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

arXiv: https://arxiv.org/abs/2604.09019 · HTML: https://mlsanity.com/paper/2604.09019/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 9 references that are in the map.
- First posted on arXiv 10 Apr 2026.

## Builds on (most cited first, 3 of 3)

- [Interleaving Retrieval with Chain-of-Thought Reasoning for Knowledge-Intensive Multi-Step Questions](https://mlsanity.com/paper/2212.10509/) (2022)
- [NV-Embed: Improved Techniques for Training LLMs as Generalist Embedding Models](https://mlsanity.com/paper/2405.17428/) (2024)
- [From RAG to Memory: Non-Parametric Continual Learning for Large Language Models](https://mlsanity.com/paper/2502.14802/) (2025)

## Built on by (most cited first, 1 of 1)

- [Per-Query Gating of LLM Rerankers for Multi-Hop Retrieval](https://mlsanity.com/paper/2609.22880/) (2026)

## Abstract (arXiv)

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.