Daily Papers

Enhancing large language models (LLMs) with real-time APIs can help generate more accurate and up-to-date responses. However, evaluating the function calling abilities of LLMs in real-world scenarios remains under-explored due to the complexity of data collection and evaluation. In this work, we introduce ComplexFuncBench, a benchmark for complex function calling across five real-world scenarios. Compared to existing benchmarks, ComplexFuncBench encompasses multi-step and constrained function calling, which requires long-parameter filing, parameter value reasoning, and 128k long context. Additionally, we propose an automatic framework, ComplexEval, for quantitatively evaluating complex function calling tasks. Through comprehensive experiments, we demonstrate the deficiencies of state-of-the-art LLMs in function calling and suggest future directions for optimizing these capabilities. The data and code are available at https://github.com/THUDM/ComplexFuncBench.

We show that PLDR-LLMs pretrained at self-organized criticality exhibit reasoning at inference time. The characteristics of PLDR-LLM deductive outputs at criticality is similar to second-order phase transitions. At criticality, the correlation length diverges, and the deductive outputs attain a metastable steady state. The steady state behaviour suggests that deductive outputs learn representations equivalent to scaling functions, universality classes and renormalization groups from the training dataset, leading to generalization and reasoning capabilities in the process. We can then define an order parameter from the global statistics of the model's deductive output parameters at inference. The reasoning capabilities of a PLDR-LLM is better when its order parameter is close to zero at criticality. This observation is supported by the benchmark scores of the models trained at near-criticality and sub-criticality. Our results provide a self-contained explanation on how reasoning manifests in large language models, and the ability to reason can be quantified solely from global model parameter values of the deductive outputs at steady state, without any need for evaluation of curated benchmark datasets through inductive output for reasoning and comprehension.

Recent Large Reasoning Language Models (LRLMs) employ long chain-of-thought reasoning with complex reflection behaviors, typically signaled by specific trigger words (e.g., "Wait" and "Alternatively") to enhance performance. However, these reflection behaviors can lead to the overthinking problem where the generation of redundant reasoning steps that unnecessarily increase token usage, raise inference costs, and reduce practical utility. In this paper, we propose Certainty-Guided Reflection Suppression (CGRS), a novel method that mitigates overthinking in LRLMs while maintaining reasoning accuracy. CGRS operates by dynamically suppressing the model's generation of reflection triggers when it exhibits high confidence in its current response, thereby preventing redundant reflection cycles without compromising output quality. Our approach is model-agnostic, requires no retraining or architectural modifications, and can be integrated seamlessly with existing autoregressive generation pipelines. Extensive experiments across four reasoning benchmarks (i.e., AIME24, AMC23, MATH500, and GPQA-D) demonstrate CGRS's effectiveness: it reduces token usage by an average of 18.5% to 41.9% while preserving accuracy. It also achieves the optimal balance between length reduction and performance compared to state-of-the-art baselines. These results hold consistently across model architectures (e.g., DeepSeek-R1-Distill series, QwQ-32B, and Qwen3 family) and scales (4B to 32B parameters), highlighting CGRS's practical value for efficient reasoning.

Understanding and reasoning over non-speech sounds and music are crucial for both humans and AI agents to interact effectively with their environments. In this paper, we introduce Audio Flamingo 2 (AF2), an Audio-Language Model (ALM) with advanced audio understanding and reasoning capabilities. AF2 leverages (i) a custom CLAP model, (ii) synthetic Audio QA data for fine-grained audio reasoning, and (iii) a multi-stage curriculum learning strategy. AF2 achieves state-of-the-art performance with only a 3B parameter small language model, surpassing large open-source and proprietary models across over 20 benchmarks. Next, for the first time, we extend audio understanding to long audio segments (30 secs to 5 mins) and propose LongAudio, a large and novel dataset for training ALMs on long audio captioning and question-answering tasks. Fine-tuning AF2 on LongAudio leads to exceptional performance on our proposed LongAudioBench, an expert annotated benchmark for evaluating ALMs on long audio understanding capabilities. We conduct extensive ablation studies to confirm the efficacy of our approach. Project Website: https://research.nvidia.com/labs/adlr/AF2/.

Large pre-trained Transformer models achieve state-of-the-art results across diverse language and reasoning tasks, but full fine-tuning incurs substantial storage, memory, and computational overhead. Parameter-efficient fine-tuning (PEFT) methods mitigate these costs by learning only a small subset of task-specific parameters, yet existing approaches either introduce inference-time latency (adapter modules), suffer from suboptimal convergence (randomly initialized low-rank updates), or rely on fixed rank choices that may not match task complexity (Kronecker-based decompositions). We propose SoKA (SVD on Kronecker Adaptation), a novel PEFT strategy that combines Kronecker-product tensor factorization with SVD-driven initialization and spectrum-aware dynamic rank selection. Our Kronecker-Product SVD (KPSVD) procedure extracts principal components of the full weight update into compact Kronecker factors, while an adaptive rank selection algorithm uses energy-threshold and elbow-point criteria to prune negligible components. Empirical evaluation on LLaMA2-7B across arithmetic reasoning (GSM8K), formal mathematics (MATH), and code generation (MBPP) demonstrates that SoKA requires only 0.99M trainable parameters, 25% fewer than LoRA/PiSSA, while matching or exceeding baseline performance. Moreover, SoKA exhibits faster convergence and more stable gradients, highlighting its robustness and efficiency for large-scale model adaptation.

Large language models (LLMs) have demonstrated remarkable capabilities in function calling for autonomous agents, yet current mechanisms lack explicit reasoning transparency during parameter generation, particularly for complex functions with interdependent parameters. While existing approaches like chain-of-thought prompting operate at the agent level, they fail to provide fine-grained reasoning guidance for individual function parameters. To address these limitations, we propose Think-Augmented Function Calling (TAFC), a novel framework that enhances function calling accuracy through explicit reasoning at both function and parameter levels. Our method introduces a universal "think" parameter augmentation that enables models to articulate their decision-making process, with dynamic optimization for parameter descriptions to improve reasoning quality. For complex parameters, TAFC automatically triggers granular reasoning based on complexity scoring, ensuring appropriate justification for critical decisions. Additionally, we propose reasoning-guided optimization to align generated reasoning with human expectations. TAFC requires no architectural modifications to existing LLMs while maintaining full API compatibility. Evaluation on ToolBench across proprietary and open-source models demonstrates significant improvements in parameter generation accuracy and reasoning coherence for multi-parameter functions, while providing enhanced interpretability for debugging AI agent behaviors.

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

Can reinforcement learning with hard, verifiable rewards teach a compact language model to reason about physics, or does it primarily learn to pattern-match toward correct answers? We study this question by training a 1.5B-parameter reasoning model on beam statics, a classic engineering problem, using parameter-efficient RLVR with binary correctness rewards from symbolic solvers, without teacher-generated reasoning traces. The best BeamPERL checkpoint achieves a 66.7% improvement in Pass@1 over the base model. However, the learned competence is anisotropic: the model generalizes compositionally (more loads) but fails under topological shifts (moved supports) that require the same equilibrium equations. Intermediate checkpoints yield the strongest reasoning, while continued optimization degrades robustness while maintaining reward. These findings reveal a key limitation of outcome-level alignment: reinforcement learning with exact physics rewards induces procedural solution templates rather than internalization of governing equations. The precision of the reward signal - even when analytically exact - does not by itself guarantee transferable physical reasoning. Our results suggest that verifiable rewards may need to be paired with structured reasoning scaffolding to move beyond template matching toward robust scientific reasoning.

We present VAPO, Value-based Augmented Proximal Policy Optimization framework for reasoning models., a novel framework tailored for reasoning models within the value-based paradigm. Benchmarked the AIME 2024 dataset, VAPO, built on the Qwen 32B pre-trained model, attains a state-of-the-art score of 60.4. In direct comparison under identical experimental settings, VAPO outperforms the previously reported results of DeepSeek-R1-Zero-Qwen-32B and DAPO by more than 10 points. The training process of VAPO stands out for its stability and efficiency. It reaches state-of-the-art performance within a mere 5,000 steps. Moreover, across multiple independent runs, no training crashes occur, underscoring its reliability. This research delves into long chain-of-thought (long-CoT) reasoning using a value-based reinforcement learning framework. We pinpoint three key challenges that plague value-based methods: value model bias, the presence of heterogeneous sequence lengths, and the sparsity of reward signals. Through systematic design, VAPO offers an integrated solution that effectively alleviates these challenges, enabling enhanced performance in long-CoT reasoning tasks.

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.

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.

This paper presents a practical investigation into fine-tuning model parameters for mathematical reasoning tasks through experimenting with various configurations including randomness control, reasoning depth, and sampling strategies, careful tuning demonstrates substantial improvements in efficiency as well as performance. A holistically optimized framework is introduced for five state-of-the-art models on mathematical reasoning tasks, exhibiting significant performance boosts while maintaining solution correctness. Through systematic parameter optimization across Qwen2.5-72B, Llama-3.1-70B, DeepSeek-V3, Mixtral-8x22B, and Yi-Lightning, consistent efficiency gains are demonstrated with 100% optimization success rate. The methodology achieves an average 29.4% reduction in computational cost and 23.9% improvement in inference speed across all tested models. This framework systematically searches parameter spaces including temperature (0.1-0.5), reasoning steps (4-12), planning periods (1-4), and nucleus sampling (0.85-0.98), determining optimal configurations through testing on mathematical reasoning benchmarks. Critical findings show that lower temperature regimes (0.1-0.4) and reduced reasoning steps (4-6) consistently enhance efficiency without compromising accuracy. DeepSeek-V3 achieves the highest accuracy at 98%, while Mixtral-8x22B delivers the most cost-effective performance at 361.5 tokens per accurate response. Key contributions include: (1) the first comprehensive optimization study for five diverse SOTA models in mathematical reasoning, (2) a standardized production-oriented parameter optimization framework, (3) discovery of universal optimization trends applicable across model architectures, and (4) production-ready configurations with extensive performance characterization.

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.

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.

How cost-effectively can strong reasoning abilities be achieved in language models? Driven by this fundamental question, we present Tina, a family of tiny reasoning models achieved with high cost-efficiency. Notably, Tina demonstrates that substantial reasoning performance can be developed using only minimal resources, by applying parameter-efficient updates during reinforcement learning (RL), using low-rank adaptation (LoRA), to an already tiny 1.5B parameter base model. This minimalist approach produces models that achieve reasoning performance which is competitive with, and sometimes surpasses, SOTA RL reasoning models built upon the same base model. Crucially, this is achieved at a tiny fraction of the computational post-training cost employed by existing SOTA models. In fact, the best Tina model achieves a >20\% reasoning performance increase and 43.33\% Pass@1 accuracy on AIME24, at only \$9 USD post-training and evaluation cost (i.e., an estimated 260x cost reduction). Our work reveals the surprising effectiveness of efficient RL reasoning via LoRA. We validate this across multiple open-source reasoning datasets and various ablation settings starting with a single, fixed set of hyperparameters. Furthermore, we hypothesize that this effectiveness and efficiency stem from LoRA rapidly adapting the model to the structural format of reasoning rewarded by RL, while largely preserving the base model's underlying knowledge. In service of accessibility and open research, we fully open-source all code, training logs, and model weights \& checkpoints.

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

Reasoning is an essential capacity for large language models (LLMs) to address complex tasks, where the identification of process errors is vital for improving this ability. Recently, process-level reward models (PRMs) were proposed to provide step-wise rewards that facilitate reinforcement learning and data production during training and guide LLMs toward correct steps during inference, thereby improving reasoning accuracy. However, existing benchmarks of PRMs are text-based and focus on error detection, neglecting other scenarios like reasoning search. To address this gap, we introduce MPBench, a comprehensive, multi-task, multimodal benchmark designed to systematically assess the effectiveness of PRMs in diverse scenarios. MPBench employs three evaluation paradigms, each targeting a specific role of PRMs in the reasoning process: (1) Step Correctness, which assesses the correctness of each intermediate reasoning step; (2) Answer Aggregation, which aggregates multiple solutions and selects the best one; and (3) Reasoning Process Search, which guides the search for optimal reasoning steps during inference. Through these paradigms, MPBench makes comprehensive evaluations and provides insights into the development of multimodal PRMs.

