Dissecting Logical Reasoning in LLMs: A Fine-Grained Evaluation and Supervision Study

Logical reasoning is a core capability for many applications of large language models (LLMs), yet existing benchmarks often rely solely on final-answer accuracy, failing to capture the quality and structure of the reasoning process. We propose FineLogic, a fine-grained evaluation framework that assesses logical reasoning across three dimensions: overall benchmark accuracy, stepwise soundness, and representation-level alignment. In addition, to better understand how reasoning capabilities emerge, we conduct a comprehensive study on the effects of supervision format during fine-tuning. We construct four supervision styles (one natural language and three symbolic variants) and train LLMs under each. Our findings reveal that natural language supervision yields strong generalization even on out-of-distribution and long-context tasks, while symbolic reasoning styles promote more structurally sound and atomic inference chains. Further, our representation-level probing shows that fine-tuning primarily improves reasoning behaviors through step-by-step generation, rather than enhancing shortcut prediction or internalized correctness. Together, our framework and analysis provide a more rigorous and interpretable lens for evaluating and improving logical reasoning in LLMs.

MPS-Prover: Advancing Stepwise Theorem Proving by Multi-Perspective Search and Data Curation

Automated Theorem Proving (ATP) in formal languages remains a formidable challenge in AI, demanding rigorous logical deduction and navigating vast search spaces. While large language models (LLMs) have shown promising performance, existing stepwise provers often suffer from biased search guidance, leading to inefficiencies and suboptimal proof strategies. This paper introduces the Multi-Perspective Search Prover (MPS-Prover), a novel stepwise ATP system designed to overcome these limitations. MPS-Prover incorporates two key innovations: a highly effective post-training data curation strategy that prunes approximately 40% of redundant training data without sacrificing performance, and a multi-perspective tree search mechanism. This search integrates a learned critic model with strategically designed heuristic rules to diversify tactic selection, prevent getting trapped in unproductive states, and enhance search robustness. Extensive evaluations demonstrate that MPS-Prover achieves state-of-the-art performance on multiple challenging benchmarks, including miniF2F and ProofNet, outperforming prior 7B parameter models. Furthermore, our analyses reveal that MPS-Prover generates significantly shorter and more diverse proofs compared to existing stepwise and whole-proof methods, highlighting its efficiency and efficacy. Our work advances the capabilities of LLM-based formal reasoning and offers a robust framework and a comprehensive analysis for developing more powerful theorem provers.

DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning

The capacity for complex mathematical reasoning is a key benchmark for artificial intelligence. While reinforcement learning (RL) applied to LLMs shows promise, progress is significantly hindered by the lack of large-scale training data that is sufficiently challenging, possesses verifiable answer formats suitable for RL, and is free from contamination with evaluation benchmarks. To address these limitations, we introduce DeepMath-103K, a new, large-scale dataset comprising approximately 103K mathematical problems, specifically designed to train advanced reasoning models via RL. DeepMath-103K is curated through a rigorous pipeline involving source analysis, stringent decontamination against numerous benchmarks, and filtering for high difficulty (primarily Levels 5-9), significantly exceeding existing open resources in challenge. Each problem includes a verifiable final answer, enabling rule-based RL, and three distinct R1-generated solutions suitable for diverse training paradigms like supervised fine-tuning or distillation. Spanning a wide range of mathematical topics, DeepMath-103K promotes the development of generalizable reasoning. We demonstrate that models trained on DeepMath-103K achieve significant improvements on challenging mathematical benchmarks, validating its effectiveness. We release DeepMath-103K publicly to facilitate community progress in building more capable AI reasoning systems: https://github.com/zwhe99/DeepMath.

MMVU: Measuring Expert-Level Multi-Discipline Video Understanding

We introduce MMVU, a comprehensive expert-level, multi-discipline benchmark for evaluating foundation models in video understanding. MMVU includes 3,000 expert-annotated questions spanning 27 subjects across four core disciplines: Science, Healthcare, Humanities & Social Sciences, and Engineering. Compared to prior benchmarks, MMVU features three key advancements. First, it challenges models to apply domain-specific knowledge and perform expert-level reasoning to analyze specialized-domain videos, moving beyond the basic visual perception typically assessed in current video benchmarks. Second, each example is annotated by human experts from scratch. We implement strict data quality controls to ensure the high quality of the dataset. Finally, each example is enriched with expert-annotated reasoning rationals and relevant domain knowledge, facilitating in-depth analysis. We conduct an extensive evaluation of 32 frontier multimodal foundation models on MMVU. The latest System-2-capable models, o1 and Gemini 2.0 Flash Thinking, achieve the highest performance among the tested models. However, they still fall short of matching human expertise. Through in-depth error analyses and case studies, we offer actionable insights for future advancements in expert-level, knowledge-intensive video understanding for specialized domains.

