{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:UVVINAUB7CQTTDQPRUSEVN7IX7","short_pith_number":"pith:UVVINAUB","canonical_record":{"source":{"id":"2402.04520","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2024-02-07T01:58:21Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"60f8405829a06c19bff1ccf6e0c1abb1e5267056a4717f710a44ba1faed72c7d","abstract_canon_sha256":"88bc5e5ae541b0d628cc6edc1405b068b4f9b04f3f9d58db25d51a88964051aa"},"schema_version":"1.0"},"canonical_sha256":"a56a868281f8a1398e0f8d244ab7e8bfe7a86c34c3fedf47a2b5c183ad337a16","source":{"kind":"arxiv","id":"2402.04520","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.04520","created_at":"2026-07-05T08:25:52Z"},{"alias_kind":"arxiv_version","alias_value":"2402.04520v5","created_at":"2026-07-05T08:25:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.04520","created_at":"2026-07-05T08:25:52Z"},{"alias_kind":"pith_short_12","alias_value":"UVVINAUB7CQT","created_at":"2026-07-05T08:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"UVVINAUB7CQTTDQP","created_at":"2026-07-05T08:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"UVVINAUB","created_at":"2026-07-05T08:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:UVVINAUB7CQTTDQPRUSEVN7IX7","target":"record","payload":{"canonical_record":{"source":{"id":"2402.04520","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2024-02-07T01:58:21Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"60f8405829a06c19bff1ccf6e0c1abb1e5267056a4717f710a44ba1faed72c7d","abstract_canon_sha256":"88bc5e5ae541b0d628cc6edc1405b068b4f9b04f3f9d58db25d51a88964051aa"},"schema_version":"1.0"},"canonical_sha256":"a56a868281f8a1398e0f8d244ab7e8bfe7a86c34c3fedf47a2b5c183ad337a16","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:25:52.260715Z","signature_b64":"GuVsLcs9NpfiqbBPXlXQVq3dv5618CsPZUg4megtAIX9PNUZTe7lWSxgaiTiq416BWMGl9ILhOj5AqpJpN6YBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a56a868281f8a1398e0f8d244ab7e8bfe7a86c34c3fedf47a2b5c183ad337a16","last_reissued_at":"2026-07-05T08:25:52.260143Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:25:52.260143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2402.04520","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:25:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N0MLdZdETojjRHkLOfwfo4yQaogaYmJNLtJhDsFoJcfEB+IUF+lrydfOkH6D5J/svJdnqbvZEuTAfR7sI2GMAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T20:47:56.750775Z"},"content_sha256":"bd9e59e2849640d5adecdd0350c9370422aef9c7411299eebe58b766a5822f71","schema_version":"1.0","event_id":"sha256:bd9e59e2849640d5adecdd0350c9370422aef9c7411299eebe58b766a5822f71"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:UVVINAUB7CQTTDQPRUSEVN7IX7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Computational Limits of Modern Hopfield Models: A Fine-Grained Complexity Analysis","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.AI","stat.ML"],"primary_cat":"cs.LG","authors_text":"Han Liu, Jerry Yao-Chieh Hu, Thomas Lin, Zhao Song","submitted_at":"2024-02-07T01:58:21Z","abstract_excerpt":"We investigate the computational limits of the memory retrieval dynamics of modern Hopfield models from the fine-grained complexity analysis. Our key contribution is the characterization of a phase transition behavior in the efficiency of all possible modern Hopfield models based on the norm of patterns. Specifically, we establish an upper bound criterion for the norm of input query patterns and memory patterns. Only below this criterion, sub-quadratic (efficient) variants of the modern Hopfield model exist, assuming the Strong Exponential Time Hypothesis (SETH). To showcase our theory, we pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.04520","kind":"arxiv","version":5},"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/2402.04520/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:25:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KpQlxOgebRW05kDJkRjOc75xSpqijD3th8B3sPkgfCrSAMmzFstSBZQXAarjfZ/xqwmprKNzFrdlWIXZYn1hCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T20:47:56.751152Z"},"content_sha256":"f96e6bb6890d251c2a0d0fed3b856cf01dcd8a2ea867c3b790a70c885fd0ee08","schema_version":"1.0","event_id":"sha256:f96e6bb6890d251c2a0d0fed3b856cf01dcd8a2ea867c3b790a70c885fd0ee08"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UVVINAUB7CQTTDQPRUSEVN7IX7/bundle.json","state_url