Process reward models (PRMs) play a central role in guiding inference-time scaling algorithms for large language models (LLMs). However, we observe that even state-of-the-art PRMs can be poorly calibrated and often overestimate success probabilities. To address this, we present a calibration approach, performed via quantile regression, that adjusts PRM outputs to better align with true success probabilities. Leveraging these calibrated success estimates and their associated confidence bounds, we introduce an instance-adaptive scaling (IAS) framework that dynamically adjusts the inference budget based on the estimated likelihood that a partial reasoning trajectory will yield a correct final answer. Unlike conventional methods that allocate a fixed number of reasoning trajectories per query, this approach successfully adapts to each instance and reasoning step when using our calibrated PRMs. Experiments on mathematical reasoning benchmarks show that (i) our PRM calibration method successfully achieves small calibration error, outperforming the baseline methods, (ii) calibration is crucial for enabling effective adaptive scaling, and (iii) the proposed IAS strategy reduces inference costs while maintaining final answer accuracy, utilizing less compute on more confident problems as desired.

Reasoning language models have demonstrated remarkable performance on many challenging tasks in math, science, and coding. Choosing the right reasoning model for practical deployment involves a performance and cost tradeoff at two key levels: model size and reasoning budget, where larger models and higher reasoning budget lead to better performance but with increased cost and latency. In this work, we tackle this tradeoff from the angle of model configuration routing for different queries, and present RADAR (Reasoning-Ability and Difficulty-Aware Routing), a lightweight, interpretable, and scalable routing framework. Inspired by psychometrics, RADAR learns an item response model from model responses with different budgets to different queries, with interpretable parameters including query difficulties and model-budget abilities. RADAR then routes queries with higher difficulty to model-budget pairs with higher ability, and vice versa. We conduct extensive experiments on 8 widely used challenging reasoning benchmarks, demonstrating the superior performance of RADAR compared to state-of-the-art model routing methods. RADAR also exhibits query generalization capabilities, showing strong performance on out-of-distribution queries in all benchmarks. RADAR is also scalable and can efficiently integrate additional models by dynamically selecting a small set of evaluation queries to estimate their abilities.

We study reasoning for accessing world knowledge stored in a language model's parameters. For example, recalling that Canberra is Australia's capital may benefit from thinking through major cities and the concept of purpose-built capitals. While reasoning language models are trained via reinforcement learning to produce reasoning traces on tasks such as mathematics, they may not reason well for accessing their own world knowledge. We first find that models do not generate their best world knowledge reasoning by default: adding a simple "think step-by-step" cue demonstrates statistically significant improvement in knowledge recall but not math. Motivated by this, we propose training models to reason over their parametric knowledge using world-knowledge question answering as a verifiable reward. After reinforcement learning on TriviaQA (+9.9%), performance also improves on Natural Questions, HotpotQA, SimpleQA, and StrategyQA by 4.2%, 2.1%, 0.6%, and 3.0%, respectively. Reasoning models are under-optimized for parametric knowledge access, but can be easily trained to reason better.

Language models can use verifiable rewards to improve at a wide variety of reasoning tasks. However, both parametric (e.g. RLVR) and non-parametric (e.g. prompt optimization) approaches to doing so typically require hundreds of training samples and thousands of model rollouts, making them expensive in the best case and intractable in the worst. To address this challenge, we introduce Contrastive Reflection (CORE), a non-parametric learning algorithm that compares past reasoning traces to generate insights: short natural-language descriptions of reasoning strategies and constraints that capture differences between successful and unsuccessful problem attempts. Across four reasoning tasks, we demonstrate that CORE enables more rapid improvement than both parametric (GRPO) and non-parametric (GEPA, episodic RAG, and MemRL) methods, while using fewer rollouts. Under fixed rollout budgets with as few as five training samples, we then show that CORE also achieves comparable or greater performance gains than each baseline. Finally, we highlight how CORE is also substantially more context-efficient than non-parametric baselines, requiring fewer prompt tokens while storing learned knowledge as compact, interpretable natural-language insights. Our results therefore suggest that distilling contrasts between successful and unsuccessful reasoning traces into abstract and useful insights can provide a more efficient and interpretable route to model self-improvement than weight updates, prompt optimization, or direct reuse of stored reasoning traces.

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.

Large language models often require costly optimization, such as reinforcement learning, to master complex reasoning tasks. This work demonstrates that reasoning ability, once learned, can be extracted and transferred between models as a compact task vector. We source two publicly available, identically initialized Qwen2.5 models, one fine-tuned with supervised fine-tuning (SFT) and the other with group relative policy optimization (GRPO) on the same dataset. From these, we extract a reasoning vector: v_{reason} = theta_{GRPO} - theta_{SFT}. We hypothesize that this vector captures the reasoning capability instilled by reinforcement learning while factoring out shared knowledge from the SFT process. When added to compatible instruction-tuned models through simple arithmetic, this vector consistently improves performance across diverse reasoning benchmarks: GSM8K (+4.9%), HumanEval (+4.3%), SciQ (+1.7%), and BigBenchHard (+12.3% for the 1.5B model). The performance improvements persist under adversarial conditions. Conversely, subtracting the vector causes significant performance degradation (-11.8% on GSM8K), demonstrating the vector's strong contribution to the model's reasoning abilities. This work shows how reasoning capabilities, typically developed through expensive training, can be extracted from existing open-source models and reused through simple tensor arithmetic, offering a practical way to enhance models by recycling prior computational investments.

Recent advancements in large language models (LLMs) have substantially enhanced their mathematical reasoning abilities. However, these models still struggle with complex problems that require multiple reasoning steps, frequently leading to logical or numerical errors. While numerical mistakes can be largely addressed by integrating a code interpreter, identifying logical errors within intermediate steps is more challenging. Moreover, manually annotating these steps for training is not only expensive but also labor-intensive, requiring the expertise of professional annotators. In our study, we introduce an innovative approach that bypasses the need for process annotations (from human or GPTs) by utilizing the Monte Carlo Tree Search (MCTS) framework. This technique automatically generates both the process supervision and the step-level evaluation signals. Our method iteratively trains the policy and value models, leveraging the capabilities of a well-pretrained LLM to progressively enhance its mathematical reasoning skills. Furthermore, we propose an efficient inference strategy-step-level beam search, where the value model is crafted to assist the policy model (i.e., LLM) in navigating more effective reasoning paths, rather than solely relying on prior probabilities. The experimental results on both in-domain and out-of-domain datasets demonstrate that even without GPT-4 or human-annotated process supervision, our AlphaMath framework achieves comparable or superior results to previous state-of-the-art methods.

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.

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 mechanism by which RL contributes to reasoning capabilities-whether it incentivizes the synthesis of new skills or merely amplifies existing behaviors-remains a subject of intense debate. In this work, we investigate this question through the lens of Complementary Reasoning, a complex task that requires integrating internal parametric knowledge with external contextual information. Using a controlled synthetic dataset of human biographies, we strictly decouple this ability into two atomic skills: Parametric Reasoning (relying on internal knowledge) and Contextual Reasoning (depending on external information). To rigorously assess capability boundaries, we evaluate generalization across three distinct levels of difficulty: I.I.D., Composition, and Zero-shot settings. We find that while SFT is sufficient for in-distribution performance, it struggles with O.O.D. generalization, particularly in Zero-shot settings where relational combinations are novel. Crucially, we identify the SFT Generalization Paradox: Models supervised solely on the composite task achieve near-perfect in-distribution accuracy but collapse on out-of-distribution generalization, indicating their reliance on rote memorization of path shortcuts. In contrast, we find that RL acts as a reasoning synthesizer rather than a probability amplifier. However, we uncover a strict atomic prerequisite: RL can only synthesize these complex strategies if the base model has first mastered the independent atomic skills (Parametric and Contextual) via SFT. These findings challenge the view of RL as a mere amplifier, suggesting that given sufficient atomic foundations, RL can actively synthesize complex reasoning strategies from learned primitives without explicit supervision on such complex strategies. This indicates that decoupled atomic training followed by RL offers a scalable path to generalization for complex reasoning tasks.

Large language models (LLMs) often struggle with maintaining accuracy across a sequence of intermediate reasoning steps in mathematical reasoning, leading to error propagation that undermines the final result. The current methodology to mitigate this issue primarily involves using a verifier model to assess the correctness of generated solution candidates, focusing either on the overall reasoning path or on an incomplete reasoning path. By rethinking this approach, we argue that assessing potentials of incomplete reasoning paths could be more advantageous as it guides towards correct final answers, transforming the task into a planning problem. Our proposed verifier, the Outcome-supervision Value Model (OVM), employs outcome supervision for training, offering an efficient and intuitive method for planning by prioritizing steps that lead to accurate conclusions over mere per-step correctness. Furthermore, the OVM eschews the need for labor-intensive annotations on step-level correctness, enhancing its scalability. Our experiments on two multi-step mathematical reasoning datasets, GSM8K and Game of 24, demonstrate the superior performance of the OVM model. Notably, in GSM8K, our OVM-7B model achieves state-of-the-art results among LLMs up to 13B parameters; especially it does not utilize GPT-4 or code execution. These findings offer a novel perspective on the role of outcome supervision in training verifiers for multi-step reasoning tasks and provide theoretical justification for its advantage in value estimation for planning.

This technical report introduces VibeThinker-3B, a compact dense model with 3B parameters developed to investigate how far verifiable reasoning can be pushed within a strictly small-model regime. Building upon the Spectrum-to-Signal post-training paradigm, we systematically enhance the model through an optimized pipeline that includes curriculum-based supervised fine-tuning, multi-domain reinforcement learning, and offline self-distillation. Experimental evaluations demonstrate that VibeThinker-3B achieves frontier-level performance on highly demanding verifiable tasks. Specifically, it attains a score of 94.3 on AIME26 (improving to 97.1 with claim-level test-time scaling), an 80.2 Pass@1 on LiveCodeBench v6, and exhibits strong out-of-distribution generalization with a 96.1\% acceptance rate on recent unseen LeetCode contests. This effectively places it in the performance band of first-tier reasoning systems, matching or exceeding flagship models that are orders of magnitude larger, such as DeepSeek V3.2, GLM-5, and Gemini 3 Pro. Furthermore, a score of 93.4 on IFEval confirms that this extreme reasoning enhancement does not compromise strict instruction controllability. Extending our previous 1.5B work, these findings motivate the Parametric Compression-Coverage Hypothesis, which views verifiable reasoning as compressible into compact reasoning cores, while open-domain knowledge and general-purpose competence require broad parameter coverage over facts, concepts, and long-tail scenarios. This perspective suggests that compact models are not merely deployment-efficient substitutes, but a complementary path toward frontier-level performance in parameter-dense capability regimes.

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

We show that training a single d-dimensional steering vector per layer with reinforcement learning, while freezing all base weights, matches the accuracy of fully RL-tuned reasoning models on mathematical-reasoning tasks. On an 8 billion-parameter model this adds only approx 0.0016% additional parameters and reproduces performance across a range of base models and mathematical-reasoning benchmarks. These results tighten the upper bound on the parameter budget required for high-level chain-of-thought reasoning, indicating that millions of adapter weights are unnecessary. The minimal trainable footprint reduces optimizer memory and inter-GPU communication, lowering the overall cost of fine-tuning. Moreover, a logit-lens analysis shows that the learned vectors amplify coherent token directions, providing clearer insight into the model's internal computations.

Reasoning in large language models is typically trained via supervised fine-tuning (SFT) on expert traces, often framed as knowledge distillation, or reinforcement learning (RL) with outcome-based verifiable rewards. However, SFT focuses on imitation rather than optimisation, while outcome-based RL requires a well-defined reward function. We propose an inverse reinforcement learning (IRL) framework that learns (partially) dense token-level reasoning reward models directly from expert demonstrations. We show that this learned reward serves a dual purpose: (1) as a dense training signal that optimises policies to reason more effectively, outperforming SFT baselines on GSM8K (79\% vs. 56\%) and MedReason (74\% vs. 65\%); and (2) as an inference-time assistant that improves performance via reward-guided reranking, yielding gains of up to 12 percentage points on Llama3 architectures. Furthermore, our dense rewards provide interpretable, step-wise diagnostics that can indicate the location of logical errors. This work proposes a process-level reasoning learning framework from data, bridging the gap between imitation and reinforcement learning for reasoning.

