Mathematical Reasoning

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17 papers in the last four weeks, against 2 the four weeks before. 0.1% of all new papers.

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Latest papers 113

Apr 27, 2026cs.CL

IRIS: Interleaved Reinforcement with Incremental Staged Curriculum for Cross-Lingual Mathematical Reasoning

Curriculum learning helps language models tackle complex reasoning by gradually increasing task difficulty. However, it often fails to generate consistent step-by-step reasoning, especially in multilingual and low-resource settings where cross-lingual transfer from English to Indian languages remains limited. We propose IRIS: Interleaved Reinforcement with Incremental Staged Curriculum, a two-axis framework that combines Supervised Fine-Tuning on progressively harder problems (vertical axis) with Reverse Curriculum Reinforcement Learning to reduce reliance on step-by-step guidance (horizontal axis). We design a composite reward combining correctness, step-wise alignment, continuity, and numeric incentives, optimized via Group Relative Policy Optimization (GRPO). We release CL-Math, a dataset of 29k problems with step-level annotations in English, Hindi, and Marathi. Across standard benchmarks and curated multilingual test sets, IRIS consistently improves performance, with strong results on math reasoning tasks and substantial gains in low-resource and bilingual settings, alongside modest improvements in high-resource languages.

Navya Gupta, Rishitej Reddy Vyalla, Avinash Anand +8

1Singapore Institute of Technology, Singapore · 2IIIT Delhi, New Delhi, India · University of California, San Diego, USA +2

Cross-Lingual Reasoning in Language Models RL for Language Model Reasoning Mathematical Reasoning Curriculum Learning Low-Resource Language Processing Cross-Lingual Transfer

Apr 22, 2026cs.CV

OMIBench: Benchmarking Olympiad-Level Multi-Image Reasoning in Large Vision-Language Model

Large vision-language models (LVLMs) have made substantial advances in reasoning tasks at the Olympiad level. Nevertheless, current Olympiad-level multimodal reasoning benchmarks for these models often emphasize single-image analysis and fail to exploit contextual information across multiple images. We present OMIBench, a benchmark designed to evaluate Olympiad-level reasoning when the required evidence is distributed over multiple images. It contains problems from biology, chemistry, mathematics, and physics Olympiads, together with manually annotated rationales and evaluation protocols for both exact and semantic answer matching. Across extensive experiments on OMIBench, we observe meaningful performance gaps in existing models. Even the strongest LVLMs, such as Gemini-3-Pro, attain only about 50% on the benchmark. These results position OMIBench as a focused resources for studying and improving multi-image reasoning in LVLMs.

Qiguang Chen, Chengyu Luan, Jiajun Wu +7

Research Center for Social Computing and Interactive Robotics, Harbin Institute of Technology · Central South University · Fudan University +3

VLM Evaluation Visual Reasoning Multimodal Reasoning Mathematical Reasoning VLM Reasoning

Apr 22, 2026cs.AI

HiPO: Hierarchical Preference Optimization for Adaptive Reasoning in LLMs

Direct Preference Optimization (DPO) is an effective framework for aligning large language models with human preferences, but it struggles with complex reasoning tasks. DPO optimizes for the likelihood of generating preferred over dispreferred responses in their entirety and lacks the granularity to provide feedback on subsections of many-step solutions typical of reasoning tasks. Existing methods excel at either stable preference learning (e.g., DPO variants like KTO and RSO) or structured reasoning (e.g., ReMA's multi-agent RL framework, Tree of Thoughts), but fail to merge these complementary strengths. We propose HiPO (Hierarchical Preference Optimization), an extension of DPO that separates responses into reasoning segments (query clarification and context, reasoning steps, and answer) and computes loss as a weighted sum of the DPO loss for each segment. Our approach enables segment-specific training while maintaining DPO's computational efficiency and training stability. We demonstrate that for multiple 7B LLMs fine-tuned using HiPO and DPO on the Math Stack Exchange preference dataset, the models trained with HiPO outperform the others on a variety of common math benchmarks and achieve greater organization, logical flow, and consistency as measured by GPT-4.1.

