DICE: Detecting In-distribution Contamination in LLM's Fine-tuning Phase for Math Reasoning

The advancement of large language models (LLMs) relies on evaluation using public benchmarks, but data contamination can lead to overestimated performance. Previous researches focus on detecting contamination by determining whether the model has seen the exact same data during training. Besides, prior work has already shown that even training on data similar to benchmark data inflates performance, namely \emph{In-distribution contamination}. In this work, we argue that in-distribution contamination can lead to the performance drop on OOD benchmarks. To effectively detect in-distribution contamination, we propose DICE, a novel method that leverages the internal states of LLMs to locate-then-detect the contamination. DICE first identifies the most sensitive layer to contamination, then trains a classifier based on the internal states of that layer. Experiments reveal DICE's high accuracy in detecting in-distribution contamination across various LLMs and math reasoning datasets. We also show the generalization capability of the trained DICE detector, which is able to detect contamination across multiple benchmarks with similar distributions. Additionally, we find that DICE's predictions correlate with the performance of LLMs fine-tuned by either us or other organizations, achieving a coefficient of determination ($R^2$) between 0.61 and 0.75. The code and data are available at https://github.com/THU-KEG/DICE.