Reasoning-based language models have demonstrated strong performance across various domains, with the most notable gains seen in mathematical and coding tasks. Recent research has shown that reasoning also offers significant benefits for LLM safety and guardrail applications. In this work, we conduct a comprehensive analysis of training reasoning-based guardrail models for content moderation, with an emphasis on generalization to custom safety policies at inference time. Our study focuses on two key dimensions: data efficiency and inference efficiency. On the data front, we find that reasoning-based models exhibit strong sample efficiency, achieving competitive performance with significantly fewer training examples than their non-reasoning counterparts. This unlocks the potential to repurpose the remaining data for mining high-value, difficult samples that further enhance model performance. On the inference side, we evaluate practical trade-offs by introducing reasoning budgets, examining the impact of reasoning length on latency and accuracy, and exploring dual-mode training to allow runtime control over reasoning behavior. Our findings will provide practical insights for researchers and developers to effectively and efficiently train and deploy reasoning-based guardrails models in real-world systems.

Existing methods usually leverage a fixed strategy, such as natural language reasoning, code-augmented reasoning, tool-integrated reasoning, or ensemble-based reasoning, to guide Large Language Models (LLMs) to perform mathematical reasoning. Our analysis reveals that the single strategy cannot adapt to problem-specific requirements and thus overlooks the trade-off between effectiveness and efficiency. To address these issues, we propose Planning and Routing through Instance-Specific Modeling (PRISM), a novel framework that decouples mathematical reasoning into two stages: strategy planning and targeted execution. Specifically, we first curate a multi-strategy preference dataset, which we call MathStrat, capturing correctness, process quality, and computational efficiency for each problem--strategy pair. Then, we train a lightweight Strategy Adapter based on the dataset to obtain confidence distributions over the mentioned four reasoning strategies. At inference time, an adaptive routing policy dynamically tailors the reasoning approach based on predictor confidence. It directs the model to use single-strategy execution for high-confidence predictions, dual-strategy verification for competitive scenarios, or comprehensive multi-strategy exploration for uncertain cases. Extensive experiments across five mathematical reasoning benchmarks demonstrate that PRISM consistently outperforms individual strategies and ensemble baselines, achieving improvements ranging from 0.9% to 7.6% across different base models. The adaptive routing approach shows particularly strong benefits for mathematical reasoning tasks across diverse model architectures. Our code is released at https://github.com/reml-group/PRISM.

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

Large Language Models (LLMs) have achieved impressive performance on reasoning-intensive tasks, yet optimizing their reasoning efficiency remains an open challenge. While Test-Time Scaling (TTS) improves reasoning quality, it often leads to overthinking, wasting tokens on redundant computations. This work investigates how to efficiently and adaptively guide LLM test-time scaling without additional training. Inspired by the concept of momentum in physics, we propose Momentum Uncertainty-guided Reasoning (MUR), which dynamically allocates thinking budgets to critical reasoning steps by tracking and aggregating stepwise uncertainty over time. To support flexible inference-time control, we introduce gamma-control, a simple mechanism that tunes the reasoning budget via a single hyperparameter. We provide in-depth theoretical proof to support the superiority of MUR in terms of stability and biases. MUR is comprehensively evaluated against various TTS methods across four challenging benchmarks (MATH-500, AIME24, AIME25, and GPQA-diamond) using different sizes of recent Qwen3 models (1.7B, 4B, and 8B). Results demonstrate that MUR reduces computation by over 50% on average while improving accuracy by 0.62-3.37%.

Large language models (LLMs) inevitably make mistakes when performing step-by-step mathematical reasoning. Process Reward Models (PRMs) have emerged as a promising solution by evaluating each reasoning step. However, existing PRMs typically output evaluation scores directly, limiting both learning efficiency and evaluation accuracy, which is further exacerbated by the scarcity of annotated data. To address these issues, we propose Reasoning-Driven Process Reward Modeling (R-PRM). First, we leverage stronger LLMs to generate seed data from limited annotations, effectively bootstrapping our model's reasoning capabilities and enabling comprehensive step-by-step evaluation. Second, we further enhance performance through preference optimization, without requiring additional annotated data. Third, we introduce inference-time scaling to fully harness the model's reasoning potential. Extensive experiments demonstrate R-PRM's effectiveness: on ProcessBench and PRMBench, it surpasses strong baselines by 11.9 and 8.5 points in F1 scores, respectively. When applied to guide mathematical reasoning, R-PRM achieves consistent accuracy improvements of over 8.5 points across six challenging datasets. Further analysis reveals that R-PRM exhibits more comprehensive evaluation and stronger generalization capabilities, thereby highlighting its significant potential.

Large language models (LLMs) are increasingly deployed in settings where reasoning, such as multi-step problem solving and chain-of-thought, is essential. Yet, current evaluation practices overwhelmingly report single-run accuracy while ignoring the intrinsic uncertainty that naturally arises from stochastic decoding. This omission creates a blind spot because practitioners cannot reliably assess whether a method's reported performance is stable, reproducible, or cost-consistent. We introduce ReasonBENCH, the first benchmark designed to quantify the underlying instability in LLM reasoning. ReasonBENCH provides (i) a modular evaluation library that standardizes reasoning frameworks, models, and tasks, (ii) a multi-run protocol that reports statistically reliable metrics for both quality and cost, and (iii) a public leaderboard to encourage variance-aware reporting. Across tasks from different domains, we find that the vast majority of reasoning strategies and models exhibit high instability. Notably, even strategies with similar average performance can display confidence intervals up to four times wider, and the top-performing methods often incur higher and less stable costs. Such instability compromises reproducibility across runs and, consequently, the reliability of reported performance. To better understand these dynamics, we further analyze the impact of prompts, model families, and scale on the trade-off between solve rate and stability. Our results highlight reproducibility as a critical dimension for reliable LLM reasoning and provide a foundation for future reasoning methods and uncertainty quantification techniques. ReasonBENCH is publicly available at https://github.com/au-clan/ReasonBench .

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.

Reasoning in knowledge-intensive domains remains challenging as intermediate steps are often not locally verifiable: unlike math or code, evaluating step correctness may require synthesizing clues across large external knowledge sources. As a result, subtle errors can propagate through reasoning traces, potentially never to be detected. Prior work has proposed process reward models (PRMs), including retrieval-augmented variants, but these methods operate post hoc, scoring completed trajectories, which prevents their integration into dynamic inference procedures. Here, we introduce Process Reward Agents (PRA), a test-time method for providing domain-grounded, online, step-wise rewards to a frozen policy. In contrast to prior retrieval-augmented PRMs, PRA enables search-based decoding to rank and prune candidate trajectories at every generation step. Experiments on multiple medical reasoning benchmarks demonstrate that PRA consistently outperforms strong baselines, achieving 80.8% accuracy on MedQA with Qwen3-4B, a new state of the art at the 4B scale. Importantly, PRA generalizes to unseen frozen policy models ranging from 0.5B to 8B parameters, improving their accuracy by up to 25.7% without any policy model updates. More broadly, PRA suggests a paradigm in which frozen reasoners are decoupled from domain-specific reward modules, allowing the deployment of new backbones in complex domains without retraining.

We present Ring-1T, the first open-source, state-of-the-art thinking model with a trillion-scale parameter. It features 1 trillion total parameters and activates approximately 50 billion per token. Training such models at a trillion-parameter scale introduces unprecedented challenges, including train-inference misalignment, inefficiencies in rollout processing, and bottlenecks in the RL system. To address these, we pioneer three interconnected innovations: (1) IcePop stabilizes RL training via token-level discrepancy masking and clipping, resolving instability from training-inference mismatches; (2) C3PO++ improves resource utilization for long rollouts under a token budget by dynamically partitioning them, thereby obtaining high time efficiency; and (3) ASystem, a high-performance RL framework designed to overcome the systemic bottlenecks that impede trillion-parameter model training. Ring-1T delivers breakthrough results across critical benchmarks: 93.4 on AIME-2025, 86.72 on HMMT-2025, 2088 on CodeForces, and 55.94 on ARC-AGI-v1. Notably, it attains a silver medal-level result on the IMO-2025, underscoring its exceptional reasoning capabilities. By releasing the complete 1T parameter MoE model to the community, we provide the research community with direct access to cutting-edge reasoning capabilities. This contribution marks a significant milestone in democratizing large-scale reasoning intelligence and establishes a new baseline for open-source model performance.

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

Supervised fine-tuning (SFT) has emerged as one of the most effective ways to improve the performance of large language models (LLMs) in downstream tasks. However, SFT can have difficulty generalizing when the underlying data distribution changes, even when the new data does not fall completely outside the training domain. Recent reasoning-focused models such as o1 and R1 have demonstrated consistent gains over their non-reasoning counterparts, highlighting the importance of reasoning for improved generalization and reliability. However, collecting high-quality reasoning traces for SFT remains challenging -- annotations are costly, subjective, and difficult to scale. To address this limitation, we leverage Reinforcement Learning (RL) to enable models to learn reasoning strategies directly from task outcomes. We propose a pipeline in which LLMs generate reasoning steps that guide both the invocation of tools (e.g., function calls) and the final answer generation for conversational agents. Our method employs Group Relative Policy Optimization (GRPO) with rewards designed around tool accuracy and answer correctness, allowing the model to iteratively refine its reasoning and actions. Experimental results demonstrate that our approach improves both the quality of reasoning and the precision of tool invocations, achieving a 1.5% relative improvement over the SFT model (trained without explicit thinking) and a 40% gain compared to the base of the vanilla Qwen3-1.7B model. These findings demonstrate the promise of unifying reasoning and action learning through RL to build more capable and generalizable conversational agents.

Large language models (LLMs) demonstrate remarkable reasoning capabilities in tasks such as algorithmic coding and mathematical problem-solving. Recent methods have improved reasoning through expanded corpus and multistage training combining reinforcement learning and supervised fine-tuning. Although some methods suggest that small but targeted dataset can incentivize reasoning via only distillation, a reasoning scaling laws is still taking shape, increasing computational costs. To address this, we propose a data-efficient distillation framework (DED) that optimizes the Pareto frontier of reasoning distillation. Inspired by the on-policy learning and diverse roll-out strategies of reinforcement learning, the key idea of our approach is threefold: (1) We identify that benchmark scores alone do not determine an effective teacher model. Through comprehensive comparisons of leading reasoning LLMs, we develop a method to select an optimal teacher model. (2) While scaling distillation can enhance reasoning, it often degrades out-of-domain performance. A carefully curated, smaller corpus achieves a balanced trade-off between in-domain and out-of-domain capabilities. (3) Diverse reasoning trajectories encourage the student model to develop robust reasoning skills. We validate our method through evaluations on mathematical reasoning (AIME 2024/2025, MATH-500) and code generation (LiveCodeBench), achieving state-of-the-art results with only 0.8k carefully curated examples, bypassing the need for extensive scaling. Our systematic analysis demonstrates that DED outperforms existing methods by considering factors beyond superficial hardness, token length, or teacher model capability. This work offers a practical and efficient pathway to advanced reasoning while preserving general capabilities.

Reinforcement Learning with Verifiable Rewards (RLVR) demonstrates promising potential in advancing the reasoning capabilities of LLMs. However, its success remains largely confined to mathematical and code domains. This primary limitation stems from the heavy reliance on domain-specific verifiers, which results in prohibitive complexity and limited scalability. To address the challenge, our key observation is that LLM's intrinsic probability of generating a correct free-form answer directly indicates its own evaluation of the reasoning reward (i.e., how well the reasoning process leads to the correct answer). Building on this insight, we propose RLPR, a simple verifier-free framework that extrapolates RLVR to broader general domains. RLPR uses the LLM's own token probability scores for reference answers as the reward signal and maximizes the expected reward during training. We find that addressing the high variance of this noisy probability reward is crucial to make it work, and propose prob-to-reward and stabilizing methods to ensure a precise and stable reward from LLM intrinsic probabilities. Comprehensive experiments in four general-domain benchmarks and three mathematical benchmarks show that RLPR consistently improves reasoning capabilities in both areas for Gemma, Llama, and Qwen based models. Notably, RLPR outperforms concurrent VeriFree by 7.6 points on TheoremQA and 7.5 points on Minerva, and even surpasses strong verifier-model-dependent approaches General-Reasoner by 1.6 average points across seven benchmarks.