Darsh Kachroo, Arjun Prasaath Anbazhagan, Adriana Caraeni +2

Vellore Institute of Technology, Chennai · Northwestern University · University of Massachusetts Amherst +2

LLM Alignment Direct Preference Optimization Mathematical Reasoning Preference Optimization LLM Reasoning

Apr 21, 2026cs.CL

How Do Answer Tokens Read Reasoning Traces? Self-Reading Patterns in Thinking LLMs for Quantitative Reasoning

Thinking LLMs produce reasoning traces before answering. Prior activation steering work mainly targets on shaping these traces. It remains less understood how answer tokens actually read and integrate the reasoning to produce reliable outcomes. Focusing on quantitative reasoning, we analyze the answer-to-reasoning attention and observe a benign self-reading pattern aligned with correctness, characterized by a forward drift of the reading focus along the reasoning trace and a persistent concentration on key semantic anchors, whereas incorrect solutions exhibit diffuse and irregular attention pattern. We interpret this as internal certainty during answer decoding, where the model commits to a viable solution branch and integrates key evidence. Following this, we propose a training-free steering method driven by Self-Reading Quality (SRQ) scores combining geometric metrics for process control with semantic metrics for content monitoring. SRQ selects data to build steering vectors that guide inference toward benign self-reading and away from uncertain and disorganized reading. Experiments show that our method yields consistent accuracy gains.

Haoyang Chen, Yi Liu, Jianzhi Shao +3

State Key Laboratory for Novel Software Technology, Nanjing University, China · Alibaba Group, China · Ant Group, China

LLM Interpretability Mathematical Reasoning Activation Steering LLM Reasoning Reasoning Trace Analysis

Apr 20, 2026cs.CL

Less Is More: Cognitive Load and the Single-Prompt Ceiling in LLM Mathematical Reasoning

We present a systematic empirical study of prompt engineering for formal mathematical reasoning in the context of the SAIR Equational Theories Stage 1 competition. The task requires deciding whether one equational law implies another over all magmas -- a problem that is undecidable in general but decidable for FALSE via finite model search. Over five weeks, we designed, tested, and analyzed more than 40 prompt variants, ranging from 0 to 4,878 bytes, across four evaluation splits and three language models (gpt-oss-120b, Llama 3.3 70B, Gemma 4 31B). Our central finding is a single-prompt ceiling: despite substantial engineering effort, balanced hard accuracy plateaus in an empirical saturation region of approximately 60--79% for gpt-oss-120b, compared to a 59.75% no-cheatsheet baseline. We identify three mechanisms underlying this ceiling: (1) the mathematical undecidability of the TRUE case limits what any finite prompt can encode; (2) complex rule systems decrease performance on weaker models (Llama 3.3 70B collapses to 0% TRUE recall with prompts exceeding 2KB); and (3) prompt ordering effects interact with model attention in fragile, non-monotonic ways. Our best submission (AN45c, 2,252 bytes) achieves 79.25% accuracy on hard3 (n=400; 95% CI: [75.0%, 82.9%]), with TRUE recall of 95.9% and FALSE recall of 63.4%, representing a +19.5 percentage-point improvement over the no-cheatsheet baseline (59.75%). We release all prompt variants, evaluation scripts, and results at https://github.com/israelcazares/sair-prompt-engineering

Manuel Israel Cazares

Bytepro AI Mazatlán, Sinaloa, Mexico

Prompt Sensitivity LLM Prompting Mathematical Reasoning LLM Mathematical Reasoning

Apr 19, 2026cs.CL

Probabilistic Programs of Thought

LLMs are widely used for code generation and mathematical reasoning tasks where they are required to generate structured output. They either need to reason about code, generate code for a given specification, or reason using programs of thought. The typical approach to code generation is to prompt the model and generate samples until an appropriate program is obtained. Within this process, sampling

n

programs from the language model requires

n

GPU compute-intensive generations which becomes prohibitively expensive for larger values of

n

. In this work, we address this limitation by exposing the LLM's distribution within the generated programs themselves. We propose a novel test-time framework we dub probabilistic programs of thought to obtain more samples from the model with fewer LLM generations. Given a program generated by a model and the associated next-token probabilities, we build a probabilistic program that compactly represents exponentially many deterministic programs. Since performing probabilistic reasoning in this probabilistic program is much cheaper, our approach allows sampling new programs without any additional GPU compute and little CPU overhead. We instantiate our approach on benchmarks for code generation, code understanding and mathematical reasoning and report improvements in performance with fewer generations from the LLM.

