$\mathrm{ECI}_{\mathrm{sem}}$: Semantic Residual Effective Contrastive Information for Evaluating Hard Negatives

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arXiv:2603.20990v4 Announce Type: replace-cross Abstract: Hard-negative source selection for dense retrieval is usually decided only after fine-tuning and downstream evaluation. We propose ECIsem, a validity-weighted diagnostic that ranks candidate hard-negative sources using frozen target-encoder embeddings. ECIsem is training-free, not label-free: each scored example requires a query, a labeled positive, and an explicit candidate negative. Each negative is weighted by target consistency, semantic locality, and lexical residuality, and the source score aggregates weighted residual directions through a log-determinant. At the scale we study, the log-determinant operates in its linear regime, so the score reduces to the mean validity weight; we report this reduction as a finding, and gate ablations show that a single lexical scalar, mean lexical residuality, reproduces the transfer ordering in every block. On MS MARCO negative sources, in-family ECIsem recovers the aggregate BEIR transfer ordering across DistilBERT, E5-base, and Contriever. Constructed controls expose an identifiability limit: a plausible false negative is non-inverted, near the positive, and lexically novel, exactly the profile the gates reward, and across twelve weightings of the three gates and three backbones only one of thirty-six cells is safe, and it is not transfer aligned, a limit that extends to margin-style filters built from the same statistics. The same gate statistics separate the controls sharply when used as audit features rather than as rewards, so we pair the score with a reported audit …

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