{"paper":{"title":"High-dimensional manifold of solutions in neural networks: insights from statistical physics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.PR","math.ST","stat.TH"],"primary_cat":"cond-mat.dis-nn","authors_text":"Enrico M. Malatesta","submitted_at":"2023-09-17T11:10:25Z","abstract_excerpt":"In these pedagogic notes I review the statistical mechanics approach to neural networks, focusing on the paradigmatic example of the perceptron architecture with binary an continuous weights, in the classification setting. I will review the Gardner's approach based on replica method and the derivation of the SAT/UNSAT transition in the storage setting. Then, I discuss some recent works that unveiled how the zero training error configurations are geometrically arranged, and how this arrangement changes as the size of the training set increases. I also illustrate how different regions of solutio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.09240","kind":"arxiv","version":2},"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/2309.09240/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"}