Poorva Garg, Renato Lui Geh, Daniel Israel +3

University of California Los Angeles · Allen Institute for AI

LLM-Based Program Synthesis Efficient Language Model Reasoning LLM Inference Acceleration Mathematical Reasoning Probabilistic Programming LLM Reasoning

Apr 17, 2026cs.CV

DenTab: A Dataset for Table Recognition and Visual QA on Real-World Dental Estimates

Tables condense key transactional and administrative information into compact layouts, but practical extraction requires more than text recognition: systems must also recover structure (rows, columns, merged cells, headers) and interpret roles such as line items, subtotals, and totals under common capture artifacts. Many existing resources for table structure recognition and TableVQA are built from clean digital-born sources or rendered tables, and therefore only partially reflect noisy administrative conditions. We introduce DenTab, a dataset of 2{,}000 cropped table images from dental estimates with high-quality HTML annotations, enabling evaluation of table recognition (TR) and table visual question answering (TableVQA) on the same inputs. DenTab includes 2{,}208 questions across eleven categories spanning retrieval, aggregation, and logic/consistency checks. We benchmark 16 systems, including 14 vision--language models (VLMs) and two OCR baselines. Across models, strong structure recovery does not consistently translate into reliable performance on multi-step arithmetic and consistency questions, and these reasoning failures persist even when using ground-truth HTML table inputs. To improve arithmetic reliability without training, we propose the Table Router Pipeline, which routes arithmetic questions to deterministic execution. The pipeline combines (i) a VLM that produces a baseline answer, a structured table representation, and a constrained table program with (ii) a rule-based executor that performs exact computation over the parsed table. The source code and dataset will be made publicly available at https://github.com/hamdilaziz/DenTab.

Laziz Hamdi, Amine Tamasna, Thierry Paquet

LITIS, Normandy, France · Malakoff Humanis, Paris, France

Table QA Table Structure Recognition Mathematical Reasoning Document Image Understanding

Apr 15, 2026cs.CL

Correct Prediction, Wrong Steps? Consensus Reasoning Knowledge Graph for Robust Chain-of-Thought Synthesis

Large language models (LLMs) have become increasingly used for various tasks, often coupled with Chain-of-Thought (CoT) prompting to boost accuracy. Recent work has shown that high label-prediction accuracy does not guarantee correct intermediate reasoning, and the causes of reasoning flaws vary from sample to sample, yet existing remedies either focus on a single domain or assume that one flaw type applies uniformly across samples. A simple mitigation method is to provide the model with the correct answer, but we show that this yields no consistent improvement in reasoning quality. This indicates that the problem cannot be fixed by LLMs' awareness of answers, and must instead be addressed through the structure of reasoning. Motivated by this, we propose CRAFT (Consensus Reasoning-knowledge-graph Aggregation for Flaw-aware Trace synthesis), which aggregates the consensus components shared across multiple candidate reasoning traces to synthesize improved ones. CRAFT consistently improves label-prediction accuracy on both logical and mathematical reasoning benchmarks, outperforming most baselines, while its post-processed traces achieve higher quality under fine-grained benchmark evaluation.

Zipeng Ling, Shuliang Liu, Seonil Son +4

The Hong Kong University of Science and Technology (Guangzhou) · University of Alberta · Alberta Machine Intelligence Institute +3

Logical Reasoning Self-Consistency Decoding CoT Reasoning Mathematical Reasoning Structured Reasoning LLM Reliability+2

Apr 6, 2026cs.CL

What Makes Good Multilingual Reasoning? Disentangling Traces with Measurable Features

