Large language models (LLMs) have achieved remarkable performance in generating human-like text and solving reasoning tasks of moderate complexity, such as question-answering and mathematical problem-solving. However, their capabilities in tasks requiring deeper cognitive skills, such as common-sense understanding and abstract reasoning, remain under-explored. In this paper, we systematically evaluate abstract common-sense reasoning in LLMs using the ConceptNet knowledge graph. We propose two prompting approaches: instruct prompting, where models predict plausible semantic relationships based on provided definitions, and few-shot prompting, where models identify relations using examples as guidance. Our experiments with the gpt-4o-mini model show that in instruct prompting, consistent performance is obtained when ranking multiple relations but with substantial decline when the model is restricted to predicting only one relation. In few-shot prompting, the model's accuracy improves significantly when selecting from five relations rather than the full set, although with notable bias toward certain relations. These results suggest significant gaps still, even in commercially used LLMs' abstract common-sense reasoning abilities, compared to human-level understanding. However, the findings also highlight the promise of careful prompt engineering, based on selective retrieval, for obtaining better performance.
Large language models (LLMs) have demonstrated remarkable capabilities across a range of text-generation tasks. However, LLMs still struggle with problems requiring multi-step decision-making and environmental feedback, such as online shopping, scientific reasoning, and mathematical problem-solving. Unlike pure text data, collecting large-scale decision-making data is challenging. Moreover, many powerful LLMs are only accessible through APIs, which hinders their fine-tuning for agent tasks due to cost and complexity. To address LLM agents' limitations, we propose a framework that can automatically learn a reward model from the environment without human annotations. This model can be used to evaluate the action trajectories of LLM agents and provide heuristics for task planning. Specifically, our approach involves employing one LLM-based agent to navigate an environment randomly, generating diverse action trajectories. Subsequently, a separate LLM is leveraged to assign a task intent and synthesize a negative response alongside the correct response for each trajectory. These triplets (task intent, positive response, and negative response) are then utilized as training data to optimize a reward model capable of scoring action trajectories. The effectiveness and generalizability of our framework are demonstrated through evaluations conducted on different agent benchmarks. In conclusion, our proposed framework represents a significant advancement in enhancing LLM agents' decision-making capabilities. By automating the learning of reward models, we overcome the challenges of data scarcity and API limitations, potentially revolutionizing the application of LLMs in complex and interactive environments. This research paves the way for more sophisticated AI agents capable of tackling a wide range of real-world problems requiring multi-step decision-making.
Claim verification is the task of determining whether a claim is supported or refuted by evidence. Self-improvement methods, where reasoning chains are generated and those leading to correct results are selected for training, have succeeded in tasks like mathematical problem solving. However, in claim verification, this approach struggles. Low-quality reasoning chains may falsely match binary truth labels, introducing faulty reasoning into the self-improvement process and ultimately degrading performance. To address this, we propose STRIVE: Structured Reasoning for Self-Improved Verification. Our method introduces a structured reasoning design with Claim Decomposition, Entity Analysis, and Evidence Grounding Verification. These components improve reasoning quality, reduce errors, and provide additional supervision signals for self-improvement. STRIVE begins with a warm-up phase, where the base model is fine-tuned on a small number of annotated examples to learn the structured reasoning design. It is then applied to generate reasoning chains for all training examples, selecting only those that are correct and structurally sound for subsequent self-improvement training. We demonstrate that STRIVE achieves significant improvements over baseline models, with a 31.4% performance gain over the base model and 20.7% over Chain of Thought on the HOVER datasets, highlighting its effectiveness.
