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.

大型语言模型在数学推理的许多基准测试上取得了令人瞩目的成功，但人们越来越担心其中的一部分性能实际上是由于数据集污染，而不是真正的推理能力。调查显示，许多模型可能已经部分记忆了基准测试的例子，导致在新的基准测试上准确度下降。

关于小学算术的大型语言模型性能的仔细检查