{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:OPJ6GYGWLRUJDPW4GOWJSNPW3J","short_pith_number":"pith:OPJ6GYGW","canonical_record":{"source":{"id":"2505.19488","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-05-26T04:15:38Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"0956e1d5dbb62cf03be573cdd50f75f45a7d96e17dc18b08bc4ff4461c5261f5","abstract_canon_sha256":"2043d681789825b087874499c504fcbba739868717f1ef0dc4d7faae60294987"},"schema_version":"1.0"},"canonical_sha256":"73d3e360d65c6891bedc33ac9935f6da5a331d1656f8a8742c5312faa80919a7","source":{"kind":"arxiv","id":"2505.19488","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.19488","created_at":"2026-07-05T11:09:31Z"},{"alias_kind":"arxiv_version","alias_value":"2505.19488v1","created_at":"2026-07-05T11:09:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.19488","created_at":"2026-07-05T11:09:31Z"},{"alias_kind":"pith_short_12","alias_value":"OPJ6GYGWLRUJ","created_at":"2026-07-05T11:09:31Z"},{"alias_kind":"pith_short_16","alias_value":"OPJ6GYGWLRUJDPW4","created_at":"2026-07-05T11:09:31Z"},{"alias_kind":"pith_short_8","alias_value":"OPJ6GYGW","created_at":"2026-07-05T11:09:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:OPJ6GYGWLRUJDPW4GOWJSNPW3J","target":"record","payload":{"canonical_record":{"source":{"id":"2505.19488","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-05-26T04:15:38Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"0956e1d5dbb62cf03be573cdd50f75f45a7d96e17dc18b08bc4ff4461c5261f5","abstract_canon_sha256":"2043d681789825b087874499c504fcbba739868717f1ef0dc4d7faae60294987"},"schema_version":"1.0"},"canonical_sha256":"73d3e360d65c6891bedc33ac9935f6da5a331d1656f8a8742c5312faa80919a7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:09:31.084771Z","signature_b64":"wQOSvZCphlR/TZhpO4V3ZSK4IVGGZ734b5jRxiyr99bR9cfUnoe/BNXm42zREgCdPYJF8dXFM+heZyy+m3cZCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73d3e360d65c6891bedc33ac9935f6da5a331d1656f8a8742c5312faa80919a7","last_reissued_at":"2026-07-05T11:09:31.084279Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:09:31.084279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.19488","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":"2026-07-05T11:09:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4UNIuaHeHoJtdxpvzbzadDEvDWIvqz+jAdGH+qJ76FLO/WgAVdlMMey3jN1MqNv43k5tvgUdeO0LinN1Fx6jBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T02:20:27.505009Z"},"content_sha256":"d52a4373decfbe3669d91a89f2d6c1bdeaaad7158476ab10fd89e612880b19fe","schema_version":"1.0","event_id":"sha256:d52a4373decfbe3669d91a89f2d6c1bdeaaad7158476ab10fd89e612880b19fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:OPJ6GYGWLRUJDPW4GOWJSNPW3J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Understanding Transformer from the Perspective of Associative Memory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Guang Shi, Mingyu Xu, Shu Zhong, Tenglong Ao","submitted_at":"2025-05-26T04:15:38Z","abstract_excerpt":"In this paper, we share our reflections and insights on understanding Transformer architectures through the lens of associative memory--a classic psychological concept inspired by human cognition. We start with the basics of associative memory (think simple linear attention) and then dive into two dimensions:\n  Memory Capacity: How much can a Transformer really remember, and how well? We introduce retrieval SNR to measure this and use a kernel perspective to mathematically reveal why Softmax Attention is so effective. We also show how FFNs can be seen as a type of associative memory, leading t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.19488","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/2505.19488/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":"2026-07-05T11:09:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rwSaMvmyby6vF5nuPPAKcg7zlAw4EMZIK45249Xw5GS7R4ppXddrVg0jyF34A8rMD8FpIE0ud/+AziZp4wPkBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T02:20:27.505911Z"},"content_sha256":"cfe851be0ff24617258047c657be9d7e6b6ca17efdf5912ced82c9d90581d776","schema_version":"1.0","event_id":"sha256:cfe851be0ff24617258047c657be9d7e6b6ca17efdf5912ced82c9d90581d776"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OPJ6GYGWLRUJDPW4GOWJSNPW3J/bundle.json","state_url":"https://pith.science/pith/OPJ6GYGWLRUJDPW4GOWJSNPW3J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OPJ6GYGWLRUJDPW4GOWJSNPW3J/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":"2026-08-05T02:20:27Z","links":{"resolver":"https://pith.science/pith/OPJ6GYGWLRUJDPW4GOWJSNPW3J","bundle":"https://pith.science/pith/OPJ6GYGWLRUJDPW4GOWJSNPW3J/bundle.json","state":"https://pith.science/pith/OPJ6GYGWLRUJDPW4GOWJSNPW3J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OPJ6GYGWLRUJDPW4GOWJSNPW3J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:OPJ6GYGWLRUJDPW4GOWJSNPW3J","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":"2043d681789825b087874499c504fcbba739868717f1ef0dc4d7faae60294987","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-05-26T04:15:38Z","title_canon_sha256":"0956e1d5dbb62cf03be573cdd50f75f45a7d96e17dc18b08bc4ff4461c5261f5"},"schema_version":"1.0","source":{"id":"2505.19488","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.19488","created_at":"2026-07-05T11:09:31Z"},{"alias_kind":"arxiv_version","alias_value":"2505.19488v1","created_at":"2026-07-05T11:09:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.19488","created_at":"2026-07-05T11:09:31Z"},{"alias_kind":"pith_short_12","alias_value":"OPJ6GYGWLRUJ","created_at":"2026-07-05T11:09:31Z"},{"alias_kind":"pith_short_16","alias_value":"OPJ6GYGWLRUJDPW4","created_at":"2026-07-05T11:09:31Z"},{"alias_kind":"pith_short_8","alias_value":"OPJ6GYGW","created_at":"2026-07-05T11:09:31Z"}],"graph_snapshots":[{"event_id":"sha256:cfe851be0ff24617258047c657be9d7e6b6ca17efdf5912ced82c9d90581d776","target":"graph","created_at":"2026-07-05T11:09:31Z","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/2505.19488/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we share our reflections and insights on understanding Transformer architectures through the lens of associative memory--a classic psychological concept inspired by human cognition. We start with the basics of associative memory (think simple linear attention) and then dive into two dimensions:\n  Memory Capacity: How much can a Transformer really remember, and how well? We introduce retrieval SNR to measure this and use a kernel perspective to mathematically reveal why Softmax Attention is so effective. We also show how FFNs can be seen as a type of associative memory, leading t","authors_text":"Guang Shi, Mingyu Xu, Shu Zhong, Tenglong Ao","cross_cats":["cs.AI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-05-26T04:15:38Z","title":"Understanding Transformer from the Perspective of Associative Memory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.19488","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:d52a4373decfbe3669d91a89f2d6c1bdeaaad7158476ab10fd89e612880b19fe","target":"record","created_at":"2026-07-05T11:09:31Z","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":"2043d681789825b087874499c504fcbba739868717f1ef0dc4d7faae60294987","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-05-26T04:15:38Z","title_canon_sha256":"0956e1d5dbb62cf03be573cdd50f75f45a7d96e17dc18b08bc4ff4461c5261f5"},"schema_version":"1.0","source":{"id":"2505.19488","kind":"arxiv","version":1}},"canonical_sha256":"73d3e360d65c6891bedc33ac9935f6da5a331d1656f8a8742c5312faa80919a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73d3e360d65c6891bedc33ac9935f6da5a331d1656f8a8742c5312faa80919a7","first_computed_at":"2026-07-05T11:09:31.084279Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:09:31.084279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wQOSvZCphlR/TZhpO4V3ZSK4IVGGZ734b5jRxiyr99bR9cfUnoe/BNXm42zREgCdPYJF8dXFM+heZyy+m3cZCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:09:31.084771Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.19488","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d52a4373decfbe3669d91a89f2d6c1bdeaaad7158476ab10fd89e612880b19fe","sha256:cfe851be0ff24617258047c657be9d7e6b6ca17efdf5912ced82c9d90581d776"],"state_sha256":"195511afe7de0491f345357fa247a58873196e109675b726ea2adeb8d289d322"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WHGVg5JzXEuwUReEmFAhvhnC5HpqmLAeHnuJJ4xFApJDCYJOyO5rr+NoheaUnpjbsLvj8oQ6KUjB1Wh+LogODw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T02:20:27.512466Z","bundle_sha256":"f3b026c1a1e9ebab4674fa1e1fffb17ea1a749dd53dad684e118b4badb23c38e"}}