Leak It: Per-Document Extraction Beyond Aggregate Membership Inference

Membership inference (MIA) on language models is usually summarised by aggregate ROC-AUC, but such evaluations are confounded: model-free blind baselines can separate members from non-members using surface text alone. Building on probabilistic discoverable extraction, we study black-box training-data leakage using N samples from p theta(. x), placing mean overlap, extreme-value overlap, and self-concentration on a common functional-estimation footing. On WikiMIA, a blind bag-of-words classifier reaches AUC 0.97 (TPR 0.90 at 5% FPR) while sampling adds nothing. On an IID Pile split (MIMIR), neither self-concentration nor gold-continuation recovery significantly exceeds a blind baseline in aggregate. Aggregate metrics hide the real harm: sampling verbatim-extracts training data for a tail of documents no blind attack can reach. On Pythia-6.9B, 16.6% of 500 Pile documents bearing a real identifier (83 documents; 21.3% of those bearing an email address) have that identifier reproduced and not reproduced under a mismatched-prefix control. Each leak is attributable to that document rather than a globally common string. This per-document disclosure is invisible to aggregate AUC. Risk is uneven: identifier leakage is about 3x stronger in code than prose, though prose remains positive and grows with capacity (4.0% to 12.1% from 410M to 6.9B); recovery of arbitrary held-out continuations is essentially confined to code (+0.44 member gap on GitHub vs at most +0.014 on prose). Temperature and nucleus sampling have minor effect, a 16-token prefix suffices, and the sample-budget relationship corroborates prior probabilistic-extraction results. We detect no reduction from deduplication. Privacy audits should report per-document extraction, not only aggregate membership, and motivate differential privacy as the mitigation. We release leakit, a black-box tool implementing this probe and its control.