Long chains of thought (CoT) from current language models frequently contain logical gaps and unjustified leaps, limiting the gains from additional test-time compute. Improving reasoning quality directly would require process reward models, but the step-level annotations needed to train them are expensive and scarce. We find such a signal in how the model's confidence evolves during reasoning: premature confidence, the tendency to commit to an answer early and use the remaining tokens to rationalize it, strongly predicts flawed reasoning across tasks and model scales. We exploit this in progressive confidence shaping, a reinforcement learning objective that trains models to update their confidence as they reason rather than commit early -- rewarding gradual confidence growth and penalizing early commitment, with no external labels or reward models. The method improves accuracy and reasoning quality from 1.5B to 8B parameters across arithmetic (Countdown), math (DAPO, AIME), and science (ScienceQA): on Countdown, accuracy improves 3.2x (+42.0pp) and flawed reasoning drops 48pp; on AIME, Pass@64 improves 6.6pp. Consistent with this mechanism, the method also improves faithfulness: on a safety benchmark, our models more transparently surface misleading content in their reasoning traces rather than concealing it. Controlled experiments reveal that the problem and its remedy scale together: premature confidence grows with model size and task difficulty, and so do the gains from addressing it.

Large Language Models (LLMs) have achieved significant advances in reasoning tasks. A key approach is tree-based search with verifiers, which expand candidate reasoning paths and use reward models to guide pruning and selection. Although effective in improving accuracy, these methods are not optimal in terms of efficiency: they perform simple decomposition on the reasoning process, but ignore the planning-execution nature of tasks such as math reasoning or code generation. This results in inefficient exploration of reasoning process. To address this, we propose a dual-phase test-time scaling framework that explicitly separates reasoning into planning and execution, and performs search over the two phases individually. Specifically, we decompose reasoning trajectories and develop reward models for each phase, enabling the search to explore and prune plans and executions separately. We further introduce a dynamic budget allocation mechanism that adaptively redistributes sampling effort based on reward feedback, allowing early stopping on confident steps and reallocation of computation to more challenging parts of the reasoning process. Experiments on both mathematical reasoning and code generation benchmarks demonstrate that our approach consistently improves accuracy while reducing redundant computation.

Large reasoning models (LRMs) have recently achieved significant progress in complex reasoning tasks, aided by reinforcement learning with verifiable rewards. However, LRMs often suffer from overthinking, expending excessive computation on simple problems and reducing efficiency. Existing efficient reasoning methods typically require accurate task assessment to preset token budgets or select reasoning modes, which limits their flexibility and reliability. In this work, we revisit the essence of overthinking and identify that encouraging effective steps while penalizing ineffective ones is key to its solution. To this end, we propose a novel rule-based verifiable stepwise reward mechanism (VSRM), which assigns rewards based on the performance of intermediate states in the reasoning trajectory. This approach is intuitive and naturally fits the step-by-step nature of reasoning tasks. We conduct extensive experiments on standard mathematical reasoning benchmarks, including AIME24 and AIME25, by integrating VSRM with PPO and Reinforce++. Results show that our method achieves substantial output length reduction while maintaining original reasoning performance, striking an optimal balance between efficiency and accuracy. Further analysis of overthinking frequency and pass@k score before and after training demonstrates that our approach in deed effectively suppresses ineffective steps and encourages effective reasoning, fundamentally alleviating the overthinking problem. All code will be released upon acceptance.

In Reinforcement Learning with Verifiable Rewards (RLVR), constructing a robust advantage baseline is critical for policy gradients, effectively guiding the policy model to reinforce desired behaviors. Recent research has introduced Generalist Value Models (such as V_0), which achieve pre-trained value estimation by explicitly encoding model capabilities in-context, eliminating the need to synchronously update the value model alongside the policy model. In this paper, we propose V_{0.5}, which adaptively fuses the baseline predicted by such value model (acting as a prior) with the empirical mean derived from sparse rollouts. This constructs a robust baseline that balances computational efficiency with extremely low variance. Specifically, we introduce a real-time statistical testing and dynamic budget allocation. This balances the high variance caused by sparse sampling against the systematic bias (or hallucinations) inherent in the value model's prior. By constructing a hypothesis test to evaluate the prior's reliability in real-time, the system dynamically allocates additional rollout budget on demand. This mechanism minimizes the baseline estimator's Mean Squared Error (MSE), guaranteeing stable policy gradients, even under extreme sparsity with a group size of 4. Extensive evaluations across six mathematical reasoning benchmarks demonstrate that V_{0.5} significantly outperforms GRPO and DAPO, achieving faster convergence and over some 10% performance improvement.

The inherent capabilities of a language model (LM) and the reasoning strategies it employs jointly determine its performance in reasoning tasks. While test-time scaling is regarded as an effective approach to tackling complex reasoning tasks, it incurs substantial computational costs and often leads to "overthinking", where models become trapped in "thought pitfalls". To address this challenge, we propose Route-To-Reason (RTR), a novel unified routing framework that dynamically allocates both LMs and reasoning strategies according to task difficulty under budget constraints. RTR learns compressed representations of both expert models and reasoning strategies, enabling their joint and adaptive selection at inference time. This method is low-cost, highly flexible, and can be seamlessly extended to arbitrary black-box or white-box models and strategies, achieving true plug-and-play functionality. Extensive experiments across seven open source models and four reasoning strategies demonstrate that RTR achieves an optimal trade-off between accuracy and computational efficiency among all baselines, achieving higher accuracy than the best single model while reducing token usage by over 60%.

Large language models (LLMs) achieve promising performance, yet their ability to reason remains poorly understood. Existing evaluations largely emphasize task-level accuracy, often conflating pattern matching with reasoning capability. We present X-RAY, an explainable reasoning analysis system that maps the LLM reasoning capability using calibrated, formally verified probes. We model reasoning capability as a function of extractable structure, operationalized through formal properties such as constraint interaction, reasoning depth, and solution-space geometry. X-Ray generates probes via formal tools with controlled structural variations, enabling precise isolation of incremental structural information through formal calibration and verification. We evaluate state-of-the-art LLMs on problems ranging from junior-level to advanced in mathematics, physics, and chemistry. Our analysis reveals a systematic asymmetry in LLM reasoning: models are relatively robust to constraint refinement, where additional conditions shrink an existing solution space, but degrade sharply under solution-space restructuring, where modifications alter the underlying structural form of the solution manifold. Moreover, calibrated formal probes differentiate models that appear indistinguishable on standard benchmarks and reveal failure modes that are structurally interpretable rather than opaque. Beyond evaluation, our framework is contamination-free and supports the training and testing of reasoning models.

K2-Think is a reasoning system that achieves state-of-the-art performance with a 32B parameter model, matching or surpassing much larger models like GPT-OSS 120B and DeepSeek v3.1. Built on the Qwen2.5 base model, our system shows that smaller models can compete at the highest levels by combining advanced post-training and test-time computation techniques. The approach is based on six key technical pillars: Long Chain-of-thought Supervised Finetuning, Reinforcement Learning with Verifiable Rewards (RLVR), Agentic planning prior to reasoning, Test-time Scaling, Speculative Decoding, and Inference-optimized Hardware, all using publicly available open-source datasets. K2-Think excels in mathematical reasoning, achieving state-of-the-art scores on public benchmarks for open-source models, while also performing strongly in other areas such as Code and Science. Our results confirm that a more parameter-efficient model like K2-Think 32B can compete with state-of-the-art systems through an integrated post-training recipe that includes long chain-of-thought training and strategic inference-time enhancements, making open-source reasoning systems more accessible and affordable. K2-Think is freely available at k2think.ai, offering best-in-class inference speeds of over 2,000 tokens per second per request via the Cerebras Wafer-Scale Engine.

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

The VAPO framework has demonstrated significant empirical success in enhancing the efficiency and reliability of reinforcement learning for long chain-of-thought (CoT) reasoning tasks with large language models (LLMs). By systematically addressing challenges such as value model bias, heterogeneous sequence lengths, and sparse reward signals, VAPO achieves state-of-the-art performance. While its practical benefits are evident, a deeper theoretical understanding of its underlying mechanisms and potential limitations is crucial for guiding future advancements. This paper aims to initiate such a discussion by exploring VAPO from a theoretical perspective, highlighting areas where its assumptions might be challenged and where further investigation could yield more robust and generalizable reasoning agents. We delve into the intricacies of value function approximation in complex reasoning spaces, the optimality of adaptive advantage estimation, the impact of token-level optimization, and the enduring challenges of exploration and generalization.

Improving the reasoning abilities of large language models (LLMs) has largely relied on iterative self-training with model-generated data. While effective at boosting accuracy, existing approaches primarily reinforce successful reasoning paths, incurring a substantial calibration cost: models become overconfident and lose the ability to represent uncertainty. This failure has been characterized as a form of model collapse in alignment, where predictive distributions degenerate toward low-variance point estimates. We address this issue by reframing reasoning training as an epistemic learning problem, in which models must learn not only how to reason, but also when their reasoning should be trusted. We propose epistemically-calibrated reasoning (EpiCaR) as a training objective that jointly optimizes reasoning performance and calibration, and instantiate it within an iterative supervised fine-tuning framework using explicit self-evaluation signals. Experiments on Llama-3 and Qwen-3 families demonstrate that our approach achieves Pareto-superiority over standard baselines in both accuracy and calibration, particularly in models with sufficient reasoning capacity (e.g., 3B+). This framework generalizes effectively to OOD mathematical reasoning (GSM8K) and code generation (MBPP). Ultimately, our approach enables a 3X reduction in inference compute, matching the K=30 performance of STaR with only K=10 samples in capable models.

While LLMs have seen substantial improvement in reasoning capabilities, they also sometimes overthink, generating unnecessary reasoning steps, particularly under uncertainty, given ill-posed or ambiguous queries. We introduce statistically principled early stopping methods that monitor uncertainty signals during generation to mitigate this issue. Our first approach is parametric: it models inter-arrival times of uncertainty keywords as a renewal process and applies sequential testing for stopping. Our second approach is nonparametric and provides finite-sample guarantees on the probability of halting too early on well-posed queries. We conduct empirical evaluations on reasoning tasks across several domains and models. Our results indicate that uncertainty-aware early stopping can improve both efficiency and reliability in LLM reasoning, and we observe especially significant gains for math reasoning.

Test-time scaling has enabled Large Language Models (LLMs) with remarkable reasoning capabilities, particularly in mathematical domains, through intermediate chain-of-thought (CoT) reasoning before generating final answers. However, the specific sources and mechanisms underlying these reasoning capabilities remain insufficiently understood. Optimization reasoning, i.e. finding extrema under constraints, represents a fundamental abstraction that underpins critical applications in planning, control, resource allocation, and prompt search. To systematically evaluate this capability, we introduce ExtremBench, a benchmark dataset for solving mathematical extremal problems, curated from inequality exercises used for Chinese Mathematical Olympiad and transformed into 93 standardized extrema-finding problems. We conduct extensive evaluations across various state-of-the-art open-source model families, including the Qwen3, GPT-OSS, and DeepSeek. Our results reveal that LLMs' extremal-solving reasoning capabilities do not always align with those of current mathematical benchmarks such as AIME25 and MATH-500, with some models showing strong general mathematical reasoning but poor extremal-solving skills, and vice versa. This discrepancy highlights a critical gap in current evaluation practices and suggests that existing benchmarks may not comprehensively capture the full spectrum of mathematical reasoning abilities.

Large language models are increasingly used as agents in social, economic, and policy simulations. A common assumption is that stronger reasoning should improve simulation fidelity. We argue that this assumption can fail when the objective is not to solve a strategic problem, but to sample plausible boundedly rational behavior. In such settings, reasoning-enhanced models can become better solvers and worse simulators: they can over-optimize for strategically dominant actions, collapse compromise-oriented terminal behavior, and sometimes exhibit a diversity-without-fidelity pattern in which local variation survives without outcome-level fidelity. We study this solver-sampler mismatch in three multi-agent negotiation environments adapted from earlier simulation work: an ambiguous fragmented-authority trading-limits scenario, an ambiguous unified-opposition trading-limits scenario, and a new-domain grid-curtailment case in emergency electricity management. We compare three reflection conditions, no reflection, bounded reflection, and native reasoning, across two primary model families and then extend the same protocol to direct OpenAI runs with GPT-4.1 and GPT-5.2. Across all three experiments, bounded reflection produces substantially more diverse and compromise-oriented trajectories than either no reflection or native reasoning. In the direct OpenAI extension, GPT-5.2 native ends in authority decisions in 45 of 45 runs across the three experiments, while GPT-5.2 bounded recovers compromise outcomes in every environment. The contribution is not a claim that reasoning is generally harmful. It is a methodological warning: model capability and simulation fidelity are different objectives, and behavioral simulation should qualify models as samplers, not only as solvers.