Large Reasoning Models (LRMs) still exhibit large performance gaps between English and other languages, yet much current work assumes these gaps can be closed simply by making reasoning in every language resemble English reasoning. This work challenges this assumption by asking instead: what actually characterizes successful reasoning traces in multilingual settings, and to what extent do English-derived reasoning features genuinely help in other languages? We first define a suite of measurable reasoning features spanning multilingual alignment, reasoning step, and reasoning flow aspects of reasoning traces, and use logistic regression to quantify how each feature associates with final answer accuracy. We further train sparse autoencoders over multilingual traces to automatically discover latent reasoning concepts that instantiate or extend these features. Finally, we use the features to re-rank traces and measure their impact on accuracy at test time. Across two mathematical reasoning benchmarks, four LRMs, and ten languages, we find that most features are positively associated with accuracy, but the strength of association varies considerably across languages and can even reverse in some. Our findings challenge English-centric reward designs and point toward adaptive objectives that accommodate language-specific reasoning patterns, with concrete implications for multilingual benchmark and reward design.

Dayeon Ki, Kevin Duh, Marine Carpuat

University of Maryland · Johns Hopkins University

Multilingual Language Model Evaluation Cross-Lingual Reasoning in Language Models Mathematical Reasoning Large Reasoning Models Reasoning Trace Analysis

Feb 5, 2026cs.LG

BRIDGE: Bridging Reasoning In Distillation Gap Elimination via Structure-Aware Masking

Chain-of-Thought (CoT) reasoning has significantly improved LLMs' mathematical problem-solving capabilities, but distilling such capabilities into smaller models remains challenging due to the capacity mismatch between verbose teachers and compact students. Directly copying teachers' lengthy reasoning chains causes capacity overload, resulting in truncated outputs or repetitive failure. Existing remedies each sacrifice a critical property of CoT: implicit reasoning methods (e.g., compressing reasoning into hidden states) trade away interpretability and verifiability, while heuristic compression strategies (e.g., random step pruning) destroy logical integrity. To address this, we propose BRIDGE, a curriculum framework that first establishes structural understanding via masked reconstruction, then uses GRPO-based reinforcement learning to guide students in self-discovering the optimal balance between accuracy and brevity, and finally internalizes complex reasoning through teacher-guided rewriting on failure cases. On GSM8K, BRIDGE enables Qwen2.5-3B to achieve 11.29% accuracy improvement and 27.4% token reduction over the original model, outperforming instruction-tuned variants and distillation baselines. Zero-shot transfer experiments on SVAMP and MATH-500 further confirm the generalization of internalized reasoning. Our code and model checkpoints are publicly available at https://github.com/Applied-Machine-Learning-Lab/SDM2026_BRIDGE and https://huggingface.co/bowen0815/BRIDGE.

Bowen Yu, Sheng Zhang, Binhao Wang +8

1City University of Hong Kong · 2Mohamed Bin Zayed University of Artificial Intelligence

CoT Distillation Mathematical Reasoning Teacher-Student Learning CoT Compression

Feb 2, 2026cs.CL

ProofVerifier: A Scalable, Diversity-Driven Framework for Natural-Language Proof Verification

While large language models (LLMs) have achieved strong performance on mathematical problems with verifiable answers, many advanced problems are proof-based and require evaluating full proofs. However, training such verifiers requires diverse and trustworthy question-proof-check (QPC) examples at scale, which are scarce. To address this challenge, we develop a human-audited, LLM-assisted data pipeline that produces large-scale QPC triplets with limited human effort. By systematically varying problem sources, generation strategies, and generator models, the pipeline creates diverse problem-proof pairs spanning multiple difficulty levels, linguistic styles, and error types. We combine multi-LLM agreement with hierarchical human auditing to obtain accurate proof-correctness labels. Using these data, we train generative proof verifiers and introduce an auxiliary fluency filter together with balanced token weighting to stabilize binary-reward long-form verification RL. Experiments show that our verifier improves proof-judgment accuracy across different proof styles and provides useful guidance for test-time selection. Overall, our results provide a practical data and training framework for natural-language proof verification.

