Min-K Language Models

The problem of pre-training data detection for large language models (LLMs) has received growing attention due to its implications in critical issues like copyright violation and test data contamination. A common intuition for this problem is to identify training data by checking if the input comes from a mode of the LLM's distribution. However, existing approaches, including the state-of-the-art Min-K are less robust in determining local maxima than second-order statistics. In this work, we propose a novel methodology Min-K detection that measures how sharply peaked the likelihood is around the input, a measurement analogous to the curvature of continuous distribution. Our method is theoretically motivated by the observation that maximum likelihood training implicitly optimizes the trace of the Hessian matrix of likelihood through score matching. Empirically, the proposed method achieves new SOTA performance across multiple settings. On the WikiMIA benchmark, Min-K runner-up by 6.2 more challenging MIMIR benchmark, it consistently improves upon reference-free methods while performing on par with reference-based method that requires an extra reference model.