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.

Mathematical reasoning has long served as a stringent test of machine intelligence; over the past decade, it has moved from a niche problem within NLP to one of the most consequential AI frontiers. This survey provides a unified account of the field's evolution, from early rule-based math word problem (MWP) solvers and template-driven geometry systems, through neural expression generation and LLM prompting, to contemporary reasoning models, multi-agent systems, neuro-symbolic theorem provers, and verified discovery workflows. We organize the landscape along four axes: (i) informal reasoning over text and diagrams, spanning MWP solving, multimodal geometry, and VLMs; (ii) formal reasoning in proof assistants, including autoformalization, tactic prediction, compiler-guided repair, and proof search; (iii) mathematical discovery, where systems propose constructions, improve bounds, or assist attacks on open problems; and (iv) the inference and training-time techniques, including CoT prompting, tool use, process reward models, and RLVR, that increasingly connect generation with verification. We catalog major benchmarks across grade-school arithmetic, competition mathematics, geometry, formal proving, multimodal and multilingual reasoning, and expert evaluation, and we examine benchmark saturation, contamination, reporting mismatches, and the distinction between pass@1, majority voting, and verifier-assisted pass@k. We critically assess failure modes: brittleness under perturbation, reward hacking, multimodal grounding failures, fragile formalization, and the energy cost of reasoning-scale inference. Drawing on recent perspectives from working mathematicians, we identify future directions centered on verified-discovery workflows, reasoning efficiency, and infrastructure to make AI-assisted formalization broadly usable. Companion materials: https://github.com/Starscream-11813/awesome-AI4Math.

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

Recent years have seen considerable advancements in multi-step reasoning with Large Language Models (LLMs). The previous studies have elucidated the merits of integrating feedback or search mechanisms during model inference to improve the reasoning accuracy. The Process-Supervised Reward Model (PRM), typically furnishes LLMs with step-by-step feedback during the training phase, akin to Proximal Policy Optimization (PPO) or reject sampling. Our objective is to examine the efficacy of PRM in the inference phase to help discern the optimal solution paths for multi-step tasks such as mathematical reasoning and code generation. To this end, we propose a heuristic greedy search algorithm that employs the step-level feedback from PRM to optimize the reasoning pathways explored by LLMs. This tailored PRM demonstrated enhanced results compared to the Chain of Thought (CoT) on mathematical benchmarks like GSM8K and MATH. Additionally, to explore the versatility of our approach, we develop a novel method to automatically generate step-level reward dataset for coding tasks and observed similar improved performance in the code generation tasks. Thus highlighting the robust nature of our reward-model-based approach to inference for reasoning tasks.

Despite the superior performance of Large Reasoning Models (LRMs), their reasoning behaviors are often counterintuitive, leading to suboptimal reasoning capabilities. To theoretically formalize the desired reasoning behaviors, this paper presents the Laws of Reasoning (LoRe), a unified framework that characterizes intrinsic reasoning patterns in LRMs. We first propose compute law with the hypothesis that the reasoning compute should scale linearly with question complexity. Beyond compute, we extend LoRe with a supplementary accuracy law. Since the question complexity is difficult to quantify in practice, we examine these hypotheses by two properties of the laws, monotonicity and compositionality. We therefore introduce LoRe-Bench, a benchmark that systematically measures these two tractable properties for large reasoning models. Evaluation shows that most reasoning models exhibit reasonable monotonicity but lack compositionality. In response, we develop an effective finetuning approach that enforces compute-law compositionality. Extensive empirical studies demonstrate that better compliance with compute laws yields consistently improved reasoning performance on multiple benchmarks, and uncovers synergistic effects across properties and laws. Project page: https://lore-project.github.io/

Model merging, typically on Instruct and Thinking models, has shown remarkable performance for efficient reasoning. In this paper, we systematically revisit the simplest merging method that interpolates two weights directly. Particularly, we observe that model interpolation follows a three-stage evolutionary paradigm with distinct behaviors on the reasoning trajectory. These dynamics provide a principled guide for navigating the performance-cost trade-off. Empirical results demonstrate that a strategically interpolated model surprisingly surpasses sophisticated model merging baselines on both efficiency and effectiveness. We further validate our findings with extensive ablation studies on model layers, modules, and decoding strategies. Ultimately, this work demystifies model interpolation and offers a practical framework for crafting models with precisely targeted reasoning capabilities. Code is available at https://github.com/wutaiqiang/MI{Github}.

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

Training on verifiable symbolic data is a promising way to expand the reasoning frontier of language models beyond what standard pre-training corpora provide. Yet existing procedural generators often rely on fixed puzzles or templates and do not deliver the distributional breadth needed at scale. We introduce Reasoning Core, a scalable suite that procedurally generates verifiable symbolic reasoning data across core formal domains: PDDL planning over randomized domains, first-order logic with equality, context-free grammar parsing and generation, causal reasoning over random Bayesian networks, and systems of equations. Each task is paired with an external solver for rigorous verification and admits continuous difficulty control for curriculum design. Examples can optionally include solver-derived reasoning traces, enabling supervised training from the earliest pre-training stages, and the same interface provides verifiable reward functions for reinforcement learning. Our experiments show that mixing Reasoning Core data into pre-training improves downstream reasoning while preserving, or slightly improving, language modeling quality. Zero-shot evaluations confirm these tasks challenge frontier models such as GPT-5. The code and data are publicly available under the MIT license.

Reinforcement Learning from Verifiable Rewards (RLVR) on chain-of-thought reasoning has become a standard part of language model post-training recipes. A common assumption is that the reasoning chains trained through RLVR reliably represent how a model gets to its answer. In this paper, we develop two metrics for critically examining this assumption: Causal Importance of Reasoning (CIR), which measures the cumulative effect of reasoning tokens on the final answer, and Sufficiency of Reasoning (SR), which measures whether a verifier can arrive at an unambiguous answer based on the reasoning alone. Through experiments with the Qwen2.5 model series and ReasoningGym tasks, we find that: (1) while RLVR does improve task accuracy, it does not reliably improve CIR or SR, calling the role of reasoning in model performance into question; (2) a small amount of SFT before RLVR can be a remedy for low CIR and SR; and (3) CIR and SR can be improved even without SFT by applying auxiliary CIR/SR rewards on top of the outcome-based reward. This joint reward matches the accuracy of RLVR while also leading to causally important and sufficient reasoning. These results show that RLVR does not always lead models to rely on reasoning in the way that is commonly thought, but this issue can be remedied with simple modifications to the post-training procedure.

Language models frequently produce plausible yet incorrect reasoning traces that are difficult to verify. We investigate fine-tuning models to use Prolog as an external symbolic reasoning tool, training Qwen2.5-3B-Instruct with Group Relative Policy Optimization (GRPO) on a cleaned version of GSM8K (which we release as gsm8k-prolog-prover). We systematically vary prompt structure, reward composition (execution, syntax, semantics, structure), and inference protocol (single-try, multiple-try, and two agentic modes). Our reinforcement learning approach outperforms supervised fine-tuning on GSM8K, and the resulting 3B model achieves zero-shot performance on MMLU-STEM and MMLU-Pro competitive with 7B few-shot baselines. Most importantly, we identify an accuracy--auditability trade-off: configurations tuned for correctness alone learn to delegate reasoning to natural language and use Prolog only for the final computation, while configurations rewarded for symbolic structure produce fully auditable programs at a cost in accuracy. We interpret this trade-off as a form of reward hacking and discuss its implications for deploying neurosymbolic systems in safety-critical domains. The source code for our experiments is available under https://github.com/aisilab/Prolog-as-a-Tool

Test-Time Scaling (TTS) has significantly enhanced the capabilities of Large Reasoning Models (LRMs) but introduces a critical side-effect known as Overthinking. We conduct a preliminary study to rethink this phenomenon from a fine-grained perspective. We observe that LRMs frequently conduct repetitive self-verification without revision even after obtaining the final answer during the reasoning process. We formally define this specific position where the answer first stabilizes as the Reasoning Anchor. By analyzing pre- and post-anchor reasoning behaviors, we uncover the structural redundancy fixed in LRMs: the meaningless repetitive verification after deriving the first complete answer, which we term the Answer-Stable Tail (AST). Motivated by this observation, we propose Anchor-based Process Reward (APR), a structure-aware reward shaping method that localizes the reasoning anchor and penalizes exclusively the post-anchor AST. Leveraging the policy optimization algorithm suitable for length penalties, our APR models achieved the performance-efficiency Pareto frontier at 1.5B and 7B scales averaged across five mathematical reasoning datasets while requiring substantially fewer computational resources for RL training.

While recent advances have boosted LM proficiency in linguistic benchmarks, LMs consistently struggle to reason correctly on complex tasks like mathematics. We turn to Reinforcement Learning from Human Feedback (RLHF) as a method with which to shape model reasoning processes. In particular, we explore two reward schemes, outcome-supervised reward models (ORMs) and process-supervised reward models (PRMs), to optimize for logical reasoning. Our results show that the fine-grained reward provided by PRM-based methods enhances accuracy on simple mathematical reasoning (GSM8K) while, unexpectedly, reducing performance in complex tasks (MATH). Furthermore, we show the critical role reward aggregation functions play in model performance. Providing promising avenues for future research, our study underscores the need for further exploration into fine-grained reward modeling for more reliable language models.

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

Large reasoning models (LRMs) have recently shown promise in solving complex math problems when optimized with Reinforcement Learning (RL). But conventional approaches rely on outcome-only rewards that provide sparse feedback, resulting in inefficient optimization process. In this work, we investigate the function of process reward models (PRMs) to accelerate the RL training for LRMs. We propose a novel intrinsic signal-driven generative process evaluation mechanism operating at the thought level to address major bottlenecks in RL-based training. Specifically, instead of requiring PRMs to know how to solve problems, our method uses intrinsic signals in solutions to judge stepwise correctness and aggregate contiguous correct/incorrect steps into coherent 'thought' units. This structured, thought-level rewards enable more reliable credit assignment by reducing ambiguity in step segmentation and alleviating reward hacking. We further introduce a capability-adaptive reward mechanism that dynamically balances exploration and exploitation based on the LRM's current proficiency, guiding learning without stifling creative trial-and-error. These innovations are integrated into a new off-policy RL algorithm, TP-GRPO, which extends grouped proximal optimization with process-based rewards and improves training efficiency. Experiments on 1.5B and 7B parameter LRMs demonstrate that our method achieves higher problem-solving accuracy with significantly fewer training samples than outcome-only reward baselines. The results validate that well-structured process rewards can substantially accelerate LRM optimization in math reasoning tasks. Code is available at https://github.com/cs-holder/tp_grpo.

Recent advances in synergizing large reasoning models (LRMs) with retrieval-augmented generation (RAG) have shown promising results, yet two critical challenges remain: (1) reasoning models typically operate from a single, unchallenged perspective, limiting their ability to conduct deep, self-correcting reasoning over external documents, and (2) existing training paradigms rely excessively on outcome-oriented rewards, which provide insufficient signal for shaping the complex, multi-step reasoning process. To address these issues, we propose an Reasoner-Verifier framework named Adversarial Reasoning RAG (ARR). The Reasoner and Verifier engage in reasoning on retrieved evidence and critiquing each other's logic while being guided by process-aware advantage that requires no external scoring model. This reward combines explicit observational signals with internal model uncertainty to jointly optimize reasoning fidelity and verification rigor. Experiments on multiple benchmarks demonstrate the effectiveness of our method.

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

We examine the reasoning and planning capabilities of large language models (LLMs) in solving complex tasks. Recent advances in inference-time techniques demonstrate the potential to enhance LLM reasoning without additional training by exploring intermediate steps during inference. Notably, OpenAI's o1 model shows promising performance through its novel use of multi-step reasoning and verification. Here, we explore how scaling inference-time techniques can improve reasoning and planning, focusing on understanding the tradeoff between computational cost and performance. To this end, we construct a comprehensive benchmark, known as Sys2Bench, and perform extensive experiments evaluating existing inference-time techniques on eleven diverse tasks across five categories, including arithmetic reasoning, logical reasoning, common sense reasoning, algorithmic reasoning, and planning. Our findings indicate that simply scaling inference-time computation has limitations, as no single inference-time technique consistently performs well across all reasoning and planning tasks.

