{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:U7IQQBAFZIDRO65J7ZY2STAYKE","short_pith_number":"pith:U7IQQBAF","canonical_record":{"source":{"id":"2402.03982","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-02-06T13:19:26Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"fa08acc58894f463f6c1ecc0caf58a9626c5c11f5e80ab49fd996c47a4a90f14","abstract_canon_sha256":"7b7d9c255f06be701d5eea2bbddcfecaf5c356729884d0db850e94cbd732e9b1"},"schema_version":"1.0"},"canonical_sha256":"a7d1080405ca07177ba9fe71a94c185127650d9acfee0e6f888dd7730b7ecc6e","source":{"kind":"arxiv","id":"2402.03982","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.03982","created_at":"2026-07-05T10:18:07Z"},{"alias_kind":"arxiv_version","alias_value":"2402.03982v2","created_at":"2026-07-05T10:18:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.03982","created_at":"2026-07-05T10:18:07Z"},{"alias_kind":"pith_short_12","alias_value":"U7IQQBAFZIDR","created_at":"2026-07-05T10:18:07Z"},{"alias_kind":"pith_short_16","alias_value":"U7IQQBAFZIDRO65J","created_at":"2026-07-05T10:18:07Z"},{"alias_kind":"pith_short_8","alias_value":"U7IQQBAF","created_at":"2026-07-05T10:18:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:U7IQQBAFZIDRO65J7ZY2STAYKE","target":"record","payload":{"canonical_record":{"source":{"id":"2402.03982","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-02-06T13:19:26Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"fa08acc58894f463f6c1ecc0caf58a9626c5c11f5e80ab49fd996c47a4a90f14","abstract_canon_sha256":"7b7d9c255f06be701d5eea2bbddcfecaf5c356729884d0db850e94cbd732e9b1"},"schema_version":"1.0"},"canonical_sha256":"a7d1080405ca07177ba9fe71a94c185127650d9acfee0e6f888dd7730b7ecc6e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:18:07.685464Z","signature_b64":"ZzYREVh9L4lfnKnKF+wcGb5wa9odK6DP495kqht/573CHhyo13S6Hk+K+RATQfYwYNJPDohqXpp/4zJNpXqsAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7d1080405ca07177ba9fe71a94c185127650d9acfee0e6f888dd7730b7ecc6e","last_reissued_at":"2026-07-05T10:18:07.684997Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:18:07.684997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2402.03982","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:18:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pwkpZdzkzYxRGK/F7x8hMj4EzbXscG8oZkMgA1IG9RuSLKwR7CSsuO27jTSTTWehAQeB7d4u6BRXyzv5OQUDCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T13:20:10.990361Z"},"content_sha256":"4f495ae9165338adffab5bbc81aae9df495bf2130856d743741a57616676e3d3","schema_version":"1.0","event_id":"sha256:4f495ae9165338adffab5bbc81aae9df495bf2130856d743741a57616676e3d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:U7IQQBAFZIDRO65J7ZY2STAYKE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Convergence of Adam for Stochastic Optimization under Relaxed Assumptions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"math.OC","authors_text":"Junhong Lin, Yusu Hong","submitted_at":"2024-02-06T13:19:26Z","abstract_excerpt":"The Adaptive Momentum Estimation (Adam) algorithm is highly effective in training various deep learning tasks. Despite this, there's limited theoretical understanding for Adam, especially when focusing on its vanilla form in non-convex smooth scenarios with potential unbounded gradients and affine variance noise. In this paper, we study vanilla Adam under these challenging conditions. We introduce a comprehensive noise model which governs affine variance noise, bounded noise and sub-Gaussian noise. We show that Adam can find a stationary point with a $\\mathcal{O}(\\text{poly}(\\log T)/\\sqrt{T})$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.03982","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/2402.03982/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":"2026-07-05T10:18:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WAhpV9V6wisxxwxjq/tazUOtf2HhSzSw9kcgqV5owA2VWJR2F3//1FFXS0iarz4eBg9HfUt/FWJgrfxlBLcDAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T13:20:10.990905Z"},"content_sha256":"5366ca55096a37b11818cf25278f0f2d71ee6ce1883ee6f160904c62c79c8c1f","schema_version":"1.0","event_id":"sha256:5366ca55096a37b11818cf25278f0f2d71ee6ce1883ee6f160904c62c79c8c1f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U7IQQBAFZIDRO65J7ZY2STAYKE/bundle.json","state_url":"https://pith.science/pith/U7IQQBAFZIDRO65J7ZY2STAYKE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U7IQQBAFZIDRO65J7ZY2STAYKE/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":"2026-08-07T13:20:10Z","links":{"resolver":"https://pith.science/pith/U7IQQBAFZIDRO65J7ZY2STAYKE","bundle":"https://pith.science/pith/U7IQQBAFZIDRO65J7ZY2STAYKE/bundle.json","state":"https://pith.science/pith/U7IQQBAFZIDRO65J7ZY2STAYKE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U7IQQBAFZIDRO65J7ZY2STAYKE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:U7IQQBAFZIDRO65J7ZY2STAYKE","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":"7b7d9c255f06be701d5eea2bbddcfecaf5c356729884d0db850e94cbd732e9b1","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-02-06T13:19:26Z","title_canon_sha256":"fa08acc58894f463f6c1ecc0caf58a9626c5c11f5e80ab49fd996c47a4a90f14"},"schema_version":"1.0","source":{"id":"2402.03982","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.03982","created_at":"2026-07-05T10:18:07Z"},{"alias_kind":"arxiv_version","alias_value":"2402.03982v2","created_at":"2026-07-05T10:18:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.03982","created_at":"2026-07-05T10:18:07Z"},{"alias_kind":"pith_short_12","alias_value":"U7IQQBAFZIDR","created_at":"2026-07-05T10:18:07Z"},{"alias_kind":"pith_short_16","alias_value":"U7IQQBAFZIDRO65J","created_at":"2026-07-05T10:18:07Z"},{"alias_kind":"pith_short_8","alias_value":"U7IQQBAF","created_at":"2026-07-05T10:18:07Z"}],"graph_snapshots":[{"event_id":"sha256:5366ca55096a37b11818cf25278f0f2d71ee6ce1883ee6f160904c62c79c8c1f","target":"graph","created_at":"2026-07-05T10:18:07Z","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/2402.03982/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Adaptive Momentum Estimation (Adam) algorithm is highly effective in training various deep learning tasks. Despite this, there's limited theoretical understanding for Adam, especially when focusing on its vanilla form in non-convex smooth scenarios with potential unbounded gradients and affine variance noise. In this paper, we study vanilla Adam under these challenging conditions. We introduce a comprehensive noise model which governs affine variance noise, bounded noise and sub-Gaussian noise. We show that Adam can find a stationary point with a $\\mathcal{O}(\\text{poly}(\\log T)/\\sqrt{T})$","authors_text":"Junhong Lin, Yusu Hong","cross_cats":["cs.LG","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-02-06T13:19:26Z","title":"On Convergence of Adam for Stochastic Optimization under Relaxed Assumptions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.03982","kind":"arxiv","version":2},"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":"sha256:4f495ae9165338adffab5bbc81aae9df495bf2130856d743741a57616676e3d3","target":"record","created_at":"2026-07-05T10:18:07Z","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":"7b7d9c255f06be701d5eea2bbddcfecaf5c356729884d0db850e94cbd732e9b1","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-02-06T13:19:26Z","title_canon_sha256":"fa08acc58894f463f6c1ecc0caf58a9626c5c11f5e80ab49fd996c47a4a90f14"},"schema_version":"1.0","source":{"id":"2402.03982","kind":"arxiv","version":2}},"canonical_sha256":"a7d1080405ca07177ba9fe71a94c185127650d9acfee0e6f888dd7730b7ecc6e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7d1080405ca07177ba9fe71a94c185127650d9acfee0e6f888dd7730b7ecc6e","first_computed_at":"2026-07-05T10:18:07.684997Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:18:07.684997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZzYREVh9L4lfnKnKF+wcGb5wa9odK6DP495kqht/573CHhyo13S6Hk+K+RATQfYwYNJPDohqXpp/4zJNpXqsAg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:18:07.685464Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.03982","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f495ae9165338adffab5bbc81aae9df495bf2130856d743741a57616676e3d3","sha256:5366ca55096a37b11818cf25278f0f2d71ee6ce1883ee6f160904c62c79c8c1f"],"state_sha256":"5225442765a44a539bd581a0a9aa2d2ce1150307493e2a870e73ef9f0efaaf87"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fU1HpPCu81pnufTF465zwwLC/4cL9uUTQl3nneh9bwtf3B/JRSfU3bkz53qUHtuYWQ4IL7szJKMCy+ChG+U+Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T13:20:10.995846Z","bundle_sha256":"75bd2358f02c59ff48007c8ae093d0e5272466372dd7bfe0ea0b528e860a0f3d"}}