{"paper":{"title":"Binary perceptrons capacity via fully lifted random duality theory","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.dis-nn","cs.IT","math.IT","math.ST","stat.ML","stat.TH"],"primary_cat":"math.PR","authors_text":"Mihailo Stojnic","submitted_at":"2023-11-29T22:22:32Z","abstract_excerpt":"We study the statistical capacity of the classical binary perceptrons with general thresholds $\\kappa$. After recognizing the connection between the capacity and the bilinearly indexed (bli) random processes, we utilize a recent progress in studying such processes to characterize the capacity. In particular, we rely on \\emph{fully lifted} random duality theory (fl RDT) established in \\cite{Stojnicflrdt23} to create a general framework for studying the perceptrons' capacities. Successful underlying numerical evaluations are required for the framework (and ultimately the entire fl RDT machinery)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.00073","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/2312.00073/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"}