Putnam-AXIOM: A Functional and Static Benchmark for Measuring Higher Level Mathematical Reasoning in LLMs

• URL: http://arxiv.org/abs/2508.08292v2
• Date: Wed, 27 Aug 2025 02:14:01 GMT
• Title: Putnam-AXIOM: A Functional and Static Benchmark for Measuring Higher Level Mathematical Reasoning in LLMs
• Authors: Aryan Gulati, Brando Miranda, Eric Chen, Emily Xia, Kai Fronsdal, Bruno Dumont, Elyas Obbad, Sanmi Koyejo,
• Abstract summary: Current benchmarks for large language models (LLMs) are approaching saturation and are increasingly compromised by trainingset contamination.<n>We introduce Putnam-AXIOM, a benchmark drawn from the prestigious William Lowell Putnam Mathematical Competition.<n>The variation protocol produces an unlimited stream of equally difficult, unseen instances -- yielding contamination-resilient test bed.
• Score: 19.592385109516268
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Current mathematical reasoning benchmarks for large language models (LLMs) are approaching saturation, with some achieving > 90% accuracy, and are increasingly compromised by training-set contamination. We introduce Putnam-AXIOM, a benchmark of 522 university-level competition problems drawn from the prestigious William Lowell Putnam Mathematical Competition, and Putnam-AXIOM Variation, an unseen companion set of 100 functional variants generated by programmatically perturbing variables and constants. The variation protocol produces an unlimited stream of equally difficult, unseen instances -- yielding a contamination-resilient test bed. On the Original set, OpenAI's o1-preview -- the strongest evaluated model -- scores 41.9%, but its accuracy drops by 19.6% (46.8% relative decrease) on the paired Variations. The remaining eighteen models show the same downward trend, ten of them with non-overlapping 95% confidence intervals. These gaps suggest memorization and highlight the necessity of dynamic benchmarks. We complement "boxed" accuracy with Teacher-Forced Accuracy (TFA), a lightweight metric that directly scores reasoning traces and automates natural language proof evaluations. Putnam-AXIOM therefore provides a rigorous, contamination-resilient evaluation framework for assessing advanced mathematical reasoning of LLMs. Data and evaluation code are publicly available at https://github.com/brando90/putnam-axiom.