Existing approaches to mathematical reasoning with large language models (LLMs) rely on Chain-of-Thought (CoT) for generalizability or Tool-Integrated Reasoning (TIR) for precise computation. While efforts have been made to combine these methods, they primarily rely on post-selection or predefined strategies, leaving an open question: whether LLMs can autonomously adapt their reasoning strategy based on their inherent capabilities. In this work, we propose TATA (Teaching LLMs According to Their Aptitude), an adaptive framework that enables LLMs to personalize their reasoning strategy spontaneously, aligning it with their intrinsic aptitude. TATA incorporates base-LLM-aware data selection during supervised fine-tuning (SFT) to tailor training data to the model's unique abilities. This approach equips LLMs to autonomously determine and apply the appropriate reasoning strategy at test time. We evaluate TATA through extensive experiments on six mathematical reasoning benchmarks, using both general-purpose and math-specialized LLMs. Empirical results demonstrate that TATA effectively combines the complementary strengths of CoT and TIR, achieving superior or comparable performance with improved inference efficiency compared to TIR alone. Further analysis underscores the critical role of aptitude-aware data selection in enabling LLMs to make effective and adaptive reasoning decisions and align reasoning strategies with model capabilities.
Mathematical reasoning represents a critical frontier in advancing large language models (LLMs). While step-by-step approaches have emerged as the dominant paradigm for mathematical problem-solving in LLMs, the quality of reasoning steps in training data fundamentally constrains the performance of the models. Recent studies has demonstrated that more detailed intermediate steps can enhance model performance, yet existing methods for step expansion either require more powerful external models or incur substantial computational costs. In this paper, we introduce MathFimer, a novel framework for mathematical reasoning step expansion inspired by the "Fill-in-the-middle" task from code completion. By decomposing solution chains into prefix-suffix pairs and training models to reconstruct missing intermediate steps, we develop a specialized model, MathFimer-7B, on our carefully curated NuminaMath-FIM dataset. We then apply these models to enhance existing mathematical reasoning datasets by inserting detailed intermediate steps into their solution chains, creating MathFimer-expanded versions. Through comprehensive experiments on multiple mathematical reasoning datasets, including MathInstruct, MetaMathQA and etc., we demonstrate that models trained on MathFimer-expanded data consistently outperform their counterparts trained on original data across various benchmarks such as GSM8K and MATH. Our approach offers a practical, scalable solution for enhancing mathematical reasoning capabilities in LLMs without relying on powerful external models or expensive inference procedures.
Large Language Models (LLMs) have demonstrated impressive capabilities in natural language processing tasks, such as text generation and semantic understanding. However, their performance on numerical reasoning tasks, such as basic arithmetic, numerical retrieval, and magnitude comparison, remains surprisingly poor. This gap arises from their reliance on surface-level statistical patterns rather than understanding numbers as continuous magnitudes. Existing benchmarks primarily focus on either linguistic competence or structured mathematical problem-solving, neglecting fundamental numerical reasoning required in real-world scenarios. To bridge this gap, we propose NumericBench, a comprehensive benchmark to evaluate six fundamental numerical capabilities: number recognition, arithmetic operations, contextual retrieval, comparison, summary, and logical reasoning. NumericBench includes datasets ranging from synthetic number lists to the crawled real-world data, addressing challenges like long contexts, noise, and multi-step reasoning. Extensive experiments on state-of-the-art LLMs, including GPT-4 and DeepSeek, reveal persistent weaknesses in numerical reasoning, highlighting the urgent need to improve numerically-aware language modeling. The benchmark is released in: https://github.com/TreeAI-Lab/NumericBench.
This paper introduces Code-Vision, a benchmark designed to evaluate the logical understanding and code generation capabilities of Multimodal Large Language Models (MLLMs). It challenges MLLMs to generate a correct program that fulfills specific functionality requirements based on a given flowchart, which visually represents the desired algorithm or process. Code-Vision comprises three subsets: HumanEval-V, Algorithm, and MATH, which evaluate MLLMs' coding abilities across basic programming, algorithmic, and mathematical problem-solving domains. Our experiments evaluate 12 MLLMs on Code-Vision. Experimental results demonstrate that there is a large performance difference between proprietary and open-source models. On Hard problems, GPT-4o can achieve 79.3% pass@1, but the best open-source model only achieves 15%. Further experiments reveal that Code-Vision can pose unique challenges compared to other multimodal reasoning benchmarks MMCode and MathVista. We also explore the reason for the poor performance of the open-source models. All data and codes are available at https://github.com/wanghanbinpanda/CodeVision.
