{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:CYPUYFRF2LJWFZND5RWSEGOSER","short_pith_number":"pith:CYPUYFRF","schema_version":"1.0","canonical_sha256":"161f4c1625d2d362e5a3ec6d2219d22464d62722c1b4ae6aceea40bc3fa061ef","source":{"kind":"arxiv","id":"2605.13721","version":1},"attestation_state":"computed","paper":{"title":"Do Hopfield Networks Dream of Stored Patterns? A Statistical-Mechanical Theory of Dreaming in Multidirectional Associative Memories","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"Adriano Barra, Andrea Ladiana, Fabrizio Durante, Michela Marra Solazzo","submitted_at":"2026-05-13T16:05:36Z","abstract_excerpt":"We introduce the Dreaming $L$-directional Associative Memory (DLAM), a multi-layer Hebbian architecture in which off-line dreaming and supervised heteroassociative coupling coexist within a single energy function, placing our approach within the framework of energy-based models (EBMs). The replica-symmetric free energy, derived via the Guerra interpolation scheme, yields self-consistency equations governing the order parameters across the control-parameter space. The effective local field decomposes into signal, intra-layer dreaming noise, and inter-layer noise. Dreaming improves retrieval by "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2605.13721","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-05-13T16:05:36Z","cross_cats_sorted":[],"title_canon_sha256":"d86da0590bec05b4b8a77ce0dc69adbf18c8986dc42141478f839a246f104995","abstract_canon_sha256":"ccc744c40031f7f5e873ab5ba86b9a7bcf17a432fa216d6e2f65b412f7d9ea22"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:16.653949Z","signature_b64":"4KkSP0XRBSN0OmwQ5KUKeDHB04xl3yjAoUh6AxInsXcQyWlsR1AbmZMSYP8yvB7IF1sVaCtzZ8ggHwAQIQaiDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"161f4c1625d2d362e5a3ec6d2219d22464d62722c1b4ae6aceea40bc3fa061ef","last_reissued_at":"2026-05-18T02:44:16.653428Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:16.653428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Do Hopfield Networks Dream of Stored Patterns? A Statistical-Mechanical Theory of Dreaming in Multidirectional Associative Memories","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"Adriano Barra, Andrea Ladiana, Fabrizio Durante, Michela Marra Solazzo","submitted_at":"2026-05-13T16:05:36Z","abstract_excerpt":"We introduce the Dreaming $L$-directional Associative Memory (DLAM), a multi-layer Hebbian architecture in which off-line dreaming and supervised heteroassociative coupling coexist within a single energy function, placing our approach within the framework of energy-based models (EBMs). The replica-symmetric free energy, derived via the Guerra interpolation scheme, yields self-consistency equations governing the order parameters across the control-parameter space. The effective local field decomposes into signal, intra-layer dreaming noise, and inter-layer noise. Dreaming improves retrieval by "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.13721","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2605.13721","created_at":"2026-05-18T02:44:16.653511+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.13721v1","created_at":"2026-05-18T02:44:16.653511+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.13721","created_at":"2026-05-18T02:44:16.653511+00:00"},{"alias_kind":"pith_short_12","alias_value":"CYPUYFRF2LJW","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"CYPUYFRF2LJWFZND","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"CYPUYFRF","created_at":"2026-05-18T12:33:37.589309+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CYPUYFRF2LJWFZND5RWSEGOSER","json":"https://pith.science/pith/CYPUYFRF2LJWFZND5RWSEGOSER.json","graph_json":"https://pith.science/api/pith-number/CYPUYFRF2LJWFZND5RWSEGOSER/graph.json","events_json":"https://pith.science/api/pith-number/CYPUYFRF2LJWFZND5RWSEGOSER/events.json","paper":"https://pith.science/paper/CYPUYFRF"},"agent_actions":{"view_html":"https://pith.science/pith/CYPUYFRF2LJWFZND5RWSEGOSER","download_json":"https://pith.science/pith/CYPUYFRF2LJWFZND5RWSEGOSER.json","view_paper":"https://pith.science/paper/CYPUYFRF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.13721&json=true","fetch_graph":"https://pith.science/api/pith-number/CYPUYFRF2LJWFZND5RWSEGOSER/graph.json","fetch_events":"https://pith.science/api/pith-number/CYPUYFRF2LJWFZND5RWSEGOSER/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CYPUYFRF2LJWFZND5RWSEGOSER/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CYPUYFRF2LJWFZND5RWSEGOSER/action/storage_attestation","attest_author":"https://pith.science/pith/CYPUYFRF2LJWFZND5RWSEGOSER/action/author_attestation","sign_citation":"https://pith.science/pith/CYPUYFRF2LJWFZND5RWSEGOSER/action/citation_signature","submit_replication":"https://pith.science/pith/CYPUYFRF2LJWFZND5RWSEGOSER/action/replication_record"}},"created_at":"2026-05-18T02:44:16.653511+00:00","updated_at":"2026-05-18T02:44:16.653511+00:00"}