Related papers

• Evaluating LLMs When They Do Not Know the Answer: Statistical Evaluation of Mathematical Reasoning via Comparative Signals [18.612081365101464]
  We develop a framework that combines standard labeled outcomes with pairwise comparison signals obtained by having models judge auxiliary reasoning chains.<n>Across simulations, our one-step estimator substantially improves ranking accuracy with gains increasing as model output noise grows.<n>Experiments on GPQA Diamond, AIME 2025 and GSM8K further demonstrate more precise performance estimation and more reliable model rankings.
  arXiv  Detail & Related papers  (2026-02-03T03:40:01Z)
• From Abstract to Contextual: What LLMs Still Cannot Do in Mathematics [79.81905350372067]
  We study gap through contextual mathematical reasoning.<n>We introduce ContextMATH, a benchmark that repurposes AIME and MATH-500 problems into two contextual settings.<n>Open-source models decline by 13 and 34 points on SG and CS, while proprietary models drop by 13 and 20.
  arXiv  Detail & Related papers  (2026-01-30T14:56:04Z)
• MSC-180: A Benchmark for Automated Formal Theorem Proving from Mathematical Subject Classification [21.9173105378467]
  Current large language model (LLM)-based theorem provers suffer from limitations such as restricted domain coverage and weak generalization in mathematical reasoning.<n>We propose MSC-180, a benchmark for evaluation based on the MSC 2020 mathematical subject classification.<n>It comprises 180 formal verification problems, 3 advanced problems from each of 60 mathematical branches, spanning from undergraduate to graduate levels.
  arXiv  Detail & Related papers  (2025-12-20T07:39:19Z)
• Relative Scaling Laws for LLMs [91.73497548097775]
  Scaling laws describe how language models improve with additional data, parameters, and compute.<n>We introduce relative scaling laws, which track how performance gaps between test distributions evolve with scale.<n>These results show that although scaling improves overall performance, it is not a universal equalizer.
  arXiv  Detail & Related papers  (2025-10-28T16:55:22Z)
• WirelessMathLM: Teaching Mathematical Reasoning for LLMs in Wireless Communications with Reinforcement Learning [51.13280433665446]
  Large language models (LLMs) excel at general mathematical reasoning but fail catastrophically on specialized technical mathematics.<n>In wireless communications, where problems require precise manipulation of information-theoretic bounds, even state-of-the-art models struggle to achieve competent performance.<n>We present WirelessMathLM, demonstrating that compact models (0.5B-7B parameters) can match or exceed much larger models through domain-specific reinforcement learning.
  arXiv  Detail & Related papers  (2025-09-27T09:58:03Z)
• VAR-MATH: Probing True Mathematical Reasoning in Large Language Models via Symbolic Multi-Instance Benchmarks [25.295071827427677]
  emphbenchmark contamination arises from the public availability of test problems.<n>emphevaluation fragility stems from the reliance on single-instance assessments.<n>IME-MATH is a symbolic evaluation framework designed to probe genuine reasoning ability.
  arXiv  Detail & Related papers  (2025-07-17T08:10:55Z)
• Solving Inequality Proofs with Large Language Models [46.71658812761115]
  Inequality proving is crucial across diverse scientific and mathematical fields.<n>This makes it a demanding frontier for large language models (LLMs)<n>We release IneqMath, an expert-curated dataset of Olympiad-level inequalities.
  arXiv  Detail & Related papers  (2025-06-09T16:43:38Z)
• LookAlike: Consistent Distractor Generation in Math MCQs [42.19039301965107]
  We propose LookAlike, a method that improves error-distractor consistency via preference optimization.<n>Our two main innovations are: (a) mining synthetic preference pairs from model inconsistencies, and (b) alternating supervised fine-tuning.<n>LookAlike achieves 51.6% accuracy in distractor generation and 57.2% in error generation under LLM-as-a-judge evaluation.
  arXiv  Detail & Related papers  (2025-05-03T19:18:06Z)
• Sample, Don't Search: Rethinking Test-Time Alignment for Language Models [55.2480439325792]
  We introduce QAlign, a new test-time alignment approach.<n>As we scale test-time compute, QAlign converges to sampling from the optimal aligned distribution for each individual prompt.<n>By adopting recent advances in Markov chain Monte Carlo for text generation, our method enables better-aligned outputs without modifying the underlying model or even requiring logit access.
  arXiv  Detail & Related papers  (2025-04-04T00:41:40Z)
• Omni-MATH: A Universal Olympiad Level Mathematic Benchmark For Large Language Models [63.31878920079154]
  We propose a benchmark specifically designed to assess large language models' mathematical reasoning at the Olympiad level.<n>Unlike existing Olympiad-related benchmarks, our dataset focuses exclusively on mathematics and comprises a vast collection of 4428 competition-level problems with rigorous human annotation.<n>Our experimental results show that even the most advanced models, OpenAI o1-mini and OpenAI o1-preview, struggle with highly challenging Olympiad-level problems, with 60.54% and 52.55% accuracy, highlighting significant challenges in Olympiad-level mathematical reasoning.
  arXiv  Detail & Related papers  (2024-10-10T14:39:33Z)
• Noisy Correspondence Learning with Self-Reinforcing Errors Mitigation [63.180725016463974]
  Cross-modal retrieval relies on well-matched large-scale datasets that are laborious in practice. We introduce a novel noisy correspondence learning framework, namely textbfSelf-textbfReinforcing textbfErrors textbfMitigation (SREM)
  arXiv  Detail & Related papers  (2023-12-27T09:03:43Z)
• LLMs as Factual Reasoners: Insights from Existing Benchmarks and Beyond [135.8013388183257]
  We propose a new protocol for inconsistency detection benchmark creation and implement it in a 10-domain benchmark called SummEdits. Most LLMs struggle on SummEdits, with performance close to random chance. The best-performing model, GPT-4, is still 8% below estimated human performance.
  arXiv  Detail & Related papers  (2023-05-23T21:50:06Z)
• Predicting Out-of-Domain Generalization with Neighborhood Invariance [59.05399533508682]
  We propose a measure of a classifier's output invariance in a local transformation neighborhood. Our measure is simple to calculate, does not depend on the test point's true label, and can be applied even in out-of-domain (OOD) settings. In experiments on benchmarks in image classification, sentiment analysis, and natural language inference, we demonstrate a strong and robust correlation between our measure and actual OOD generalization.
  arXiv  Detail & Related papers  (2022-07-05T14:55:16Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.