":"https://pith.science/pith/UVVINAUB7CQTTDQPRUSEVN7IX7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UVVINAUB7CQTTDQPRUSEVN7IX7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-06T20:47:56Z","links":{"resolver":"https://pith.science/pith/UVVINAUB7CQTTDQPRUSEVN7IX7","bundle":"https://pith.science/pith/UVVINAUB7CQTTDQPRUSEVN7IX7/bundle.json","state":"https://pith.science/pith/UVVINAUB7CQTTDQPRUSEVN7IX7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UVVINAUB7CQTTDQPRUSEVN7IX7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:UVVINAUB7CQTTDQPRUSEVN7IX7","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":"88bc5e5ae541b0d628cc6edc1405b068b4f9b04f3f9d58db25d51a88964051aa","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2024-02-07T01:58:21Z","title_canon_sha256":"60f8405829a06c19bff1ccf6e0c1abb1e5267056a4717f710a44ba1faed72c7d"},"schema_version":"1.0","source":{"id":"2402.04520","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.04520","created_at":"2026-07-05T08:25:52Z"},{"alias_kind":"arxiv_version","alias_value":"2402.04520v5","created_at":"2026-07-05T08:25:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.04520","created_at":"2026-07-05T08:25:52Z"},{"alias_kind":"pith_short_12","alias_value":"UVVINAUB7CQT","created_at":"2026-07-05T08:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"UVVINAUB7CQTTDQP","created_at":"2026-07-05T08:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"UVVINAUB","created_at":"2026-07-05T08:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:f96e6bb6890d251c2a0d0fed3b856cf01dcd8a2ea867c3b790a70c885fd0ee08","target":"graph","created_at":"2026-07-05T08:25:52Z","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/2402.04520/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the computational limits of the memory retrieval dynamics of modern Hopfield models from the fine-grained complexity analysis. Our key contribution is the characterization of a phase transition behavior in the efficiency of all possible modern Hopfield models based on the norm of patterns. Specifically, we establish an upper bound criterion for the norm of input query patterns and memory patterns. Only below this criterion, sub-quadratic (efficient) variants of the modern Hopfield model exist, assuming the Strong Exponential Time Hypothesis (SETH). To showcase our theory, we pro","authors_text":"Han Liu, Jerry Yao-Chieh Hu, Thomas Lin, Zhao Song","cross_cats":["cs.AI","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2024-02-07T01:58:21Z","title":"On Computational Limits of Modern Hopfield Models: A Fine-Grained Complexity Analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.04520","kind":"arxiv","version":5},"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:bd9e59e2849640d5adecdd0350c9370422aef9c7411299eebe58b766a5822f71","target":"record","created_at":"2026-07-05T08:25:52Z","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":"88bc5e5ae541b0d628cc6edc1405b068b4f9b04f3f9d58db25d51a88964051aa","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2024-02-07T01:58:21Z","title_canon_sha256":"60f8405829a06c19bff1ccf6e0c1abb1e5267056a4717f710a44ba1faed72c7d"},"schema_version":"1.0","source":{"id":"2402.04520","kind":"arxiv","version":5}},"canonical_sha256":"a56a868281f8a1398e0f8d244ab7e8bfe7a86c34c3fedf47a2b5c183ad337a16","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a56a868281f8a1398e0f8d244ab7e8bfe7a86c34c3fedf47a2b5c183ad337a16","first_computed_at":"2026-07-05T08:25:52.260143Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:25:52.260143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GuVsLcs9NpfiqbBPXlXQVq3dv5618CsPZUg4megtAIX9PNUZTe7lWSxgaiTiq416BWMGl9ILhOj5AqpJpN6YBw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:25:52.260715Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.04520","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd9e59e2849640d5adecdd0350c9370422aef9c7411299eebe58b766a5822f71","sha256:f96e6bb6890d251c2a0d0fed3b856cf01dcd8a2ea867c3b790a70c885fd0ee08"],"state_sha256":"ebfd38bb1a0d28b58b4c6890ba31761068d3af7adf23cfa1eb21350707ffdd50"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"65pOA/6IfDhpvZ3bW6tYZtDA/KxG6iGuc4WOExg4XyCI2l7csaLN3hsW3vUUHrCBApOvzX12S+/8JZEWuMg6DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T20:47:56.753081Z","bundle_sha256":"a383e0bd3fd65e59c8002cd865f87155295fe6302bb315e19d529b3640a2e037"}}