The Voronoi Bottleneck: Capacity-Aware Dense Retrieval for Product Search

arXiv:2606.28359v1 Announce Type: cross Abstract: Dense embedding retrieval compresses all relevance information into a single inner product, imposing a fundamental geometric limit -- the Voronoi Bottleneck -- on the number of query-document relevance patterns expressible at fixed embedding dimension (d). We make three contributions. (1) Unified capacity theory. We prove that Voronoi complexity and sign-rank are equivalent for top-1 retrieval, yielding tight dimension bounds and a computable diagnostic, the Capacity Utilization Score (CUS), that predicts per-query retrieval failure with AUC (>

Source: arXiv cs.LG — read the full report at the original publisher.

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