{"paper":{"title":"Fast Heavy Inner Product Identification Between Weights and Inputs in Neural Network Training","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Lianke Qin, Saayan Mitra, Tianyi Zhou, Yuanyuan Yang, Zhao Song","submitted_at":"2023-11-19T21:40:16Z","abstract_excerpt":"In this paper, we consider a heavy inner product identification problem, which generalizes the Light Bulb problem~(\\cite{prr89}): Given two sets $A \\subset \\{-1,+1\\}^d$ and $B \\subset \\{-1,+1\\}^d$ with $|A|=|B| = n$, if there are exact $k$ pairs whose inner product passes a certain threshold, i.e., $\\{(a_1, b_1), \\cdots, (a_k, b_k)\\} \\subset A \\times B$ such that $\\forall i \\in [k], \\langle a_i,b_i \\rangle \\geq \\rho \\cdot d$, for a threshold $\\rho \\in (0,1)$, the goal is to identify those $k$ heavy inner products. We provide an algorithm that runs in $O(n^{2 \\omega / 3+ o(1)})$ time to find th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.11429","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/2311.11429/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"}