Large Language Models (LLMs) have succeeded remarkably in various natural language processing (NLP) tasks, yet their reasoning capabilities remain a fundamental challenge. While LLMs exhibit impressive fluency and factual recall, their ability to perform complex reasoning-spanning logical deduction, mathematical problem-solving, commonsense inference, and multi-step reasoning-often falls short of human expectations. This survey provides a comprehensive review of emerging techniques enhancing reasoning in LLMs. We categorize existing methods into key approaches, including prompting strategies (e.g., Chain-of-Thought reasoning, Self-Consistency, and Tree-of-Thought reasoning), architectural innovations (e.g., retrieval-augmented models, modular reasoning networks, and neuro-symbolic integration), and learning paradigms (e.g., fine-tuning with reasoning-specific datasets, reinforcement learning, and self-supervised reasoning objectives). Additionally, we explore evaluation frameworks used to assess reasoning in LLMs and highlight open challenges, such as hallucinations, robustness, and reasoning generalization across diverse tasks. By synthesizing recent advancements, this survey aims to provide insights into promising directions for future research and practical applications of reasoning-augmented LLMs.
Large Language Models (LLMs) have demonstrated impressive reasoning capabilities, yet their performance is highly dependent on the prompting strategy and model scale. While reinforcement learning and fine-tuning have been deployed to boost reasoning, these approaches incur substantial computational and data overhead. In this work, we introduce Adaptive Graph of Thoughts (AGoT), a dynamic, graph-based inference framework that enhances LLM reasoning solely at test time. Rather than relying on fixed-step methods like Chain of Thought (CoT) or Tree of Thoughts (ToT), AGoT recursively decomposes complex queries into structured subproblems, forming an dynamic directed acyclic graph (DAG) of interdependent reasoning steps. By selectively expanding only those subproblems that require further analysis, AGoT unifies the strengths of chain, tree, and graph paradigms into a cohesive framework that allocates computation where it is most needed. We validate our approach on diverse benchmarks spanning multi-hop retrieval, scientific reasoning, and mathematical problem-solving, achieving up to 46.2% improvement on scientific reasoning tasks (GPQA) - comparable to gains achieved through computationally intensive reinforcement learning approaches and outperforming state-of-the-art iterative approaches. These results suggest that dynamic decomposition and structured recursion offer a scalable, cost-effective alternative to post-training modifications, paving the way for more robust, general-purpose reasoning in LLMs.
This study investigates the performance of the DeepSeek R1 language model on 30 challenging mathematical problems derived from the MATH dataset, problems that previously proved unsolvable by other models under time constraints. Unlike prior work, this research removes time limitations to explore whether DeepSeek R1's architecture, known for its reliance on token-based reasoning, can achieve accurate solutions through a multi-step process. The study compares DeepSeek R1 with four other models (gemini-1.5-flash-8b, gpt-4o-mini-2024-07-18, llama3.1:8b, and mistral-8b-latest) across 11 temperature settings. Results demonstrate that DeepSeek R1 achieves superior accuracy on these complex problems but generates significantly more tokens than other models, confirming its token-intensive approach. The findings highlight a trade-off between accuracy and efficiency in mathematical problem-solving with large language models: while DeepSeek R1 excels in accuracy, its reliance on extensive token generation may not be optimal for applications requiring rapid responses. The study underscores the importance of considering task-specific requirements when selecting an LLM and emphasizes the role of temperature settings in optimizing performance.