Haotong Yang, Zitong Wang, Shijia Kang +7

Peking University, Beijing, China · Tencent

Synthetic Data Generation Mathematical Reasoning

Feb 1, 2026cs.CL

ConPress: Learning Efficient Reasoning from Multi-Question Contextual Pressure

Large reasoning models (LRMs) typically solve reasoning-intensive tasks by generating long chain-of-thought (CoT) traces, leading to substantial inference overhead. We identify a reproducible inference-time phenomenon, termed Self-Compression: when multiple independent and answerable questions are presented within a single prompt, the model spontaneously produces shorter reasoning traces for each question. This phenomenon arises from multi-question contextual pressure during generation and consistently manifests across models and benchmarks. Building on this observation, we propose ConPress (Learning from Contextual Pressure), a lightweight self-supervised fine-tuning approach. ConPress constructs multi-question prompts to induce self-compression, samples the resulting model outputs, and parses and filters per-question traces to obtain concise yet correct reasoning trajectories. These trajectories are directly used for supervised fine-tuning, internalizing compressed reasoning behavior in single-question settings without external teachers, manual pruning, or reinforcement learning. With only 8k fine-tuning examples, ConPress reduces reasoning token usage by 59% on MATH500 and 33% on AIME25, while maintaining competitive accuracy.

Jie Deng, Shining Liang, Jun Li +2

University of Chinese Academy of Sciences, Beijing, China · 2Microsoft, Beijing, China · 3Tongji University, Shanghai, China

Efficient Language Model Reasoning LLM Inference Acceleration Mathematical Reasoning CoT Compression Large Reasoning Models

Jan 26, 2026cs.LG

Teaching Models to Teach Themselves: Reasoning at the Edge of Learnability

RL methods for scaling large reasoning models stall on datasets with low initial success rates, and thus little training signal. We investigate a fundamental question: Can a pretrained LLM leverage latent knowledge to generate an automated curriculum for problems it cannot solve? We explore this with SOAR: An asymmetric self-play framework that uses meta-RL to surface these pedagogical signals. A teacher model proposes synthetic problems for a student model, and is rewarded with its improvement on a subset of hard problems, thus grounding the curriculum in real student progress rather than intrinsic proxy rewards. Our study on the hardest subsets of math benchmarks (0/128 success) reveals three core findings. First, it is possible to realize bilevel meta-RL that unlocks learning under sparse, binary rewards by sharpening a latent capacity of pretrained models to generate useful problems. Second, grounded rewards outperform intrinsic learnability rewards used in prior LLM self-play, reliably avoiding typical instability and diversity collapse modes. Third, the structure and well-posedness of questions are more critical for learning progress than solution correctness. Our results suggest that the ability to generate useful stepping stones does not require the preexisting ability to solve the hard problems, paving a principled path to escape reasoning plateaus without additional curated data

Shobhita Sundaram, John Quan, Ariel Kwiatkowski +3

1MIT · 2Meta FAIR · 3New York University

Self-Play RL RL for Language Model Reasoning Curriculum RL Mathematical Reasoning Meta-Reinforcement Learning Curriculum Learning+2

Jan 11, 2026cs.CL

DAGGER: Distractor-Aware Graph Generation for Executable Reasoning in Math Problems

Chain-of-Thought (CoT) prompting is widely adopted for mathematical problem solving, including in low-resource languages, yet its behavior under irrelevant context remains underexplored. To systematically study this challenge, we introduce DISTRACTMATH-BN, a Bangla benchmark that augments MGSM and MSVAMP with semantically coherent but computationally irrelevant information. Evaluating seven models ranging from 3B to 12B parameters, we observe substantial performance degradation under distractors: standard models drop by up to 41 points, while reasoning-specialized models decline by 14 to 20 points despite consuming five times more tokens. We propose †DAGGER, which reformulates mathematical problem solving as executable computational graph generation with explicit modeling of distractor nodes. Fine-tuning Gemma-3 models using supervised fine-tuning followed by Group Relative Policy Optimization achieves comparable weighted accuracy on augmented benchmarks while using 89 percent fewer tokens than reasoning models. Importantly, this robustness emerges without explicit training on distractor-augmented examples. Our results suggest that enforcing structured intermediate representations improves robustness and inference efficiency in mathematical reasoning compared to free-form approaches, particularly in noisy, low-resource settings.

