{"paper":{"title":"The Voronoi Bottleneck: Capacity-Aware Dense Retrieval for Product Search","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.IR","authors_text":"Aditya Singh, Charith Chandra Sai Balne, Chittaranjan Tripathy, Rithwik Maramraju, Rohit Upadhyay, Siddharth Pratap Singh, Yogananda Domlur Seetharama","submitted_at":"2026-06-09T19:34:18Z","abstract_excerpt":"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 (> 0.8) without relevance labels. (2) Diagnosis. CUS"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28359","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.28359/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}