{"paper":{"title":"Fl RDT based ultimate lowering of the negative spherical perceptron capacity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.dis-nn","cs.IT","cs.LG","math.IT","math.PR"],"primary_cat":"stat.ML","authors_text":"Mihailo Stojnic","submitted_at":"2023-12-27T11:23:40Z","abstract_excerpt":"We consider the classical \\emph{spherical} perceptrons and study their capacities. The famous zero-threshold case was solved in the sixties of the last century (see, \\cite{Wendel62,Winder,Cover65}) through the high-dimensional combinatorial considerations. The general threshold, $\\kappa$, case though turned out to be much harder and stayed out of reach for the following several decades. A substantial progress was then made in \\cite{SchTir02} and \\cite{StojnicGardGen13} where the \\emph{positive} threshold ($\\kappa\\geq 0$) scenario was finally fully settled. While the negative counterpart ($\\kap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.16531","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/2312.16531/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"}