PyraMathBench: Evaluating and Improving Mathematical Capability in Large Language Models
Authors: Zetian Ouyang, Linlin Wang, Gerard de Melo, Liang He
Organizations: East China Normal University · Hasso Plattner Institute, University of Potsdam
Abstract
Despite the pivotal role of numerical reasoning as the cornerstone of mathematical capabilities in large language models (LLMs) across applications, few benchmarks evaluate LLMs by integrating numerical processing and mathematical reasoning, hindering the interpretability of failures in math tasks. We introduce PyraMathBench, a comprehensive hierarchical benchmark with 32,505 questions derived from 7,404 math word problems, spanning 4 key cognitive aspects, 14 subcategories, and 2 modalities. Experiments reveal that LLMs' performance is severely compromised by inadequate numerical computation and weak handling of abstract numerical questions. To address this, we propose the Smart Optimization & Learning-based VErsatile module (SOLVE) and Interactive Relative Policy Optimization (IRPO), which enhance LLMs' numerical-mathematical synergy via efficient tool calls (fuzzy matching and low-quality call rejection). Comparative experiments show Qwen-2.5 achieves a 5.0 score improvement with SOLVE and IRPO training.
Recent studies have raised significant concerns regarding the reliability of current mathematics benchmarks, highlighting issues such as simplistic design and potential data contamination. Consequently, developing a reliable benchmark that effectively evaluates large language models' (LLMs) genuine capabilities in mathematical reasoning remains a critical challenge. To address these concerns, we propose RV-Bench, a novel evaluation methodology for Benchmarking LLMs with Random Variables in mathematical reasoning. Specifically, we build question-generating functions to produce random variable questions (RVQs), whose background content mirrors original benchmark problems, but with randomized variable combinations, rendering them "unseen" to LLMs. Models must completely understand the inherent question pattern to correctly answer RVQs with diverse variable combinations. Thus, an LLM's genuine reasoning capability is reflected through its accuracy and robustness on RV-Bench. We conducted extensive experiments on over 30 representative LLMs across more than 1,000 RVQs. Our findings propose that LLMs exhibit a proficiency imbalance between encountered and ``unseen'' data distributions. Furthermore, RV-Bench reveals that proficiency generalization across similar mathematical reasoning tasks is limited, but we verified it can still be effectively elicited through test-time scaling.
We present a new approach for benchmarking Large Language Model (LLM) capabilities on research-level mathematics. Existing benchmarks largely rely on static, hand-curated sets of contest or textbook-style problems as proxies for mathematical research. Instead, we establish an updatable benchmark evaluating models directly on the latest research results in mathematics. This consists of an automatic pipeline that extracts lemmas from arXiv and rewrites them into self-contained statements by making all assumptions and required definitions explicit. It results in a benchmark that can be updated regularly with new problems taken directly from human mathematical research, while previous instances can be used for training without compromising future evaluations. We benchmark current state-of-the-art LLMs, which obtain around 10-15% accuracy in theorem proving (pass@1) depending on the model, showing that there is currently a large margin of progression for LLMs to reach human-level proving capabilities in a research context.
Recent advancements in large language models have led to significant improvements across various tasks, including mathematical reasoning, which is used to assess models' intelligence in logical reasoning and problem-solving. Models are evaluated on mathematical reasoning benchmarks by verifying the correctness of the final answer against a ground truth answer. A common approach for this verification is based on symbolic mathematics comparison, which fails to generalize across diverse mathematical representations and solution formats. In this work, we offer a robust and flexible alternative to rule-based symbolic mathematics comparison. We propose an LLM-based evaluation framework for evaluating model-generated answers, enabling accurate evaluation across diverse mathematical representations and answer formats. We present failure cases of symbolic evaluation in two popular frameworks, Lighteval and SimpleRL, and compare them to our approach, demonstrating clear improvements over commonly used methods. Our framework enables more reliable evaluation and benchmarking, leading to more accurate performance monitoring, which is important for advancing mathematical problem-solving and intelligent systems.