Text-to-SQL is a challenging task involving multiple reasoning-intensive subtasks, including natural language understanding, database schema comprehension, and precise SQL query formulation. Existing approaches often rely on handcrafted reasoning paths with inductive biases that can limit their overall effectiveness. Motivated by the recent success of reasoning-enhanced models such as DeepSeek R1 and OpenAI o1, which effectively leverage reward-driven self-exploration to enhance reasoning capabilities and generalization, we propose a novel set of partial rewards tailored specifically for the Text-to-SQL task. Our reward set includes schema-linking, AI feedback, n-gram similarity, and syntax check, explicitly designed to address the reward sparsity issue prevalent in reinforcement learning (RL). Leveraging group relative policy optimization (GRPO), our approach explicitly encourages large language models (LLMs) to develop intrinsic reasoning skills necessary for accurate SQL query generation. With models of different sizes, we demonstrate that RL-only training with our proposed rewards consistently achieves higher accuracy and superior generalization compared to supervised fine-tuning (SFT). Remarkably, our RL-trained 14B-parameter model significantly outperforms larger proprietary models, e.g. o3-mini by 4% and Gemini-1.5-Pro-002 by 3% on the BIRD benchmark. These highlight the efficacy of our proposed RL-training framework with partial rewards for enhancing both accuracy and reasoning capabilities in Text-to-SQL tasks.

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

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

Reward models play a critical role in guiding large language models toward outputs that align with human expectations. However, an open challenge remains in effectively utilizing test-time compute to enhance reward model performance. In this work, we introduce Reward Reasoning Models (RRMs), which are specifically designed to execute a deliberate reasoning process before generating final rewards. Through chain-of-thought reasoning, RRMs leverage additional test-time compute for complex queries where appropriate rewards are not immediately apparent. To develop RRMs, we implement a reinforcement learning framework that fosters self-evolved reward reasoning capabilities without requiring explicit reasoning traces as training data. Experimental results demonstrate that RRMs achieve superior performance on reward modeling benchmarks across diverse domains. Notably, we show that RRMs can adaptively exploit test-time compute to further improve reward accuracy. The pretrained reward reasoning models are available at https://huggingface.co/Reward-Reasoning.

Reasoning language models (RLMs), also known as Large Reasoning Models (LRMs), such as OpenAI's o1 and o3, DeepSeek-V3, and Alibaba's QwQ, have redefined AI's problem-solving capabilities by extending large language models (LLMs) with advanced reasoning mechanisms. Yet, their high costs, proprietary nature, and complex architectures - uniquely combining Reinforcement Learning (RL), search heuristics, and LLMs - present accessibility and scalability challenges. To address these, we propose a comprehensive blueprint that organizes RLM components into a modular framework, based on a survey and analysis of all RLM works. This blueprint incorporates diverse reasoning structures (chains, trees, graphs, and nested forms), reasoning strategies (e.g., Monte Carlo Tree Search, Beam Search), RL concepts (policy, value models and others), and supervision schemes (Output-Based and Process-Based Supervision). We also provide detailed mathematical formulations and algorithmic specifications to simplify RLM implementation. By showing how schemes like LLaMA-Berry, QwQ, Journey Learning, and Graph of Thoughts fit as special cases, we demonstrate the blueprint's versatility and unifying potential. To illustrate its utility, we introduce x1, a modular implementation for rapid RLM prototyping and experimentation. Using x1 and a literature review, we provide key insights, such as multi-phase training for policy and value models, and the importance of familiar training distributions. Finally, we outline how RLMs can integrate with a broader LLM ecosystem, including tools and databases. Our work demystifies RLM construction, democratizes advanced reasoning capabilities, and fosters innovation, aiming to mitigate the gap between "rich AI" and "poor AI" by lowering barriers to RLM development and experimentation.

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.

Direct Preference Optimization (DPO) using an implicit reward model has proven to be an effective alternative to reinforcement learning from human feedback (RLHF) for fine-tuning preference aligned large language models (LLMs). However, the overall preference annotations of responses do not fully capture the fine-grained quality of model outputs in complex multi-step reasoning tasks, such as mathematical reasoning. To address this limitation, we introduce a novel algorithm called Step-level Value Preference Optimization (SVPO). Our approach employs Monte Carlo Tree Search (MCTS) to automatically annotate step-level preferences for multi-step reasoning. Furthermore, from the perspective of learning-to-rank, we train an explicit value model to replicate the behavior of the implicit reward model, complementing standard preference optimization. This value model enables the LLM to generate higher reward responses with minimal cost during inference. Experimental results demonstrate that our method achieves state-of-the-art performance on both in-domain and out-of-domain mathematical reasoning benchmarks. Our code is available at https://github.com/MARIO-Math-Reasoning/Super_MARIO.

We introduce Motif-2-12.7B-Reasoning, a 12.7B parameter language model designed to bridge the gap between open-weight systems and proprietary frontier models in complex reasoning and long-context understanding. Addressing the common challenges of model collapse and training instability in reasoning adaptation, we propose a comprehensive, reproducible training recipe spanning system, data, and algorithmic optimizations. Our approach combines memory-efficient infrastructure for 64K-token contexts using hybrid parallelism and kernel-level optimizations with a two-stage Supervised Fine-Tuning (SFT) curriculum that mitigates distribution mismatch through verified, aligned synthetic data. Furthermore, we detail a robust Reinforcement Learning Fine-Tuning (RLFT) pipeline that stabilizes training via difficulty-aware data filtering and mixed-policy trajectory reuse. Empirical results demonstrate that Motif-2-12.7B-Reasoning achieves performance comparable to models with significantly larger parameter counts across mathematics, coding, and agentic benchmarks, offering the community a competitive open model and a practical blueprint for scaling reasoning capabilities under realistic compute constraints.

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

As the widespread adoption of Large Language Models (LLMs) accelerates, token consumption from intermediate reasoning traces increasingly contributes to inference latency and operational cost. Recent studies suggest that many real-world tasks require little to no explicit reasoning, with additional reasoning sometimes even degrading performance. In this work, we propose Post-Reasoning, a simple yet effective approach that improves instruction-tuned models by conditioning them to justify their answers after generating the final response. By design, it enables the final answer to be obtained without additional latency or token cost, while still improving performance through simple instruction augmentation. We evaluate Post-Reasoning across \(117\) model--benchmark settings spanning \(13\) open and proprietary models, \(4\) model families, and \(9\) diverse reasoning and knowledge-intensive benchmarks, including AMC, HMMT, GSM8K, GPQA, MMLU-Pro, and BIG-Bench Hard. Post-Reasoning improves performance in over \(88.19\%\) of evaluated settings, achieving a mean relative improvements of \(17.37\%\). Furthermore, we propose supervised post-reason tuning, which further improves performance in over \(91.11\%\) of evaluated settings, and exceeds the prompt-based post-reasoning baseline by an average of \(8.01\%\), demonstrating that post-reasoning can be effectively internalized through training. Ultimately, Post-Reasoning establishes a new performance ceiling for direct-answer capabilities.

Recent advances in reinforcement learning (RL) have led to substantial improvements in the mathematical reasoning abilities of LLMs, as measured by standard benchmarks. Yet these gains often persist even when models are trained with flawed signals, such as random or inverted rewards. This raises a fundamental question: do such improvements reflect genuine reasoning, or are they merely artifacts of overfitting to benchmark-specific patterns? To answer this question, we adopt an evaluation-centric perspective and highlight two critical shortcomings in existing protocols. First, benchmark contamination arises because test problems are publicly available, thereby increasing the risk of data leakage. Second, evaluation fragility results from reliance on single-instance assessments, which are sensitive to stochastic outputs and fail to capture reasoning consistency. These limitations suggest the need for a new evaluation paradigm that can probe reasoning ability beyond memorization and one-off success. As response, we propose VAR-MATH, a symbolic evaluation framework that converts fixed numerical problems into parameterized templates and requires models to solve multiple instantiations of each. This design enforces consistency across structurally equivalent variants, mitigates contamination, and enhances robustness through bootstrapped metrics. We apply VAR-MATH to transform three popular benchmarks, AMC23, AIME24, and AIME25, into their symbolic counterparts, VAR-AMC23, VAR-AIME24, and VAR-AIME25. Experimental results show substantial performance drops for RL-trained models on these variabilized benchmarks, especially for smaller models, with average declines of 47.9\% on AMC23, 58.8\% on AIME24, and 72.9\% on AIME25. These findings indicate that some existing RL methods rely on superficial heuristics and fail to generalize beyond specific numerical forms.

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

Reward models (RMs) play a critical role in enhancing the reasoning performance of LLMs. For example, they can provide training signals to finetune LLMs during reinforcement learning (RL) and help select the best answer from multiple candidates during inference. In this paper, we provide a systematic introduction to RMs, along with a comprehensive survey of their applications in LLM reasoning. We first review fundamental concepts of RMs, including their architectures, training methodologies, and evaluation techniques. Then, we explore their key applications: (1) guiding generation and selecting optimal outputs during LLM inference, (2) facilitating data synthesis and iterative self-improvement for LLMs, and (3) providing training signals in RL-based finetuning. Finally, we discuss critical open questions regarding the selection, generalization, evaluation, and enhancement of RMs, based on existing research and our own empirical findings. Our analysis aims to provide actionable insights for the effective deployment and advancement of RMs for LLM reasoning.

Example-based guidance is widely used to improve mathematical reasoning at inference time, yet its effectiveness is highly unstable across problems and models-even when the guidance is correct and problem-relevant. We show that this instability arises from a previously underexplored gap between strategy usage-whether a reasoning strategy appears in successful solutions-and strategy executability-whether the strategy remains effective when instantiated as guidance for a target model. Through a controlled analysis of paired human-written and model-generated solutions, we identify a systematic dissociation between usage and executability: human- and model-derived strategies differ in structured, domain-dependent ways, leading to complementary strengths and consistent source-dependent reversals under guidance. Building on this diagnosis, we propose Selective Strategy Retrieval (SSR), a test-time framework that explicitly models executability by selectively retrieving and combining strategies using empirical, multi-route, source-aware signals. Across multiple mathematical reasoning benchmarks, SSR yields reliable and consistent improvements over direct solving, in-context learning, and single-source guidance, improving accuracy by up to +13 points on AIME25 and +5 points on Apex for compact reasoning models. Code and benchmark are publicly available at: https://github.com/lwd17/strategy-execute-pipeline.

What is reasoning? This question has driven centuries of philosophical inquiry, from Aristotle's syllogisms to modern computational complexity theory. In the age of large language models achieving superhuman performance on benchmarks like GSM8K (95\% accuracy) and HumanEval (90\% pass@1), we must ask: have these systems learned to reason, or have they learned to pattern-match over reasoning traces? This paper argues for a specific answer: reasoning is iterative operator application in state spaces, converging to fixed points. This definition is not merely philosophical -- it has concrete architectural implications that explain both the failures of current systems and the path to genuine reasoning capabilities. Our investigation begins with a puzzle (OpenXOR), progresses through theory (OpenOperator), and culminates in a working solution (OpenLM) that achieves 76\% accuracy where state-of-the-art LLMs achieve 0\%. This is not about criticizing existing systems, but about understanding what reasoning requires and building architectures that provide it.

Reasoning is a fundamental substrate for solving novel and complex problems. Deliberate efforts in learning and developing frameworks around System 2 reasoning have made great strides, yet problems of sufficient complexity remain largely out of reach for open models. To address this gap, we examine the potential of Generative Flow Networks as a fine-tuning method for LLMs to unlock advanced reasoning capabilities. In this paper, we present a proof of concept in the domain of formal reasoning, specifically in the Neural Theorem Proving (NTP) setting, where proofs specified in a formal language such as Lean can be deterministically and objectively verified. Unlike classical reward-maximization reinforcement learning, which frequently over-exploits high-reward actions and fails to effectively explore the state space, GFlowNets have emerged as a promising approach for sampling compositional objects, improving generalization, and enabling models to maintain diverse hypotheses. Our early results demonstrate GFlowNet fine-tuning's potential for enhancing model performance in a search setting, which is especially relevant given the paradigm shift towards inference time compute scaling and "thinking slowly."