Large language models (LLMs) excel in many natural language tasks, yet they struggle with complex mathemat-ical problem-solving, particularly in symbolic reasoning and maintaining consistent output. This study evalu-ates 10 LLMs with 7 to 8 billion parameters using 945 competition-level problems from the MATH dataset. The focus is on their ability to generate executable Python code as a step in their reasoning process, involving over 9,450 code executions. The research introduces an evaluation framework using mistral-large-2411 to rate answers on a 5-point scale, which helps address inconsistencies in mathematical notation. It also examines the impact of regenerating output token-by-token on refining results. The findings reveal a significant 34.5% per-formance gap between the top commercial model (gpt-4o-mini, scoring 83.7%) and the least effective open-source model (open-codestral-mamba:v0.1, scoring 49.2%). This disparity is especially noticeable in complex areas like Number Theory. While token-by-token regeneration slightly improved accuracy (+0.8%) for the model llama3.1:8b, it also reduced code execution time by 36.7%, highlighting a trade-off between efficiency and precision. The study also noted a consistent trend where harder problems correlated with lower accuracy across all models. Despite using controlled execution environments, less than 1% of the generated code was unsafe, and 3.17% of problems remained unsolved after 10 attempts, suggesting that hybrid reasoning methods may be beneficial.
Current multimodal large language models (MLLMs) often underperform on mathematical problem-solving tasks that require fine-grained visual understanding. The limitation is largely attributable to inadequate perception of geometric primitives during image-level contrastive pre-training (e.g., CLIP). While recent efforts to improve math MLLMs have focused on scaling up mathematical visual instruction datasets and employing stronger LLM backbones, they often overlook persistent errors in visual recognition. In this paper, we systematically evaluate the visual grounding capabilities of state-of-the-art MLLMs and reveal a significant negative correlation between visual grounding accuracy and problem-solving performance, underscoring the critical role of fine-grained visual understanding. Notably, advanced models like GPT-4o exhibit a 70% error rate when identifying geometric entities, highlighting that this remains a key bottleneck in visual mathematical reasoning. To address this, we propose a novel approach, SVE-Math (Selective Vision-Enhanced Mathematical MLLM), featuring a geometric-grounded vision encoder and a feature router that dynamically adjusts the contribution of hierarchical visual feature maps. Our model recognizes accurate visual primitives and generates precise visual prompts tailored to the language model's reasoning needs. In experiments, SVE-Math-Qwen2.5-7B outperforms other 7B models by 15% on MathVerse and is compatible with GPT-4V on MathVista. Despite being trained on smaller datasets, SVE-Math-7B achieves competitive performance on GeoQA, rivaling models trained on significantly larger datasets. Our findings emphasize the importance of incorporating fine-grained visual understanding into MLLMs and provide a promising direction for future research.
With the rising need for speech-based interaction models, end-to-end Spoken Language Models (SLMs) have emerged as a promising solution. While these models require comprehensive world knowledge for meaningful and reliable human interactions, existing question-answering (QA) benchmarks fall short in evaluating SLMs' knowledge understanding due to their inability to support end-to-end speech evaluation and account for varied input audio conditions. To address these limitations, we present VoxEval, a novel SpeechQA benchmark that assesses SLMs' knowledge understanding through pure speech interactions. Our benchmark 1) uniquely maintains speech format for both inputs and outputs, 2) evaluates model robustness across diverse input audio conditions, and 3) pioneers the assessment of complex tasks like mathematical reasoning in spoken format. Systematic evaluation demonstrates that VoxEval presents significant challenges to current SLMs, revealing their sensitivity to varying audio conditions and highlighting the need to enhance reasoning capabilities in future development. We hope this benchmark could guide the advancement of more sophisticated and reliable SLMs. VoxEval dataset is available at: https://github.com/dreamtheater123/VoxEval
Mathematical problem-solving is a key field in artificial intelligence (AI) and a critical benchmark for evaluating the capabilities of large language models (LLMs). While extensive research has focused on mathematical problem-solving, most existing work and datasets concentrate on computational tasks, leaving gaps in areas like mathematical analysis, which demands rigorous proofs and formal reasoning. We developed the DEMI-MathAnalysis dataset, comprising proof-based problems from mathematical analysis topics such as Sequences and Limits, Infinite Series, and Convex Functions. We also designed a guiding framework to rigorously enhance LLMs' ability to solve these problems. Through fine-tuning LLMs on this dataset and employing our framework, we observed significant improvements in their capability to generate logical, complete, and elegant proofs. This work addresses critical gaps in mathematical reasoning and contributes to advancing trustworthy AI capable of handling formalized mathematical language. The code is publicly accessible at LLMs for Mathematical Analysis.
