{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:KQWM2GPIZMBKQRU4LG43C4RH4N","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"02c5a2e234832571f1f5f6129279384eb96a5dfeb89ff1a8c7f55daaed5e3049","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2023-03-29T17:39:21Z","title_canon_sha256":"b4517ba4751ed7dbb2eaa3eca8c7a75462d28d1da3dfec72299fa31f89569b7f"},"schema_version":"1.0","source":{"id":"2303.16880","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.16880","created_at":"2026-07-05T06:05:16Z"},{"alias_kind":"arxiv_version","alias_value":"2303.16880v2","created_at":"2026-07-05T06:05:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.16880","created_at":"2026-07-05T06:05:16Z"},{"alias_kind":"pith_short_12","alias_value":"KQWM2GPIZMBK","created_at":"2026-07-05T06:05:16Z"},{"alias_kind":"pith_short_16","alias_value":"KQWM2GPIZMBKQRU4","created_at":"2026-07-05T06:05:16Z"},{"alias_kind":"pith_short_8","alias_value":"KQWM2GPI","created_at":"2026-07-05T06:05:16Z"}],"graph_snapshots":[{"event_id":"sha256:1e4ac903c713f5d43f2b2d43030d822ec0f7d20515e9f09eb57ddb78290b7471","target":"graph","created_at":"2026-07-05T06:05:16Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2303.16880/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Hopfield model is a paradigmatic model of neural networks that has been analyzed for many decades in the statistical physics, neuroscience, and machine learning communities. Inspired by the manifold hypothesis in machine learning, we propose and investigate a generalization of the standard setting that we name Random-Features Hopfield Model. Here $P$ binary patterns of length $N$ are generated by applying to Gaussian vectors sampled in a latent space of dimension $D$ a random projection followed by a non-linearity. Using the replica method from statistical physics, we derive the phase diag","authors_text":"Carlo Lucibello, Clarissa Lauditi, Enrico Malatesta, Gabriele Perugini, Matteo Negri","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2023-03-29T17:39:21Z","title":"Storage and Learning phase transitions in the Random-Features Hopfield Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.16880","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:aec8909d38d41a264f5d673e19c92feb50aeb573942ae35bedf2da57de3810ca","target":"record","created_at":"2026-07-05T06:05:16Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"02c5a2e234832571f1f5f6129279384eb96a5dfeb89ff1a8c7f55daaed5e3049","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2023-03-29T17:39:21Z","title_canon_sha256":"b4517ba4751ed7dbb2eaa3eca8c7a75462d28d1da3dfec72299fa31f89569b7f"},"schema_version":"1.0","source":{"id":"2303.16880","kind":"arxiv","version":2}},"canonical_sha256":"542ccd19e8cb02a8469c59b9b17227e36716f6540b15529319a505d3e512a916","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"542ccd19e8cb02a8469c59b9b17227e36716f6540b15529319a505d3e512a916","first_computed_at":"2026-07-05T06:05:16.057330Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:05:16.057330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DtZNuylqH176mrAEqIms1rEWAQ0bw5mCLU1jEuBtIvYAXVlBanpEKMprsA3Wrh0sifl0WkECZOswps01QEsDBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:05:16.057800Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.16880","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aec8909d38d41a264f5d673e19c92feb50aeb573942ae35bedf2da57de3810ca","sha256:1e4ac903c713f5d43f2b2d43030d822ec0f7d20515e9f09eb57ddb78290b7471"],"state_sha256":"3f76aaa0d0914fa0f3677e956a730cb810c4cb6d93d923286359c36af2fbb9d9"}