Predictable Failure in Multi-Hop Retrieval: Score-Distributional Confidence Scoring and Abstention

Andre Bacellar

Multi-hop retrieval failures are not uniformly distributed across queries: they cluster in structurally predictable subpopulations. We prove two results formalizing this structure. First (CWAR Reducibility): confident-failure reduction is achievable if and only if retrieval features carry mutual information about success, a condition satisfied by LLM-judge pipelines but substantially weaker in dense-only settings, explaining the AUC-AC gap between regimes. Second (Feature Regime Complementarity): no single ANN score feature achieves best predictive performance across all failure regimes; the dominant feature differs between datasets (query length on MuSiQue, hop-1 concentration on HoVer), and a constructive witness pair shows each is necessary in one regime and non-contributory in the other. We instantiate these principles in RegimeAbstain, which computes a Retrieval Confidence Score (RCS), a logistic function of up to nine query-ANN structural features, all available without any additional LLM call, and uses it to implement a calibrated abstention policy. We define the Confident-Wrong-Answer Rate (CWAR) metric and evaluate across three multi-hop benchmarks (MuSiQue,…