{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:OH6BTSRIMIVBDYYGITGCJF7EZX","short_pith_number":"pith:OH6BTSRI","canonical_record":{"source":{"id":"2506.11043","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2025-05-21T10:33:01Z","cross_cats_sorted":["cs.LG","cs.NE"],"title_canon_sha256":"5f2b0c5b40308e95360fb30b75c9b258f7b78299e48e1b6e407fa28b4bb1f241","abstract_canon_sha256":"fa298b9d3a6a8b3664650ce1249c4982c301e98fa06b9e3b973d79588690412b"},"schema_version":"1.0"},"canonical_sha256":"71fc19ca28622a11e30644cc2497e4cdf2e83352a6e876bdd0f09292e9a8a87c","source":{"kind":"arxiv","id":"2506.11043","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.11043","created_at":"2026-07-05T11:20:58Z"},{"alias_kind":"arxiv_version","alias_value":"2506.11043v1","created_at":"2026-07-05T11:20:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.11043","created_at":"2026-07-05T11:20:58Z"},{"alias_kind":"pith_short_12","alias_value":"OH6BTSRIMIVB","created_at":"2026-07-05T11:20:58Z"},{"alias_kind":"pith_short_16","alias_value":"OH6BTSRIMIVBDYYG","created_at":"2026-07-05T11:20:58Z"},{"alias_kind":"pith_short_8","alias_value":"OH6BTSRI","created_at":"2026-07-05T11:20:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:OH6BTSRIMIVBDYYGITGCJF7EZX","target":"record","payload":{"canonical_record":{"source":{"id":"2506.11043","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2025-05-21T10:33:01Z","cross_cats_sorted":["cs.LG","cs.NE"],"title_canon_sha256":"5f2b0c5b40308e95360fb30b75c9b258f7b78299e48e1b6e407fa28b4bb1f241","abstract_canon_sha256":"fa298b9d3a6a8b3664650ce1249c4982c301e98fa06b9e3b973d79588690412b"},"schema_version":"1.0"},"canonical_sha256":"71fc19ca28622a11e30644cc2497e4cdf2e83352a6e876bdd0f09292e9a8a87c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:20:58.424881Z","signature_b64":"tEmlIPyegSlPlt7kfpsVOzGbnFIErr++8hmSRBgzKH/SJJP8cfKsW9OqL3seIaKlLKoKazJ2789Y2RDL3F5QDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71fc19ca28622a11e30644cc2497e4cdf2e83352a6e876bdd0f09292e9a8a87c","last_reissued_at":"2026-07-05T11:20:58.424409Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:20:58.424409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.11043","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:20:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tL1fSgbxpnH1hjjMiPJWjdH2apOkkf9gE2uh5G9pWtoWpciCwjzDEGOyJ8wlIkNXZrEPat2TID63FJfqxV1nCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T16:52:22.225863Z"},"content_sha256":"b2d041af485615dff54a95b6e7c655dd795b8666613827cd8809856425cfc62b","schema_version":"1.0","event_id":"sha256:b2d041af485615dff54a95b6e7c655dd795b8666613827cd8809856425cfc62b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:OH6BTSRIMIVBDYYGITGCJF7EZX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Framework for Non-Linear Attention via Modern Hopfield Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NE"],"primary_cat":"stat.ML","authors_text":"Ahmed Farooq","submitted_at":"2025-05-21T10:33:01Z","abstract_excerpt":"In this work we propose an energy functional along the lines of Modern Hopfield Networks (MNH), the stationary points of which correspond to the attention due to Vaswani et al. [12], thus unifying both frameworks. The minima of this landscape form \"context wells\" - stable configurations that encapsulate the contextual relationships among tokens. A compelling picture emerges: across $n$ token embeddings an energy landscape is defined whose gradient corresponds to the attention computation. Non-linear attention mechanisms offer a means to enhance the capabilities of transformer models for variou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.11043","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.11043/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":"2026-07-05T11:20:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dEwrx2lycqHcyx00zutERSel25Qp+ADCvae8gpfQWgatY4DQeeP1h8cq5TWZg98MAT/PhOH26M0akv9M7GY4Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T16:52:22.226356Z"},"content_sha256":"673000a794f29f7f4dac0246e989d01fde5c2820a08dad7021bb189852f3b983","schema_version":"1.0","event_id":"sha256:673000a794f29f7f4dac0246e989d01fde5c2820a08dad7021bb189852f3b983"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OH6BTSRIMIVBDYYGITGCJF7EZX/bundle.json","state_url":"https://pith.science/pith/OH6BTSRIMIVBDYYGITGCJF7EZX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OH6BTSRIMIVBDYYGITGCJF7EZX/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":"2026-08-08T16:52:22Z","links":{"resolver":"https://pith.science/pith/OH6BTSRIMIVBDYYGITGCJF7EZX","bundle":"https://pith.science/pith/OH6BTSRIMIVBDYYGITGCJF7EZX/bundle.json","state":"https://pith.science/pith/OH6BTSRIMIVBDYYGITGCJF7EZX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OH6BTSRIMIVBDYYGITGCJF7EZX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:OH6BTSRIMIVBDYYGITGCJF7EZX","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":"fa298b9d3a6a8b3664650ce1249c4982c301e98fa06b9e3b973d79588690412b","cross_cats_sorted":["cs.LG","cs.NE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2025-05-21T10:33:01Z","title_canon_sha256":"5f2b0c5b40308e95360fb30b75c9b258f7b78299e48e1b6e407fa28b4bb1f241"},"schema_version":"1.0","source":{"id":"2506.11043","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.11043","created_at":"2026-07-05T11:20:58Z"},{"alias_kind":"arxiv_version","alias_value":"2506.11043v1","created_at":"2026-07-05T11:20:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.11043","created_at":"2026-07-05T11:20:58Z"},{"alias_kind":"pith_short_12","alias_value":"OH6BTSRIMIVB","created_at":"2026-07-05T11:20:58Z"},{"alias_kind":"pith_short_16","alias_value":"OH6BTSRIMIVBDYYG","created_at":"2026-07-05T11:20:58Z"},{"alias_kind":"pith_short_8","alias_value":"OH6BTSRI","created_at":"2026-07-05T11:20:58Z"}],"graph_snapshots":[{"event_id":"sha256:673000a794f29f7f4dac0246e989d01fde5c2820a08dad7021bb189852f3b983","target":"graph","created_at":"2026-07-05T11:20:58Z","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/2506.11043/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work we propose an energy functional along the lines of Modern Hopfield Networks (MNH), the stationary points of which correspond to the attention due to Vaswani et al. [12], thus unifying both frameworks. The minima of this landscape form \"context wells\" - stable configurations that encapsulate the contextual relationships among tokens. A compelling picture emerges: across $n$ token embeddings an energy landscape is defined whose gradient corresponds to the attention computation. Non-linear attention mechanisms offer a means to enhance the capabilities of transformer models for variou","authors_text":"Ahmed Farooq","cross_cats":["cs.LG","cs.NE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2025-05-21T10:33:01Z","title":"A Framework for Non-Linear Attention via Modern Hopfield Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.11043","kind":"arxiv","version":1},"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:b2d041af485615dff54a95b6e7c655dd795b8666613827cd8809856425cfc62b","target":"record","created_at":"2026-07-05T11:20:58Z","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":"fa298b9d3a6a8b3664650ce1249c4982c301e98fa06b9e3b973d79588690412b","cross_cats_sorted":["cs.LG","cs.NE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2025-05-21T10:33:01Z","title_canon_sha256":"5f2b0c5b40308e95360fb30b75c9b258f7b78299e48e1b6e407fa28b4bb1f241"},"schema_version":"1.0","source":{"id":"2506.11043","kind":"arxiv","version":1}},"canonical_sha256":"71fc19ca28622a11e30644cc2497e4cdf2e83352a6e876bdd0f09292e9a8a87c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71fc19ca28622a11e30644cc2497e4cdf2e83352a6e876bdd0f09292e9a8a87c","first_computed_at":"2026-07-05T11:20:58.424409Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:20:58.424409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tEmlIPyegSlPlt7kfpsVOzGbnFIErr++8hmSRBgzKH/SJJP8cfKsW9OqL3seIaKlLKoKazJ2789Y2RDL3F5QDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:20:58.424881Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.11043","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2d041af485615dff54a95b6e7c655dd795b8666613827cd8809856425cfc62b","sha256:673000a794f29f7f4dac0246e989d01fde5c2820a08dad7021bb189852f3b983"],"state_sha256":"807010b91970c0c2c1f4d072eca84ad03129fbc108afdd6b22b44927816fbff4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0z9wAlDFdlAg0zJzCgxnjOF6a9dO4XDIMveRKo/6Jex0Z4LN9czTLnRhBxdSke5zhfdJhmXvkW0Bex7qiyUVBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T16:52:22.231312Z","bundle_sha256":"51724d96d0ee0214fb6c03eb011ab3ec043f8af4c29992746ad7514c8330690e"}}