The rapid evolution of large language models (LLMs) has unlocked their capabilities in advanced reasoning tasks like mathematical problem-solving, code generation, and legal analysis. Central to this progress are inference-time reasoning algorithms, which refine outputs by exploring multiple solution paths, at the cost of increasing compute demands and response latencies. Existing serving systems fail to adapt to the scaling behaviors of these algorithms or the varying difficulty of queries, leading to inefficient resource use and unmet latency targets. We present Dynasor, a system that optimizes inference-time compute for LLM reasoning queries. Unlike traditional engines, Dynasor tracks and schedules requests within reasoning queries and uses Certaindex, a proxy that measures statistical reasoning progress based on model certainty, to guide compute allocation dynamically. Dynasor co-adapts scheduling with reasoning progress: it allocates more compute to hard queries, reduces compute for simpler ones, and terminates unpromising queries early, balancing accuracy, latency, and cost. On diverse datasets and algorithms, Dynasor reduces compute by up to 50% in batch processing and sustaining 3.3x higher query rates or 4.7x tighter latency SLOs in online serving.
The rapid advancement of large language models (LLMs) such as GPT-3, PaLM, and Llama has significantly transformed natural language processing, showcasing remarkable capabilities in understanding and generating language. However, these models often struggle with tasks requiring complex reasoning, particularly in mathematical problem-solving, due in part to the scarcity of large-scale, high-quality, domain-specific datasets necessary for training sophisticated reasoning abilities. To address this limitation, we introduce Template-based Data Generation (TDG), a novel approach that leverages LLMs (GPT-4) to automatically generate parameterized meta-templates, which are then used to synthesize a vast array of high-quality problems and solutions. Leveraging TDG, we create TemplateMath Part I: TemplateGSM, a dataset comprising over 7 million synthetically generated grade school math problems--each accompanied by code-based and natural language solutions--with the potential to generate an effectively unlimited number more. This dataset alleviates the scarcity of large-scale mathematical datasets and serves as a valuable resource for pre-training, fine-tuning, and evaluating LLMs in mathematical reasoning. Our method not only enables the generation of virtually infinite data but also elevates data augmentation to a new level by using GPT-4 for meta-template generation, ensuring diverse and high-quality problem structures. The TemplateMath Part I: TemplateGSM dataset is publicly available at https://huggingface.co/datasets/math-ai/TemplateGSM. The code is available at https://github.com/iiis-ai/TemplateMath.
This paper presents a critical examination of current approaches to replicating OpenAI's O1 model capabilities, with particular focus on the widespread but often undisclosed use of knowledge distillation techniques. While our previous work explored the fundamental technical path to O1 replication, this study reveals how simple distillation from O1's API, combined with supervised fine-tuning, can achieve superior performance on complex mathematical reasoning tasks. Through extensive experiments, we show that a base model fine-tuned on simply tens of thousands of samples O1-distilled long-thought chains outperforms O1-preview on the American Invitational Mathematics Examination (AIME) with minimal technical complexity. Moreover, our investigation extends beyond mathematical reasoning to explore the generalization capabilities of O1-distilled models across diverse tasks: hallucination, safety and open-domain QA. Notably, despite training only on mathematical problem-solving data, our models demonstrated strong generalization to open-ended QA tasks and became significantly less susceptible to sycophancy after fine-tuning. We deliberately make this finding public to promote transparency in AI research and to challenge the current trend of obscured technical claims in the field. Our work includes: (1) A detailed technical exposition of the distillation process and its effectiveness, (2) A comprehensive benchmark framework for evaluating and categorizing O1 replication attempts based on their technical transparency and reproducibility, (3) A critical discussion of the limitations and potential risks of over-relying on distillation approaches, our analysis culminates in a crucial bitter lesson: while the pursuit of more capable AI systems is important, the development of researchers grounded in first-principles thinking is paramount.