SaSR-Net: Source-Aware Semantic Representation Network for Enhancing Audio-Visual Question Answering

Audio-Visual Question Answering (AVQA) is a challenging task that involves answering questions based on both auditory and visual information in videos. A significant challenge is interpreting complex multi-modal scenes, which include both visual objects and sound sources, and connecting them to the given question. In this paper, we introduce the Source-aware Semantic Representation Network (SaSR-Net), a novel model designed for AVQA. SaSR-Net utilizes source-wise learnable tokens to efficiently capture and align audio-visual elements with the corresponding question. It streamlines the fusion of audio and visual information using spatial and temporal attention mechanisms to identify answers in multi-modal scenes. Extensive experiments on the Music-AVQA and AVQA-Yang datasets show that SaSR-Net outperforms state-of-the-art AVQA methods.

Improving LLM Reasoning through Scaling Inference Computation with Collaborative Verification

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

Learning Molecular Representation in a Cell

Predicting drug efficacy and safety in vivo requires information on biological responses (e.g., cell morphology and gene expression) to small molecule perturbations. However, current molecular representation learning methods do not provide a comprehensive view of cell states under these perturbations and struggle to remove noise, hindering model generalization. We introduce the Information Alignment (InfoAlign) approach to learn molecular representations through the information bottleneck method in cells. We integrate molecules and cellular response data as nodes into a context graph, connecting them with weighted edges based on chemical, biological, and computational criteria. For each molecule in a training batch, InfoAlign optimizes the encoder's latent representation with a minimality objective to discard redundant structural information. A sufficiency objective decodes the representation to align with different feature spaces from the molecule's neighborhood in the context graph. We demonstrate that the proposed sufficiency objective for alignment is tighter than existing encoder-based contrastive methods. Empirically, we validate representations from InfoAlign in two downstream tasks: molecular property prediction against up to 19 baseline methods across four datasets, plus zero-shot molecule-morphology matching.

Learn Beyond The Answer: Training Language Models with Reflection for Mathematical Reasoning

Supervised fine-tuning enhances the problem-solving abilities of language models across various mathematical reasoning tasks. To maximize such benefits, existing research focuses on broadening the training set with various data augmentation techniques, which is effective for standard single-round question-answering settings. Our work introduces a novel technique aimed at cultivating a deeper understanding of the training problems at hand, enhancing performance not only in standard settings but also in more complex scenarios that require reflective thinking. Specifically, we propose reflective augmentation, a method that embeds problem reflection into each training instance. It trains the model to consider alternative perspectives and engage with abstractions and analogies, thereby fostering a thorough comprehension through reflective reasoning. Extensive experiments validate the achievement of our aim, underscoring the unique advantages of our method and its complementary nature relative to existing augmentation techniques.

MathChat: Benchmarking Mathematical Reasoning and Instruction Following in Multi-Turn Interactions

Large language models (LLMs) have demonstrated impressive capabilities in mathematical problem solving, particularly in single turn question answering formats. However, real world scenarios often involve mathematical question answering that requires multi turn or interactive information exchanges, and the performance of LLMs on these tasks is still underexplored. This paper introduces MathChat, a comprehensive benchmark specifically designed to evaluate LLMs across a broader spectrum of mathematical tasks. These tasks are structured to assess the models' abilities in multiturn interactions and open ended generation. We evaluate the performance of various SOTA LLMs on the MathChat benchmark, and we observe that while these models excel in single turn question answering, they significantly underperform in more complex scenarios that require sustained reasoning and dialogue understanding. To address the above limitations of existing LLMs when faced with multiturn and open ended tasks, we develop MathChat sync, a synthetic dialogue based math dataset for LLM finetuning, focusing on improving models' interaction and instruction following capabilities in conversations. Experimental results emphasize the need for training LLMs with diverse, conversational instruction tuning datasets like MathChatsync. We believe this work outlines one promising direction for improving the multiturn mathematical reasoning abilities of LLMs, thus pushing forward the development of LLMs that are more adept at interactive mathematical problem solving and real world applications.

Defending Jailbreak Prompts via In-Context Adversarial Game

Large Language Models (LLMs) demonstrate remarkable capabilities across diverse applications. However, concerns regarding their security, particularly the vulnerability to jailbreak attacks, persist. Drawing inspiration from adversarial training in deep learning and LLM agent learning processes, we introduce the In-Context Adversarial Game (ICAG) for defending against jailbreaks without the need for fine-tuning. ICAG leverages agent learning to conduct an adversarial game, aiming to dynamically extend knowledge to defend against jailbreaks. Unlike traditional methods that rely on static datasets, ICAG employs an iterative process to enhance both the defense and attack agents. This continuous improvement process strengthens defenses against newly generated jailbreak prompts. Our empirical studies affirm ICAG's efficacy, where LLMs safeguarded by ICAG exhibit significantly reduced jailbreak success rates across various attack scenarios. Moreover, ICAG demonstrates remarkable transferability to other LLMs, indicating its potential as a versatile defense mechanism.