In this paper, we offer a guide for researchers on evaluating reasoning in language models, building the case that reasoning should be assessed through evidence of adaptive, multi-step search rather than final-answer accuracy alone. Under an evaluation-oriented definition, reasoning requires selecting intermediate steps and halting according to input-dependent conditions, which we formalize as a search-like procedure. We show that single forward passes in scalable architectures are structurally limited in their ability to realize such variable-depth computation, motivating intermediate decoding and externalized reasoning traces as appropriate evaluation interfaces. Central to our argument is that final-answer accuracy alone is an insufficient measure of reasoning, because it provides little ability to diagnose or debug the underlying processes that produce individual solutions in frontier models. We therefore argue for a shift toward process-based evaluation, in which reasoning is assessed through the faithfulness and validity of intermediate reasoning traces as first-class evaluation targets.

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

Frontier reasoning models have exhibited incredible capabilities across a wide array of disciplines, driven by posttraining large language models (LLMs) with reinforcement learning (RL). However, despite the widespread success of this paradigm, much of the literature has been devoted to disentangling truly novel behaviors that emerge during RL but are not present in the base models. In our work, we approach this question from a different angle, instead asking whether comparable reasoning capabilites can be elicited from base models at inference time by pure sampling, without any additional training. Inspired by Markov chain Monte Carlo (MCMC) techniques for sampling from sharpened distributions, we propose a simple iterative sampling algorithm leveraging the base models' own likelihoods. Over different base models, we show that our algorithm offers substantial boosts in reasoning that nearly match and even outperform those from RL on a wide variety of single-shot tasks, including MATH500, HumanEval, and GPQA. Moreover, our sampler avoids the collapse in diversity over multiple samples that is characteristic of RL-posttraining. Crucially, our method does not require training, curated datasets, or a verifier, suggesting broad applicability beyond easily verifiable domains.

Enhancing the capability of large language models (LLMs) in reasoning has gained significant attention in recent years. Previous studies have demonstrated the effectiveness of various prompting strategies in aiding LLMs in reasoning (called "reasoning actions"), such as step-by-step thinking, reflecting before answering, solving with programs, and their combinations. However, these approaches often applied static, predefined reasoning actions uniformly to all questions, without considering the specific characteristics of each question or the capability of the task-solving LLM. In this paper, we propose DOTS, an approach enabling LLMs to reason dynamically via optimal reasoning trajectory search, tailored to the specific characteristics of each question and the inherent capability of the task-solving LLM. Our approach involves three key steps: i) defining atomic reasoning action modules that can be composed into various reasoning action trajectories; ii) searching for the optimal action trajectory for each training question through iterative exploration and evaluation for the specific task-solving LLM; and iii) using the collected optimal trajectories to train an LLM to plan for the reasoning trajectories of unseen questions. In particular, we propose two learning paradigms, i.e., fine-tuning an external LLM as a planner to guide the task-solving LLM, or directly fine-tuning the task-solving LLM with an internalized capability for reasoning actions planning. Our experiments across eight reasoning tasks show that our method consistently outperforms static reasoning techniques and the vanilla instruction tuning approach. Further analysis reveals that our method enables LLMs to adjust their computation based on problem complexity, allocating deeper thinking and reasoning to harder problems.

Recent math benchmarks for large language models (LLMs) such as MathArena indicate that state-of-the-art reasoning models achieve impressive performance on mathematical competitions like AIME, with the leading model, o3-mini, achieving scores comparable to top human competitors. However, these benchmarks evaluate models solely based on final numerical answers, neglecting rigorous reasoning and proof generation which are essential for real-world mathematical tasks. To address this, we introduce the first comprehensive evaluation of full-solution reasoning for challenging mathematical problems. Using expert human annotators, we evaluated several state-of-the-art reasoning models on the six problems from the 2025 USAMO within hours of their release. Our results reveal that all tested models struggled significantly, achieving less than 5% on average. Through detailed analysis of reasoning traces, we identify the most common failure modes and find several unwanted artifacts arising from the optimization strategies employed during model training. Overall, our results suggest that current LLMs are inadequate for rigorous mathematical reasoning tasks, highlighting the need for substantial improvements in reasoning and proof generation capabilities.

Outcome-reward reinforcement learning (RL) has proven effective at improving the reasoning capabilities of large language models (LLMs). However, standard RL assigns credit only at the level of the final answer, penalizing entire reasoning traces when the outcome is incorrect and uniformly reinforcing all steps when it is correct. As a result, correct intermediate steps may be discouraged in failed traces, while spurious steps may be reinforced in successful ones. We refer to this failure mode as the problem of credit assignment. While a natural remedy is to train a process reward model, accurately optimizing such models to identify corrective reasoning steps remains challenging. We introduce Intervention Training (InT), a training paradigm in which the model performs fine-grained credit assignment on its own reasoning traces by proposing short, targeted corrections that steer trajectories toward higher reward. Using reference solutions commonly available in mathematical reasoning datasets and exploiting the fact that verifying a model-generated solution is easier than generating a correct one from scratch, the model identifies the first error in its reasoning and proposes a single-step intervention to redirect the trajectory toward the correct solution. We then apply supervised fine-tuning (SFT) to the on-policy rollout up to the point of error concatenated with the intervention, localizing error to the specific step that caused failure. We show that the resulting model serves as a far better initialization for RL training. After running InT and subsequent fine-tuning with RL, we improve accuracy by nearly 14% over a 4B-parameter base model on IMO-AnswerBench, outperforming larger open-source models such as gpt-oss-20b.

Recent advances such as OpenAI-o1 and DeepSeek R1 have demonstrated the potential of Reinforcement Learning (RL) to enhance reasoning abilities in Large Language Models (LLMs). While open-source replication efforts have primarily focused on mathematical and coding domains, methods and resources for developing general reasoning capabilities remain underexplored. This gap is partly due to the challenge of collecting diverse and verifiable reasoning data suitable for RL. We hypothesize that logical reasoning is critical for developing general reasoning capabilities, as logic forms a fundamental building block of reasoning. In this work, we present SynLogic, a data synthesis framework and dataset that generates diverse logical reasoning data at scale, encompassing 35 diverse logical reasoning tasks. The SynLogic approach enables controlled synthesis of data with adjustable difficulty and quantity. Importantly, all examples can be verified by simple rules, making them ideally suited for RL with verifiable rewards. In our experiments, we validate the effectiveness of RL training on the SynLogic dataset based on 7B and 32B models. SynLogic leads to state-of-the-art logical reasoning performance among open-source datasets, surpassing DeepSeek-R1-Distill-Qwen-32B by 6 points on BBEH. Furthermore, mixing SynLogic data with mathematical and coding tasks improves the training efficiency of these domains and significantly enhances reasoning generalization. Notably, our mixed training model outperforms DeepSeek-R1-Zero-Qwen-32B across multiple benchmarks. These findings position SynLogic as a valuable resource for advancing the broader reasoning capabilities of LLMs. We open-source both the data synthesis pipeline and the SynLogic dataset at https://github.com/MiniMax-AI/SynLogic.

Reinforcement Learning with Verifiable Rewards (RLVR) has recently demonstrated notable success in enhancing the reasoning capabilities of LLMs, particularly in mathematics and programming tasks. It is widely believed that RLVR enables LLMs to continuously self-improve, thus acquiring novel reasoning abilities that exceed corresponding base models' capacity. In this study, however, we critically re-examines this assumption by measuring the pass@k metric with large values of k to explore the reasoning capability boundary of the models across a wide range of model families and benchmarks. Surprisingly, the RL does not, in fact, elicit fundamentally new reasoning patterns. While RL-trained models outperform their base models at smaller values of k (\eg, k=1), base models can achieve a comparable or even higher pass@k score compared to their RL counterparts at large k values. The reasoning paths generated by RL-trained models are already included in the base models' sampling distribution, suggesting that most reasoning abilities manifested in RL-trained models are already obtained by base models. Further analysis shows that RL training boosts the performance by biasing the model's output distribution toward paths that are more likely to yield rewards, therefore sampling correct responses more efficiently. But this also results in a narrower reasoning capability boundary compared to base models. Similar results are observed in visual reasoning tasks trained with RLVR. Moreover, we find that distillation can genuinely introduce new knowledge into the model, different from RLVR. These findings underscore a critical limitation of RLVR in advancing LLM reasoning abilities which requires us to fundamentally rethink the impact of RL training in reasoning LLMs and the need of a better paradigm. Project Page: https://limit-of-RLVR.github.io

Currently, process reward models (PRMs) have exhibited remarkable potential for test-time scaling. Since large language models (LLMs) regularly generate flawed intermediate reasoning steps when tackling a broad spectrum of reasoning and decision-making tasks, PRMs are required to possess capabilities for detecting process-level errors in real-world scenarios. However, existing benchmarks primarily focus on mathematical reasoning, thereby failing to comprehensively evaluate the error detection ability of PRMs across diverse reasoning scenarios. To mitigate this gap, we introduce GR-Ben, a process-level benchmark specifically designed for assessing PRM's performance across two primary reasoning domains (science and logic) and nine subdomains. We conduct extensive experiments on a diverse set of 22 models, encompassing both PRMs and LLMs, and derive two key findings: (1) In domains beyond mathematical reasoning, the error-detection ability of existing PRMs and LLMs is found to be markedly weaker by comparison.(2) In general, PRMs are less adept at identifying knowledge-based errors, whereas LLMs exhibit poorer performance in detecting computational errors. We hope GR-Ben can foster future researches on PRMs for general domains, thereby enhancing the reasoning capabilities of LLMs.

A promising approach for improving reasoning in large language models is to use process reward models (PRMs). PRMs provide feedback at each step of a multi-step reasoning trace, potentially improving credit assignment over outcome reward models (ORMs) that only provide feedback at the final step. However, collecting dense, per-step human labels is not scalable, and training PRMs from automatically-labeled data has thus far led to limited gains. To improve a base policy by running search against a PRM or using it as dense rewards for reinforcement learning (RL), we ask: "How should we design process rewards?". Our key insight is that, to be effective, the process reward for a step should measure progress: a change in the likelihood of producing a correct response in the future, before and after taking the step, corresponding to the notion of step-level advantages in RL. Crucially, this progress should be measured under a prover policy distinct from the base policy. We theoretically characterize the set of good provers and our results show that optimizing process rewards from such provers improves exploration during test-time search and online RL. In fact, our characterization shows that weak prover policies can substantially improve a stronger base policy, which we also observe empirically. We validate our claims by training process advantage verifiers (PAVs) to predict progress under such provers, and show that compared to ORMs, test-time search against PAVs is >8% more accurate, and 1.5-5times more compute-efficient. Online RL with dense rewards from PAVs enables one of the first results with 5-6times gain in sample efficiency, and >6% gain in accuracy, over ORMs.

Reinforcement learning is emerging as a primary driver for improving language model reasoning capabilities. A fundamental question is whether current reinforcement learning algorithms -- such as Group Relative Policy Optimization (GRPO), the de facto standard algorithm used to improve language model reasoning -- merely sharpen the base model's distribution around problems it can already solve. We investigate this question in the context of formal theorem proving, which has access to a perfect verifier. We identify a degenerate rank bias in GRPO in which highly probable trajectories are reinforced and rare ones are neglected. This results in distribution sharpening: the model can solve some problems with fewer samples, but underperforms simply sampling more solutions from the original model. To overcome GRPO's rank bias we introduce unlikeliness reward, a simple method for explicitly up-weighting rare but correct solutions. We show that unlikeliness reward mitigates rank bias and improves pass@N across a large range of N in both synthetic and real theorem proving settings. We also uncover an unexpected link between rank bias and a seemingly mundane hyperparameter -- the number of updates per batch -- that leads to a second, complementary mitigation. We combine our insights into a revised GRPO training recipe for formal theorem proving, yielding an open pipeline that achieves competitive performance to DeepSeek-Prover-V1.5-RL on the miniF2F-test benchmark. We release our implementation at https://github.com/AndreHe02/rewarding-unlikely-release

Large language models (LLMs) continue to struggle with mathematical reasoning, and common post-training pipelines often reduce each generated solution to a binary outcome: correct or incorrect. This perspective is limiting in practice, as failures in chain-of-thought (CoT) reasoning are frequently structured; solutions may appear convincing while containing subtle logical, algebraic, or numerical flaws. Meanwhile, reinforcement learning from human feedback (RLHF) variants that rely on large reward models or LLM-as-a-judge signals are often expensive, difficult to scale, and unstable to iterate. We propose a lightweight and pragmatic post-training pipeline that targets such structured errors under realistic compute budgets. Starting from supervised fine-tuning (SFT) on MetaMathQA-style CoT data, we introduce a compact MathVerifier that decomposes a candidate solution into a six-dimensional error profile and aggregates it into interpretable wrongness and absurdity scores. These verifier signals serve two roles: (i) mining hard negatives that are near-correct yet structurally flawed, and (ii) defining per-sample importance weights that emphasize the most informative preference pairs. We integrate both into an offline Direct Preference Optimization (DPO) objective via a verifier-guided weighted formulation. Experiments on a 1.5B-parameter Qwen2.5 model show that verifier-guided, weighted DPO yields more targeted improvements than vanilla SFT and unweighted DPO, particularly on problems where solutions are numerically close to correct but logically inconsistent, while avoiding the overhead of training large reward models or relying on external judges.

