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

TL;DR

This paper formalizes the regimes in two-hop QA retrieval, introduces a theoretical framework, and proposes RegimeRouter, a lightweight classifier that improves retrieval performance across multiple datasets.

Contribution

It provides a formal theory for regime-conditional retrieval in two-hop QA and develops a transferable router that enhances retrieval accuracy.

Findings

RegimeRouter improves R@5 by up to 5.6 percentage points on benchmark datasets.

Theoretical analysis reveals key predicates for regime classification and bridge advantage.

Bridge sentence inclusion significantly boosts retrieval performance.

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.