Andre Bacellar

Andre Bacellar

In law, regulatory regimes for pharmaceuticals and software security, newer authorities can revoke older established ones even when semantically distant. We call this CAR: retrieving the currently active authority frontier for a semantic anchor q, that is, front(cl(A_k(q))). This differs from finding the most similar document by relevance score: argmax_d s(q, d). Theorem 4 characterizes when a set R truly covers the active authority set for q with TCA(R, q)=1, providing conditions necessary and sufficient for any retrieved set R: frontier inclusion (front(cl(A_k(q))) contained in R) and no-ignored-superseder (no superseding document exists in the corpus outside R). Proposition 2 shows that TCA@k <= phi(q) * R_anchor(q) in the worst case over any scope-indexed algorithm, proved by an adversarial permutation argument. We evaluated on three real-world datasets: security advisories (Dense TCA@5=0.270, two-stage 0.975), SCOTUS overruling pairs (Dense TCA=0.172, two-stage 0.926), and FDA drug records (Dense TCA=0.064, two-stage 0.774). A GPT-4o-mini experiment shows Dense RAG produces explicit "not patched" claims for 39% of queries where a patch exists; two-stage cuts this to 16%. Four benchmark datasets, domain adapters, and a single-command scorer are released at https://github.com/andremir/car-retrieval.

Andre Bacellar

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.

Andre Bacellar

Graph-augmented retrieval combines dense similarity with graph-based relevance signals such as Personalized PageRank (PPR), but these scores have different distributions and are not directly comparable. We study this as a score calibration problem for heterogeneous retrieval fusion in multi-hop question answering. Our method, PhaseGraph, maps vector and graph scores to a common unit-free scale using percentile-rank normalization (PIT) before fusion, enabling stable combination without discarding magnitude information. Across MuSiQue and 2WikiMultiHopQA, calibrated fusion improves held-out last-hop retrieval on HippoRAG2-style benchmarks: LastHop@5 increases from 75.1% to 76.5% on MuSiQue (8W/1L, p=0.039) and from 51.7% to 53.6% on 2WikiMultiHopQA (11W/2L, p=0.023), both on independent held-out test splits. A theory-driven ablation shows that percentile-based calibration is directionally more robust than min-max normalization on both tune and test splits (1W/6L, p=0.125), while Boltzmann weighting performs comparably to linear fusion after calibration (0W/3L, p=0.25). These results suggest that score commensuration is a robust design choice, and the exact post-calibration operator appears to matter less on these benchmarks.

Andre Bacellar

Multi-hop retrieval is not a single-step relevance problem: later-hop evidence should be ranked by its utility conditioned on retrieved bridge evidence, not by similarity to the original query alone. We present BridgeRAG, a training-free, graph-free retrieval method for retrieval-augmented generation (RAG) over multi-hop questions that operationalizes this view with a tripartite scorer s(q,b,c) over (question, bridge, candidate). BridgeRAG separates coverage from scoring: dual-entity ANN expansion broadens the second-hop candidate pool, while a bridge-conditioned LLM judge identifies the active reasoning chain among competing candidates without any offline graph or proposition index. Across four controlled experiments we show that this conditioning signal is (i) selective: +2.55pp on parallel-chain queries (p<0.001) vs. ~0 on single-chain subtypes; (ii) irreplaceable: substituting the retrieved passage with generated SVO query text reduces R@5 by 2.1pp, performing worse than even the lowest-SVO-similarity pool passage; (iii) predictable: cos(b,g2) correlates with per-query gain (Spearman rho=0.104, p<0.001); and (iv) mechanistically precise: bridge conditioning causes productive re-rankings (18.7% flip-win rate on parallel-chain vs. 0.6% on single-chain), not merely more churn. Combined with lightweight coverage expansion and percentile-rank score fusion, BridgeRAG achieves the best published training-free R@5 under matched benchmark evaluation on all three standard MHQA benchmarks without a graph database or any training: 0.8146 on MuSiQue (+3.1pp vs. PropRAG, +6.8pp vs. HippoRAG2), 0.9527 on 2WikiMultiHopQA (+1.2pp vs. PropRAG), and 0.9875 on HotpotQA (+1.35pp vs. PropRAG).