AdaWidth: Query-Adaptive Embedding Width for Dense Retrieval

Abstract

High-dimensional embeddings are central to dense retrieval, but not all of these dimensions need to be evaluated at retrieval time. Existing methods reduce dimensions in two ways: truncating the same leading dimensions for every query, or masking a different subset for each query while still storing and accessing the full embedding. Yet queries within a single task differ widely in the number of dimensions they need for their rankings to stabilize. We introduce AdaWidth, which adapts the number of evaluated dimensions to each query within a shared prefix representation. An orthogonal prefix adapter applies a single learned rotation to queries and documents alike, concentrating discriminative signal in leading coordinates while leaving every full width inner product unchanged. A lightweight router then reads order statistics off the ranking a query has already produced, and evaluates more dimensions only for the queries whose top results would change. We further derive a prefix sufficiency analysis showing that the required number of dimensions is set by the competing documents at the retrieval cutoff: it grows logarithmically with corpus size, decreases logarithmically with retrieval depth, and remains heavy-tailed across queries. Across six retrieval tasks and five frozen encoders, AdaWidth matches the NDCG@10 of state-of-the-art dimensionality reduction using 55% to 84% fewer dimensions per query.