Zabir Al Nazi, Shubhashis Roy Dipta, Sudipta Kar

University of California, Riverside · University of Maryland, Baltimore County · Oracle Health AI

Numerical Reasoning in Language Models Mathematical Reasoning Benchmarks LLM Reasoning with Graphs Mathematical Reasoning

Dec 17, 2025cs.AI

Stepwise Think-Critique: Interleaved Reasoning and Self-Critique in a Single LLM

Human beings solve complex problems through critical thinking, where reasoning and evaluation are intertwined to converge toward correct solutions. However, most existing large language models (LLMs) treat the reasoning and verification as separate processes: they either generate reasoning without explicit self-checking or rely on external verifiers to detect errors post hoc. The former lacks immediate feedback, while the latter increases system complexity and hinders synchronized learning. Motivated by human critical thinking, we propose Stepwise Think-Critique (STC), an end-to-end trainable framework in which a single LLM emits a structured, step-level critique inline with each reasoning step. STC is trained with reinforcement learning that complements reasoning rewards with a critique-consistency reward derived from final-answer correctness, jointly optimizing reasoning correctness and critique reliability. On five mathematical reasoning benchmarks, STC improves Pass@1 by 7.2% over the 1.5B base model and attains 67.4% step-level critique F1, surpassing seven external process reward models evaluated at their per-dataset oracle thresholds---a step toward LLMs with built-in critical thinking.

Jiaqi Xu, Cuiling Lan, Xuejin Chen +1

University of Science and Technology of China · ⋆This work was done when Jiaqi was an intern at MSRA. · Microsoft Research Asia

LLM Self-Correction CoT Reasoning Mathematical Reasoning RL for Language Models

Oct 21, 2025cs.LG

A Model Can Help Itself: Reward-Free Self-Training for LLM Reasoning

Can a language model improve reasoning by learning from its own imperfect responses, without rewards or teacher-provided solutions? We present Self-evolving Post-Training (SePT), a simple method that alternates temperature-controlled self-generation with next-token likelihood training. Each round uses the updated model to generate new training responses, with one response per prompt by default and no correctness filtering. Across six mathematical benchmarks, SePT improves a temperature-selected no-training baseline by 11.4 and 6.7 AVG points on Qwen2.5-Math-7B and Qwen2.5-7B, respectively, where AVG averages Pass@1, Pass@8 and Pass@32 across benchmarks. We analyze how sampling temperature shapes the learning signal and investigate the value of the resulting responses. Responses from a SePT-trained model improve a student initialized from the original weights, while their reasoning prefixes help an unchanged model complete solutions, even when matched in length to prefixes from a colder initial model. Comparing next-token predictions at identical contexts also reveals changes in token rankings that decoding-temperature adjustment cannot reproduce. Further evaluations across nine starting models, general reasoning and code generation examine broader applicability. Together, these results show that reward-free self-training can improve both a model's predictions and the supervision it provides. Our code is available at https://github.com/ElementQi/SePT.

Mengqi Li, Lei Zhao, Anthony Man-Cho So +2

The Chinese University of Hong Kong, Shenzhen · Shanghai Jiao Tong University · The Chinese University of Hong Kong

Self-Training for Language Models Mathematical Reasoning LLM Post-Training Language Model Self-Improvement LLM Reasoning

Oct 10, 2025cs.CL

StatEval: A Comprehensive Benchmark for Large Language Models in Statistics

Despite rapid advances in large language models (LLMs), statistical reasoning remains underrepresented in existing LLM benchmarks, which often do not reflect the layered, proof-driven nature of real statistical practice. To address this gap, we introduce \textbf{StatEval}, the first large-scale benchmark for statistical reasoning across curricular and research-level settings. StatEval includes over 100,000 curated problems, with 20,000+ foundational questions spanning undergraduate and graduate curricula and 80,000+ research-level proof tasks extracted from leading statistical journals. To construct StatEval, we develop \textbf{TRACE} (Topology and Reasoning-Aware Context Extractor), a multi-agent pipeline with human-in-the-loop validation that converts unstructured academic texts into self-contained theorem-level reasoning tasks. We also propose an Adaptive Process-Based Scoring Pipeline for complex statistical proofs, enabling fine-grained evaluation beyond final-answer matching. Experiments show that while LLMs perform reasonably on foundational tasks, they struggle with rigorous research-level reasoning. Beyond evaluation, StatEval serves as a resource for improving reasoning, as retrieval-augmented generation and domain-specific alignment consistently enhance performance. Together, these results establish StatEval as both a benchmark and an infrastructure for advancing statistical reasoning in LLMs.

