{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:WCQOK7BSYYAOKXGHTAAJXIJ7HD","short_pith_number":"pith:WCQOK7BS","schema_version":"1.0","canonical_sha256":"b0a0e57c32c600e55cc798009ba13f38d684a14dc51e8c8e6a697c2e443c27c0","source":{"kind":"arxiv","id":"2202.04557","version":2},"attestation_state":"computed","paper":{"title":"Universal Hopfield Networks: A General Framework for Single-Shot Associative Memory Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.LG"],"primary_cat":"cs.NE","authors_text":"Beren Millidge, Rafal Bogacz, Thomas Lukasiewicz, Tommaso Salvatori, Yuhang Song","submitted_at":"2022-02-09T16:48:06Z","abstract_excerpt":"A large number of neural network models of associative memory have been proposed in the literature. These include the classical Hopfield networks (HNs), sparse distributed memories (SDMs), and more recently the modern continuous Hopfield networks (MCHNs), which possesses close links with self-attention in machine learning. In this paper, we propose a general framework for understanding the operation of such memory networks as a sequence of three operations: similarity, separation, and projection. We derive all these memory models as instances of our general framework with differing similarity "},"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":"2202.04557","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2022-02-09T16:48:06Z","cross_cats_sorted":["cs.AI","cs.LG"],"title_canon_sha256":"5c019aefcc9d8b350df332dd713a56e47630766d148a19053e71f45a95932273","abstract_canon_sha256":"c5ef28d9f16c918aff831ce34530f179453048d25a73fccbfdfeb2600a016e02"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:32:39.037634Z","signature_b64":"+mn3B7DmVGZUVxX/KKkj8IIyOnhiRzjcYbq6SvicX/gtHIgsFrwl9tZ6aAtXKCv5NqLAGneu1XpAkhvgkAqvDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0a0e57c32c600e55cc798009ba13f38d684a14dc51e8c8e6a697c2e443c27c0","last_reissued_at":"2026-07-05T04:32:39.037192Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:32:39.037192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Universal Hopfield Networks: A General Framework for Single-Shot Associative Memory Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.LG"],"primary_cat":"cs.NE","authors_text":"Beren Millidge, Rafal Bogacz, Thomas Lukasiewicz, Tommaso Salvatori, Yuhang Song","submitted_at":"2022-02-09T16:48:06Z","abstract_excerpt":"A large number of neural network models of associative memory have been proposed in the literature. These include the classical Hopfield networks (HNs), sparse distributed memories (SDMs), and more recently the modern continuous Hopfield networks (MCHNs), which possesses close links with self-attention in machine learning. In this paper, we propose a general framework for understanding the operation of such memory networks as a sequence of three operations: similarity, separation, and projection. We derive all these memory models as instances of our general framework with differing similarity "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.04557","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/2202.04557/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2202.04557","created_at":"2026-07-05T04:32:39.037248+00:00"},{"alias_kind":"arxiv_version","alias_value":"2202.04557v2","created_at":"2026-07-05T04:32:39.037248+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.04557","created_at":"2026-07-05T04:32:39.037248+00:00"},{"alias_kind":"pith_short_12","alias_value":"WCQOK7BSYYAO","created_at":"2026-07-05T04:32:39.037248+00:00"},{"alias_kind":"pith_short_16","alias_value":"WCQOK7BSYYAOKXGH","created_at":"2026-07-05T04:32:39.037248+00:00"},{"alias_kind":"pith_short_8","alias_value":"WCQOK7BS","created_at":"2026-07-05T04:32:39.037248+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.05189","citing_title":"Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval","ref_index":36,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WCQOK7BSYYAOKXGHTAAJXIJ7HD","json":"https://pith.science/pith/WCQOK7BSYYAOKXGHTAAJXIJ7HD.json","graph_json":"https://pith.science/api/pith-number/WCQOK7BSYYAOKXGHTAAJXIJ7HD/graph.json","events_json":"https://pith.science/api/pith-number/WCQOK7BSYYAOKXGHTAAJXIJ7HD/events.json","paper":"https://pith.science/paper/WCQOK7BS"},"agent_actions":{"view_html":"https://pith.science/pith/WCQOK7BSYYAOKXGHTAAJXIJ7HD","download_json":"https://pith.science/pith/WCQOK7BSYYAOKXGHTAAJXIJ7HD.json","view_paper":"https://pith.science/paper/WCQOK7BS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2202.04557&json=true","fetch_graph":"https://pith.science/api/pith-number/WCQOK7BSYYAOKXGHTAAJXIJ7HD/graph.json","fetch_events":"https://pith.science/api/pith-number/WCQOK7BSYYAOKXGHTAAJXIJ7HD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WCQOK7BSYYAOKXGHTAAJXIJ7HD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WCQOK7BSYYAOKXGHTAAJXIJ7HD/action/storage_attestation","attest_author":"https://pith.science/pith/WCQOK7BSYYAOKXGHTAAJXIJ7HD/action/author_attestation","sign_citation":"https://pith.science/pith/WCQOK7BSYYAOKXGHTAAJXIJ7HD/action/citation_signature","submit_replication":"https://pith.science/pith/WCQOK7BSYYAOKXGHTAAJXIJ7HD/action/replication_record"}},"created_at":"2026-07-05T04:32:39.037248+00:00","updated_at":"2026-07-05T04:32:39.037248+00:00"}