Calibrated Fusion for Heterogeneous Graph-Vector Retrieval in Multi-Hop QA

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@10 increases from 69.1% to 71.0% on MuSiQue (15W/5L, p=0.041, n=514) and LastHop@5 from 51.7% to 53.6% on 2WikiMultiHopQA (11W/2L, p=0.023, n=491), both on independent held-out test splits. Against the official HippoRAG 2 pipeline on 2WikiMultiHopQA, calibrated fusion is ahead at LastHop@10 (+6.3pp, p<10^-3) and behind at LastHop@5 (-8.4pp), a cutoff-dependent cross-over we report in full. 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.