Yuchen Lu, Run Yang, Yichen Zhang +6

1Shanghai University of Finance and Economics

LLM Evaluation Reasoning Evaluation Mathematical Reasoning

Sep 30, 2025cs.CL

IMProofBench: Benchmarking AI on Research-Level Mathematical Proof Generation

As the mathematical capabilities of large language models (LLMs) improve, it becomes increasingly important to evaluate their performance on research-level tasks at the frontier of mathematical knowledge. However, existing benchmarks are limited, as they focus solely on final-answer questions or high-school competition problems. To address this gap, we introduce IMProofBench, a private benchmark consisting of 77 peer-reviewed problems developed by expert mathematicians. Each problem requires a detailed proof and is paired with subproblems that have final answers, supporting both an evaluation by human experts and a large-scale quantitative analysis through automated grading. Furthermore, unlike prior benchmarks, the evaluation setup simulates a realistic research environment: models operate in an agentic framework with tools like web search for literature review and mathematical software such as SageMath. Our results show that current LLMs can already solve a significant percentage of research-level questions. IMProofBench will continue to evolve as a dynamic benchmark in collaboration with the mathematical community, ensuring its relevance for evaluating the next generation of LLMs.

Johannes Schmitt, Gergely Bérczi, Jasper Dekoninck +57

Mathematical Reasoning Benchmarks LLM Evaluation Benchmark Design Mathematical Reasoning LLM Mathematical Reasoning

Aug 12, 2025cs.CL

An Investigation of Robustness of LLMs in Mathematical Reasoning: Benchmarking with Mathematically-Equivalent Transformation of Advanced Mathematical Problems

Frontier large language models (LLMs) now reach near-ceiling accuracy on standard mathematical-reasoning benchmarks and gold-medal-level performance at the International Mathematical Olympiad. As these benchmarks saturate and their items leak into training data, a high score no longer shows whether a model reasons robustly or which component of its reasoning fails. To evaluate reasoning while keeping results informative and failures diagnosable, we propose GAP (Generalisation-and-Perturbation), a methodology that automatically generates mathematically equivalent variants of existing mathematics problems at scale using two disjoint, interpretable transformations: (1) surface renames, probing the binding between identifiers and latent variable roles, and (2) kernel rewrites, probing whether a high-level proof plan survives a change of mathematical setting. Compared with existing benchmarks, GAP has two key benefits: (1) novel, likely unseen variants mitigate data leakage, and (2) performance across transformation families enables failure diagnosis, each transformation testing a hypothesis about the cause of failure. We instantiate GAP on all 1,051 William Lowell Putnam Competition problems from 1938 to 2024, adding 5,255 unseen variants to form PutnamGAP, a 6,306-item competition-level mathematics corpus and the first public machine-readable dataset from the full Putnam archive. Using PutnamGAP, we evaluated 18 commercial and open-source models spanning sizes and providers. Accuracy drops across all models and variant families, most severely under kernel rewrites. This gap does not close with model strength, suggesting that even the strongest models' dominant weakness is transferring a proof plan to a changed mathematical setting, rather than handling surface changes. Further analysis provides finer failure diagnoses and potentially useful insights for improving LLM reasoning.

Yuren Hao, Xiang Wan, ChengXiang Zhai

Department of Computer Science University of Illinois Urbana–Champaign Urbana, IL, USA · Department of Computer Science Stanford University Stanford, CA, USA

Mathematical Reasoning LLM Mathematical Reasoning Mathematical Reasoning Benchmarks

May 28, 2025cs.AI

AI Mathematician: Towards Fully Automated Frontier Mathematical Research

Large Reasoning Models (LRMs) have made significant progress in mathematical capabilities in recent times. However, these successes have been primarily confined to competition-level problems. In this work, we propose AI Mathematician (AIM) framework, which harnesses the reasoning strength of LRMs to support frontier mathematical research. We have identified two critical challenges of mathematical research compared to competition, the intrinsic complexity of research problems and the requirement of procedural rigor. To address these challenges, AIM incorporates two core strategies: an exploration mechanism to foster longer solution paths, and the pessimistic reasonable verification method to ensure reliability. This early version of AIM already exhibits strong capability in tackling research-level tasks. We conducted extensive experiments across several real-world mathematical topics and obtained promising results. AIM is able to autonomously construct substantial portions of proofs and uncover non-trivial insights within each research area. These findings highlight the potential of LRMs in mathematical discovery and suggest that LRM-based agent systems could significantly accelerate mathematical research in the future.

Yuanhang Liu, Yanxing Huang, Yanqiao Wang +2

Qiuzhen College, Tsinghua University · Department of Mathematical Sciences, Tsinghua University · Institute for AI Industry Research (AIR), Tsinghua University, Beijing, China +1

AI-Assisted Scientific Research Mathematical Reasoning Automated Theorem Proving Large Reasoning Models

Apr 7, 2025cs.LG

Efficient Reinforcement Finetuning via Adaptive Curriculum Learning

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

Taiwei Shi, Yiyang Wu, Linxin Song +2

University of Southern California · Carnegie Mellon University · Mohamed Bin Zayed University of Artificial Intelligence

RL for Language Model Reasoning Mathematical Reasoning Curriculum Learning RL Fine-Tuning Data-Efficient Learning

Sep 27, 2024cs.CL

Evaluation of OpenAI o1: Opportunities and Challenges of AGI

This comprehensive study evaluates the performance of OpenAI's o1-preview large language model across a diverse array of complex reasoning tasks, spanning multiple domains, including computer science, mathematics, natural sciences, medicine, linguistics, and social sciences. Through rigorous testing, o1-preview demonstrated remarkable capabilities, often achieving human-level or superior performance in areas ranging from coding challenges to scientific reasoning and from language processing to creative problem-solving. Key findings include: -83.3% success rate in solving complex competitive programming problems, surpassing many human experts. -Superior ability in generating coherent and accurate radiology reports, outperforming other evaluated models. -100% accuracy in high school-level mathematical reasoning tasks, providing detailed step-by-step solutions. -Advanced natural language inference capabilities across general and specialized domains like medicine. -Impressive performance in chip design tasks, outperforming specialized models in areas such as EDA script generation and bug analysis. -Remarkable proficiency in anthropology and geology, demonstrating deep understanding and reasoning in these specialized fields. -Strong capabilities in quantitative investing. O1 has comprehensive financial knowledge and statistical modeling skills. -Effective performance in social media analysis, including sentiment analysis and emotion recognition. The model excelled particularly in tasks requiring intricate reasoning and knowledge integration across various fields. While some limitations were observed, including occasional errors on simpler problems and challenges with certain highly specialized concepts, the overall results indicate significant progress towards artificial general intelligence.

Tianyang Zhong, Zhengliang Liu, Yi Pan +74

LLM Evaluation Code Generation Mathematical Reasoning Large Reasoning Models

Mar 7, 2024cs.AI

Machine learning and information theory concepts towards an AI Mathematician

The current state-of-the-art in artificial intelligence is impressive, especially in terms of mastery of language, but not so much in terms of mathematical reasoning. What could be missing? Can we learn something useful about that gap from how the brains of mathematicians go about their craft? This essay builds on the idea that current deep learning mostly succeeds at system 1 abilities -- which correspond to our intuition and habitual behaviors -- but still lacks something important regarding system 2 abilities -- which include reasoning and robust uncertainty estimation. It takes an information-theoretical posture to ask questions about what constitutes an interesting mathematical statement, which could guide future work in crafting an AI mathematician. The focus is not on proving a given theorem but on discovering new and interesting conjectures. The central hypothesis is that a desirable body of theorems better summarizes the set of all provable statements, for example by having a small description length while at the same time being close (in terms of number of derivation steps) to many provable statements.

Yoshua Bengio, Esmeralda S. Whitammer

Mathematical Reasoning