Mean-Direction Deflation Reranking for Metric Misuse Repair in Frozen Vector Search

Abstract

Vector search systems often deploy inner-product similarity for efficiency, even when embeddings were trained with normalized metrics such as cosine similarity or Euclidean distance. This \emph{metric misuse} causes severe retrieval degradation on anisotropic embeddings, where vectors concentrate around a dominant mean direction and create hub vectors that appear as nearest neighbors to many queries. We propose \textbf{Mean-Direction Deflation Reranking (MDDR)}, a deployment-time method that repairs metric misuse by deflating the query's projection onto the database mean direction with an adaptive coefficient based on query-mean alignment. On the highly anisotropic ImageNet-EVA02 dataset (radial alignment 3°), MDDR recovers 48.73% of the gap between inner-product and Euclidean distance retrieval, outperforming Distribution Normalization by 9.20 percentage points. On near-isotropic BookCorpus (radial alignment 45°), MDDR achieves 89.44% gap recovery. MDDR requires only a single precomputed mean vector and negligible query-time overhead, enabling practical deployment as a reranking layer on frozen vector indices.