Abstract
Large language models (LLMs) have achieved impressive success on many benchmarks for mathematical reasoning. However, there is growing concern that some of this performance actually reflects dataset contamination, where data closely resembling benchmark questions leaks into the training data, instead of true reasoning ability. To investigate this claim rigorously, we commission Grade School Math 1000 (GSM1k). GSM1k is designed to mirror the style and complexity of the established GSM8k benchmark, the gold standard for measuring elementary mathematical reasoning. We ensure that the two benchmarks are comparable across important metrics such as human solve rates, number of steps in solution, answer magnitude, and more. When evaluating leading open- and closed-source LLMs on GSM1k, we observe accuracy drops of up to 13%, with several families of models (e.g., Phi and Mistral) showing evidence of systematic overfitting across almost all model sizes. At the same time, many models, especially those on the frontier, (e.g., Gemini/GPT/Claude) show minimal signs of overfitting. Further analysis suggests a positive relationship (Spearman's r^2=0.32) between a model's probability of generating an example from GSM8k and its performance gap between GSM8k and GSM1k, suggesting that many models may have partially memorized GSM8k.
Abstract (translated)
大语言模型（LLMs）在许多数学推理基准测试中取得了令人印象深刻的成功。然而，越来越担心一些性能实际上反映了数据污染，即紧密类似于基准问题的数据泄露到训练数据中，而不是真正的推理能力。为了严谨地调查这个说法，我们委托了Grade School Math 1000（GSM1k）。GSM1k旨在与现有的GSM8k基准相似，这是衡量小学数学推理的标准。我们确保两个基准在重要指标（如人解率、解决问题步骤、答案大小等）上可比。在用GSM1k评估领先的开源和闭源LLM时，我们观察到准确度下降了13%，并且几个模型家族（如Φ和Mistral）在几乎所有模型大小上都表现出系统性的过拟合。同时，许多模型，特别是前沿模型（如Gemini/GPT/Claude）表现出极小的过拟合。进一步的分析表明，模型从GSM8k生成示例的概率与GSM8k和GSM1k之间的性能差异之间存在积极关系（Spearman的r^2=0.32），这表明许多模型可能已经部分记忆了GSM8k。
URL
https://arxiv.org/abs/2405.00332