Mathematical reasoning presents a significant challenge to the cognitive capabilities of LLMs. Various methods have been proposed to enhance the mathematical ability of LLMs. However, few recognize the value of state transition for LLM reasoning. In this work, we define mathematical problem-solving as a process of transiting from an initial unsolved state to the final resolved state, and propose Kwai-STaR framework, which transforms LLMs into State-Transition Reasoners to improve their intuitive reasoning capabilities. Our approach comprises three main steps: (1) Define the state space tailored to the mathematical reasoning. (2) Generate state-transition data based on the state space. (3) Convert original LLMs into State-Transition Reasoners via a curricular training strategy. Our experiments validate the effectiveness of Kwai-STaR in enhancing mathematical reasoning: After training on the small-scale Kwai-STaR dataset, general LLMs, including Mistral-7B and LLaMA-3, achieve considerable performance gain on the GSM8K and GSM-Hard dataset. Additionally, the state transition-based design endows Kwai-STaR with remarkable training and inference efficiency. Further experiments are underway to establish the generality of Kwai-STaR.
In this paper, we introduce Hunyuan-Large, which is currently the largest open-source Transformer-based mixture of experts model, with a total of 389 billion parameters and 52 billion activation parameters, capable of handling up to 256K tokens. We conduct a thorough evaluation of Hunyuan-Large's superior performance across various benchmarks including language understanding and generation, logical reasoning, mathematical problem-solving, coding, long-context, and aggregated tasks, where it outperforms LLama3.1-70B and exhibits comparable performance when compared to the significantly larger LLama3.1-405B model. Key practice of Hunyuan-Large include large-scale synthetic data that is orders larger than in previous literature, a mixed expert routing strategy, a key-value cache compression technique, and an expert-specific learning rate strategy. Additionally, we also investigate the scaling laws and learning rate schedule of mixture of experts models, providing valuable insights and guidances for future model development and optimization. The code and checkpoints of Hunyuan-Large are released to facilitate future innovations and applications. Codes: https://github.com/Tencent/Hunyuan-Large Models: https://huggingface.co/tencent/Tencent-Hunyuan-Large
Although previous research on large language models (LLMs) and large multi-modal models (LMMs) has systematically explored mathematical problem-solving (MPS) within visual contexts, the analysis of how these models process visual information during problem-solving remains insufficient. To address this gap, we present VisAidMath, a benchmark for evaluating the MPS process related to visual information. We follow a rigorous data curation pipeline involving both automated processes and manual annotations to ensure data quality and reliability. Consequently, this benchmark includes 1,200 challenging problems from various mathematical branches, vision-aid formulations, and difficulty levels, collected from diverse sources such as textbooks, examination papers, and Olympiad problems. Based on the proposed benchmark, we conduct comprehensive evaluations on ten mainstream LLMs and LMMs, highlighting deficiencies in the visual-aided reasoning process. For example, GPT-4V only achieves 45.33% accuracy in the visual-aided reasoning task, even with a drop of 2 points when provided with golden visual aids. In-depth analysis reveals that the main cause of deficiencies lies in hallucination regarding the implicit visual reasoning process, shedding light on future research directions in the visual-aided MPS process.