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. In this work, we argue that even training on data similar to benchmark data inflates performance on in-distribution tasks without improving overall capacity, which we called In-distribution contamination. 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 the DICE detection scores are positively correlated with the performance of ten LLMs fine-tuned by either us or other organizations on four math reasoning datasets (with $R^2$ values between 0.6 and 0.75). This indicates that the in-distribution contamination problem potentially lead to an overestimation of the true capabilities of many existing models. The code and data are available at https://github.com/THU-KEG/DICE.