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

Effective training of language models (LMs) for mathematical reasoning tasks demands high-quality supervised fine-tuning data. Besides obtaining annotations from human experts, a common alternative is sampling from larger and more powerful LMs. However, this knowledge distillation approach can be costly and unstable, particularly when relying on closed-source, proprietary LMs like GPT-4, whose behaviors are often unpredictable. In this work, we demonstrate that the reasoning abilities of small-scale LMs can be enhanced through self-training, a process where models learn from their own outputs. We also show that the conventional self-training can be further augmented by a preference learning algorithm called Direct Preference Optimization (DPO). By integrating DPO into self-training, we leverage preference data to guide LMs towards more accurate and diverse chain-of-thought reasoning. We evaluate our method across various mathematical reasoning tasks using different base models. Our experiments show that this approach not only improves LMs' reasoning performance but also offers a more cost-effective and scalable solution compared to relying on large proprietary LMs.

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.

Reinforcement Learning with Verifiable Rewards (RLVR) has markedly enhanced the reasoning abilities of large language models (LLMs). Its success, however, largely depends on strong base models with rich world knowledge, yielding only modest improvements for small-size language models (SLMs). To address this limitation, we investigate Guided GRPO, which injects ground-truth reasoning steps into roll-out trajectories to compensate for SLMs' inherent weaknesses. Through a comprehensive study of various guidance configurations, we find that naively adding guidance delivers limited gains. These insights motivate G^2RPO-A, an adaptive algorithm that automatically adjusts guidance strength in response to the model's evolving training dynamics. Experiments on mathematical reasoning and code-generation benchmarks confirm that G^2RPO-A substantially outperforms vanilla GRPO. Our code and models are available at https://github.com/T-Lab-CUHKSZ/G2RPO-A.

Scaling test-time compute is crucial for enhancing the reasoning capabilities of large language models (LLMs). Existing approaches typically employ reinforcement learning (RL) to maximize a verifiable reward obtained at the end of reasoning traces. However, such methods optimize only the final performance under a large and fixed token budget, which hinders efficiency in both training and deployment. In this work, we present a novel framework, AnytimeReasoner, to optimize anytime reasoning performance, which aims to improve token efficiency and the flexibility of reasoning under varying token budget constraints. To achieve this, we truncate the complete thinking process to fit within sampled token budgets from a prior distribution, compelling the model to summarize the optimal answer for each truncated thinking for verification. This introduces verifiable dense rewards into the reasoning process, facilitating more effective credit assignment in RL optimization. We then optimize the thinking and summary policies in a decoupled manner to maximize the cumulative reward. Additionally, we introduce a novel variance reduction technique, Budget Relative Policy Optimization (BRPO), to enhance the robustness and efficiency of the learning process when reinforcing the thinking policy. Empirical results in mathematical reasoning tasks demonstrate that our method consistently outperforms GRPO across all thinking budgets under various prior distributions, enhancing both training and token efficiency.

Large language models (LLMs) typically employ sampling or beam search, accompanied by prompts such as Chain-of-Thought (CoT), to boost reasoning and decoding ability. Recent work like Tree-of-Thought (ToT) and Reasoning via Planning (RAP) aim to augment the reasoning capabilities of LLMs by utilizing tree-search algorithms to guide multi-step reasoning. These methods mainly focus on LLMs' reasoning ability during inference and heavily rely on human-designed prompts to activate LLM as a value function, which lacks general applicability and scalability. To address these limitations, we present an AlphaZero-like tree-search framework for LLMs (termed TS-LLM), systematically illustrating how tree-search with a learned value function can guide LLMs' decoding ability. TS-LLM distinguishes itself in two key ways: (1) Leveraging a learned value function, our approach can be generally applied to different tasks beyond reasoning (such as RLHF alignment), and LLMs of any size, without prompting advanced, large-scale models. (2) It can guide LLM's decoding during both inference and training. Empirical evaluations across reasoning, planning, and RLHF alignment tasks validate the effectiveness of TS-LLM, even on trees with a depth of 64.

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

Recently, Zaremba et al. demonstrated that increasing inference-time computation improves robustness in large proprietary reasoning LLMs. In this paper, we first show that smaller-scale, open-source models (e.g., DeepSeek R1, Qwen3, Phi-reasoning) can also benefit from inference-time scaling using a simple budget forcing strategy. More importantly, we reveal and critically examine an implicit assumption in prior work: intermediate reasoning steps are hidden from adversaries. By relaxing this assumption, we identify an important security risk, intuitively motivated and empirically verified as an inverse scaling law: if intermediate reasoning steps become explicitly accessible, increased inference-time computation consistently reduces model robustness. Finally, we discuss practical scenarios where models with hidden reasoning chains are still vulnerable to attacks, such as models with tool-integrated reasoning and advanced reasoning extraction attacks. Our findings collectively demonstrate that the robustness benefits of inference-time scaling depend heavily on the adversarial setting and deployment context. We urge practitioners to carefully weigh these subtle trade-offs before applying inference-time scaling in security-sensitive, real-world applications.

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.

Mathematical reasoning is a cornerstone of artificial general intelligence and a primary benchmark for evaluating the capabilities of Large Language Models (LLMs). While state-of-the-art models show promise, they often falter when faced with complex problems that demand deep conceptual understanding and intricate, multi-step deliberation. To address this challenge, we introduce JT-Math-8B, a series of open-source models comprising base, instruct, and thinking versions, built upon a systematic, multi-stage optimization framework. Our pre-training corpus is a high-quality, 210B-token dataset curated through a dedicated data pipeline that uses model-based validation to ensure quality and diversity. The Instruct Model is optimized for direct, concise answers through Supervised Fine-Tuning (SFT) and a GRPO-based reinforcement learning (RL) method. The Thinking Model is trained for complex problem-solving using a Long Chain-of-Thought (Long CoT) approach, combining SFT with a novel, multi-stage RL curriculum that progressively increases task difficulty and context length up to 32K tokens. JT-Math-8B achieves state-of-the-art results among open-source models of similar size, surpassing prominent models like OpenAI's O1-mini and GPT-4o , and demonstrating superior performance on competition-level mathematics.

Recently, test-time scaling has garnered significant attention from the research community, largely due to the substantial advancements of the o1 model released by OpenAI. By allocating more computational resources during the inference phase, large language models~(LLMs) can extensively explore the solution space by generating more thought tokens or diverse solutions, thereby producing more accurate responses. However, developing an o1-like reasoning approach is challenging, and researchers have been making various attempts to advance this open area of research. In this paper, we present a preliminary exploration into enhancing the reasoning abilities of LLMs through reward-guided tree search algorithms. This framework is implemented by integrating the policy model, reward model, and search algorithm. It is primarily constructed around a tree search algorithm, where the policy model navigates a dynamically expanding tree guided by a specially trained reward model. We thoroughly explore various design considerations necessary for implementing this framework and provide a detailed report of the technical aspects. To assess the effectiveness of our approach, we focus on mathematical reasoning tasks and conduct extensive evaluations on four challenging datasets, significantly enhancing the reasoning abilities of LLMs.

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

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

This work introduces Falcon-H1R, a 7B-parameter reasoning-optimized model that establishes the feasibility of achieving competitive reasoning performance with small language models (SLMs). Falcon-H1R stands out for its parameter efficiency, consistently matching or outperforming SOTA reasoning models that are 2times to 7times larger across a variety of reasoning-intensive benchmarks. These results underscore the importance of careful data curation and targeted training strategies (via both efficient SFT and RL scaling) in delivering significant performance gains without increasing model size. Furthermore, Falcon-H1R advances the 3D limits of reasoning efficiency by combining faster inference (through its hybrid-parallel architecture design), token efficiency, and higher accuracy. This unique blend makes Falcon-H1R-7B a practical backbone for scaling advanced reasoning systems, particularly in scenarios requiring extensive chain-of-thoughts generation and parallel test-time scaling. Leveraging the recently introduced DeepConf approach, Falcon-H1R achieves state-of-the-art test-time scaling efficiency, offering substantial improvements in both accuracy and computational cost. As a result, Falcon-H1R demonstrates that compact models, through targeted model training and architectural choices, can deliver robust and scalable reasoning performance.

Large language models (LLMs) demonstrate impressive reasoning abilities, but translating reasoning into actions in the real world remains challenging. In particular, it remains unclear how to complete a given task provably within a minimum number of interactions with the external environment, e.g., through an internal mechanism of reasoning. To this end, we propose a principled framework with provable regret guarantees to orchestrate reasoning and acting, which we call "reason for future, act for now" (RAFA). Specifically, we design a prompt template for reasoning that learns from the memory buffer and plans a future trajectory over a long horizon ("reason for future"). At each step, the LLM agent takes the initial action of the planned trajectory ("act for now"), stores the collected feedback in the memory buffer, and reinvokes the reasoning routine to replan the future trajectory from the new state. The key idea is to cast reasoning in LLMs as learning and planning in Bayesian adaptive Markov decision processes (MDPs). Correspondingly, we prompt LLMs to form an updated posterior of the unknown environment from the memory buffer (learning) and generate an optimal trajectory for multiple future steps that maximizes a value function (planning). The learning and planning subroutines are performed in an "in-context" manner to emulate the actor-critic update for MDPs. Our theoretical analysis proves that the novel combination of long-term reasoning and short-term acting achieves a T regret. In particular, the regret bound highlights an intriguing interplay between the prior knowledge obtained through pretraining and the uncertainty reduction achieved by reasoning and acting. Our empirical validation shows that it outperforms various existing frameworks and achieves nearly perfect scores on a few benchmarks.

Procedural planning, which entails decomposing a high-level goal into a sequence of temporally ordered steps, is an important yet intricate task for machines. It involves integrating common-sense knowledge to reason about complex contextualized situations that are often counterfactual, e.g. "scheduling a doctor's appointment without a phone". While current approaches show encouraging results using large language models (LLMs), they are hindered by drawbacks such as costly API calls and reproducibility issues. In this paper, we advocate planning using smaller language models. We present PlaSma, a novel two-pronged approach to endow small language models with procedural knowledge and (counterfactual) planning capabilities. More concretely, we develop symbolic procedural knowledge distillation to enhance the implicit knowledge in small language models and an inference-time algorithm to facilitate more structured and accurate reasoning. In addition, we introduce a novel task, Counterfactual Planning, that requires a revision of a plan to cope with a counterfactual situation. In both the original and counterfactual setting, we show that orders-of-magnitude smaller models (770M-11B parameters) can compete and often surpass their larger teacher models' capabilities.

Large language models have achieved near-expert performance in structured reasoning domains like mathematics and programming, yet their ability to perform compositional multi-hop reasoning in specialized scientific fields remains limited. We propose a bottom-up learning paradigm in which models are grounded in axiomatic domain facts and compose them to solve complex, unseen tasks. To this end, we present a post-training pipeline, based on a combination of supervised fine-tuning and reinforcement learning (RL), in which knowledge graphs act as implicit reward models. By deriving novel reward signals from knowledge graph paths, we provide verifiable, scalable, and grounded supervision that encourages models to compose intermediate axioms rather than optimize only final answers during RL. We validate this approach in the medical domain, training a 14B model on short-hop reasoning paths (1-3 hops) and evaluating its zero-shot generalization to complex multi-hop queries (4-5 hops). Our experiments show that path-derived rewards act as a "compositional bridge", enabling our model to significantly outperform much larger models and frontier systems like GPT-5.2 and Gemini 3 Pro, on the most difficult reasoning tasks. Furthermore, we demonstrate the robustness of our approach to adversarial perturbations against option-shuffling stress tests. This work suggests that grounding the reasoning process in structured knowledge is a scalable and efficient path toward intelligent reasoning.