many problems with reproducing high-performance inference models due to incomplete disclosure of training details. This report provides an in-depth analysis of the reasoning model, covering the entire post-training workflow from data preparation and long Chain-of-Thought supervised fine-tuning (long CoT SFT) to reinforcement learning (RL), along with detailed ablation studies for each experimental component. For SFT data, our experiments show that a small number of high-quality data sources are more effective than a large number of diverse data sources, and that difficult samples can achieve better results without accuracy filtering. In addition, we investigate two key issues with current clipping mechanisms in RL: Clipping suppresses critical exploration signals and ignores suboptimal trajectories. To address these challenges, we propose Gradient-Preserving clipping Policy Optimization (GPPO) that gently backpropagates gradients from clipped tokens. GPPO not only enhances the model's exploration capacity but also improves its efficiency in learning from negative samples. Klear-Reasoner exhibits exceptional reasoning abilities in mathematics and programming, scoring 90.5\% on AIME 2024, 83.2\% on AIME 2025, 66.0\% on LiveCodeBench V5 and 58.1\% on LiveCodeBench V6.