{"paper":{"title":"Generalizations of Matrix Multiplication can solve the Light Bulb Problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Hengjie Zhang, Josh Alman","submitted_at":"2023-11-02T22:49:41Z","abstract_excerpt":"In the light bulb problem, one is given uniformly random vectors $x_1, \\ldots, x_n, y_1, \\ldots, y_n \\in \\{-1,1\\}^d$. They are all chosen independently except a planted pair $(x_{i^*}, y_{j^*})$ is chosen with correlation $\\rho>0$. The goal is to find the planted pair. This problem was introduced over 30 years ago by L.~Valiant, and is known to have many applications in data analysis, statistics, and learning theory.\n  The naive algorithm runs in $\\Omega(n^2)$ time, and algorithms based on Locality-Sensitive Hashing approach quadratic time as $\\rho \\to 0$. In 2012, G.~Valiant gave a breakthrou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.01630","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/2311.01630/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"}