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.

翻译：图增强检索将稠密相似度与基于图的关联信号（如个性化PageRank，PPR）相结合，但这些分数具有不同的分布且不可直接比较。我们将此问题视为多跳问答中异质检索融合的分数校准问题。所提方法PhaseGraph通过百分位数秩归一化（PIT）将向量分数和图分数映射到统一的无量纲尺度后再进行融合，从而在保留量级信息的同时实现稳定组合。在MuSiQue和2WikiMultiHopQA数据集上的实验表明：校准融合改进了HippoRAG2风格基准中的保留最后跳检索性能——MuSiQue上LastHop@5从75.1%提升至76.5%（8W/1L，p=0.039），2WikiMultiHopQA上从51.7%提升至53.6%（11W/2L，p=0.023），两者均基于独立保留测试集。理论驱动的消融实验表明：在调优集和测试集上（1W/6L，p=0.125），基于百分位数的校准在方向上比最小-最大归一化更稳健，而校准后的玻尔兹曼加权与线性融合性能相当（0W/3L，p=0.25）。这些结果表明分数公度化是一种稳健的设计选择，且在这些基准上，具体的校准后融合算子的影响相对较小。