Regime-Conditional Retrieval: Theory and a Transferable Router for Two-Hop QA

• URL: http://arxiv.org/abs/2604.09019v1
• Date: Fri, 10 Apr 2026 06:31:51 GMT
• Title: Regime-Conditional Retrieval: Theory and a Transferable Router for Two-Hop QA
• Abstract summary: Two-hop QA retrieval queries splits into two regimes determined by whether the hop-2 entity is explicitly named in the question (Q-dominant) or only in the bridge passage (B-dominant)<n>We formalize this split with three theorems.<n>Building on this theory, we propose a lightweight binary router that selects between question-only and question-plusrelation-sentence retrieval.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Two-hop QA retrieval splits queries into two regimes determined by whether the hop-2 entity is explicitly named in the question (Q-dominant) or only in the bridge passage (B-dominant). We formalize this split with three theorems: (T1) per-query AUC is a monotone function of the cosine separation margin, with R^2 >= 0.90 for six of eight type-encoder pairs; (T2) regime is characterized by two surface-text predicates, with P1 decisive for routing and P2 qualifying the B-dominant case, holding across three encoders and three datasets; and (T3) bridge advantage requires the relation-bearing sentence, not entity name alone, with removal causing an 8.6-14.1 pp performance drop (p < 0.001). Building on this theory, we propose RegimeRouter, a lightweight binary router that selects between question-only and question-plus-relation-sentence retrieval using five text features derived directly from the predicate definitions. Trained on 2WikiMultiHopQA (n = 881, 5-fold cross-fitted) and applied zero-shot to MuSiQue and HotpotQA, RegimeRouter achieves +5.6 pp (p < 0.001), +5.3 pp (p = 0.002), and +1.1 pp (non-significant, no-regret) R@5 improvement, respectively, with artifact-driven.

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