Title: BADI: Black-box and Anytime-valid Dataset Identification for Large Language Models
Primary area: foundation or frontier models, including LLMs
Keywords: LLM, Dataset Identification, Copyright

Abstract: Large language models (LLMs) are trained on massive, uncurated internet datasets that often include copyrighted material, making training data identification essential for intellectual property protection. *Dataset inference (DI)* addresses this challenge by extracting diverse training membership features for a suspect set, aggregating them, and applying statistical tests to assess if that suspect set contributed to the model’s training. However, current DI methods face two major limitations that hinder their practical deployment. First, they require gray-box access to token probabilities, while state-of-the-art LLM APIs usually return only generated tokens. We address this issue by approximating per-token probabilities from label-only outputs, making *black-box DI* feasible. Second, existing DIs rely on p-value for statistical tests that necessitate a fixed suspect set and a predetermined significance level. This either leads to high computational costs for large suspect sets, especially in the black-box setup, or yields inconclusive results for smaller sets, since adding new suspect data points post-hoc might be necessary to provide strong enough evidence, but it invalidates statistical guarantees based on p-values. To overcome this limitation, we introduce a black-box DI framework based on *e-values* and sequential testing. The e-values offer anytime-valid guarantees and support optional continuation, enabling safe accumulation of evidence, reducing inconclusive outcomes and compute costs. Through these two fundamental advances, our **B**lack-box and **A**nytime-valid **D**ataset **I**dentification (BADI) method enables practical data auditing for LLMs, supporting their trustworthy deployment.

TL;DR: Black-box and Anytime-valid Dataset Inference framework for LLMs that enables practical and statistically robust identification of their training datasets.