Source-balanced Capped Fisher: Bounded Evidence Aggregation for User Inference in Language Models

Yang Liu, Ran Zou, Wanrong Zhu

User inference asks whether a source contributed documents to a language-model update, even when the auditor observes only fresh documents from that source. Document-level scores can provide evidence of participation, but combining this evidence is challenging: documents differ in baseline predictability and in how strongly they reflect information learned from other documents of the same source. We propose source-balanced capped Fisher (SCF), an aggregation method that uses known nonparticipating sources to assess how unusual each document score is. It transforms the resulting reference-tail frequencies into negative-log evidence, caps individual contributions, and averages them within each source. This limits the influence of isolated extreme scores while retaining evidence across multiple documents. We complete the inference procedure with a decision rule that tests source participation using a p-value calibrated against a separate set of known nonparticipating sources. The rule provides finite-sample Type-I error control under source exchangeability. Experiments across four real-world datasets show that SCF achieves the highest AUROC among the evaluated aggregation methods in…