{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:JZS2MP3CGA5MN54W3GBYT5MMZH","short_pith_number":"pith:JZS2MP3C","canonical_record":{"source":{"id":"2310.07831","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-10-11T19:16:35Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"498a187027c6a815409477cb36d00ec5349faa9e68d5816cebf1f550d20592aa","abstract_canon_sha256":"106fa98131f18ef3b2ef73b1c7c9ca453ed1face29f9bee8d4a5baa19285d8c5"},"schema_version":"1.0"},"canonical_sha256":"4e65a63f62303ac6f796d98389f58cc9f2bf780cae6bf50d7d260ab6440e76db","source":{"kind":"arxiv","id":"2310.07831","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.07831","created_at":"2026-07-05T09:28:09Z"},{"alias_kind":"arxiv_version","alias_value":"2310.07831v2","created_at":"2026-07-05T09:28:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.07831","created_at":"2026-07-05T09:28:09Z"},{"alias_kind":"pith_short_12","alias_value":"JZS2MP3CGA5M","created_at":"2026-07-05T09:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"JZS2MP3CGA5MN54W","created_at":"2026-07-05T09:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"JZS2MP3C","created_at":"2026-07-05T09:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:JZS2MP3CGA5MN54W3GBYT5MMZH","target":"record","payload":{"canonical_record":{"source":{"id":"2310.07831","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-10-11T19:16:35Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"498a187027c6a815409477cb36d00ec5349faa9e68d5816cebf1f550d20592aa","abstract_canon_sha256":"106fa98131f18ef3b2ef73b1c7c9ca453ed1face29f9bee8d4a5baa19285d8c5"},"schema_version":"1.0"},"canonical_sha256":"4e65a63f62303ac6f796d98389f58cc9f2bf780cae6bf50d7d260ab6440e76db","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:28:09.560461Z","signature_b64":"R1oWWqs5nL/C1Taxck625I+9O4QKK9uKxMtBjRgC2ryRD4PfWk75Exd3+LJwrHJcgAlVNPsgz0vqXU0M1le7CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e65a63f62303ac6f796d98389f58cc9f2bf780cae6bf50d7d260ab6440e76db","last_reissued_at":"2026-07-05T09:28:09.559987Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:28:09.559987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2310.07831","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":"2026-07-05T09:28:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WAqpbBIv5eBD2YjQMbQPVLho9khOuft8hA6Lx6/z+yv4vj5Lt8yRoSEpVLYooXAi/2MXVKUqLbSr0Kt2yMBKAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T02:25:02.777788Z"},"content_sha256":"1487371dae4165beea701ac13543335085c421b1e7e9c58d9699cb413ebb858b","schema_version":"1.0","event_id":"sha256:1487371dae4165beea701ac13543335085c421b1e7e9c58d9699cb413ebb858b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:JZS2MP3CGA5MN54W3GBYT5MMZH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Linear Decay Learning Rate Schedules and Further Refinements","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","stat.ML"],"primary_cat":"cs.LG","authors_text":"Aaron Defazio, Ashok Cutkosky, Harsh Mehta, Konstantin Mishchenko","submitted_at":"2023-10-11T19:16:35Z","abstract_excerpt":"Learning rate schedules used in practice bear little resemblance to those recommended by theory. We close much of this theory/practice gap, and as a consequence are able to derive new problem-adaptive learning rate schedules. Our main technical contribution is a refined analysis of learning rate schedules for a wide class of optimization algorithms (including SGD). When considering only worst-case analysis, our theory predicts that the optimal choice is the linear decay schedule where the step-size is set proportional to 1 - t/T, where t is the current iteration and T is the total number of st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.07831","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/2310.07831/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":"2026-07-05T09:28:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MxvTpNraiqbPILMQPnSqJlMGNkiN3OPV5pX/Xt8cmMUQlJoqf1uIB5kwcCVqkJw5oUmy/ZhSnIMaiXynhT4qAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T02:25:02.778756Z"},"content_sha256":"23b9c5b711bf428973276bd3fea2ee9a812d0598480a1b8048dab3698217caec","schema_version":"1.0","event_id":"sha256:23b9c5b711bf428973276bd3fea2ee9a812d0598480a1b8048dab3698217caec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JZS2MP3CGA5MN54W3GBYT5MMZH/bundle.json","state_url":"https://pith.science/pith/JZS2MP3CGA5MN54W3GBYT5MMZH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JZS2MP3CGA5MN54W3GBYT5MMZH/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":"2026-08-05T02:25:02Z","links":{"resolver":"https://pith.science/pith/JZS2MP3CGA5MN54W3GBYT5MMZH","bundle":"https://pith.science/pith/JZS2MP3CGA5MN54W3GBYT5MMZH/bundle.json","state":"https://pith.science/pith/JZS2MP3CGA5MN54W3GBYT5MMZH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JZS2MP3CGA5MN54W3GBYT5MMZH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:JZS2MP3CGA5MN54W3GBYT5MMZH","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":"106fa98131f18ef3b2ef73b1c7c9ca453ed1face29f9bee8d4a5baa19285d8c5","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-10-11T19:16:35Z","title_canon_sha256":"498a187027c6a815409477cb36d00ec5349faa9e68d5816cebf1f550d20592aa"},"schema_version":"1.0","source":{"id":"2310.07831","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.07831","created_at":"2026-07-05T09:28:09Z"},{"alias_kind":"arxiv_version","alias_value":"2310.07831v2","created_at":"2026-07-05T09:28:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.07831","created_at":"2026-07-05T09:28:09Z"},{"alias_kind":"pith_short_12","alias_value":"JZS2MP3CGA5M","created_at":"2026-07-05T09:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"JZS2MP3CGA5MN54W","created_at":"2026-07-05T09:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"JZS2MP3C","created_at":"2026-07-05T09:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:23b9c5b711bf428973276bd3fea2ee9a812d0598480a1b8048dab3698217caec","target":"graph","created_at":"2026-07-05T09:28:09Z","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/2310.07831/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Learning rate schedules used in practice bear little resemblance to those recommended by theory. We close much of this theory/practice gap, and as a consequence are able to derive new problem-adaptive learning rate schedules. Our main technical contribution is a refined analysis of learning rate schedules for a wide class of optimization algorithms (including SGD). When considering only worst-case analysis, our theory predicts that the optimal choice is the linear decay schedule where the step-size is set proportional to 1 - t/T, where t is the current iteration and T is the total number of st","authors_text":"Aaron Defazio, Ashok Cutkosky, Harsh Mehta, Konstantin Mishchenko","cross_cats":["cs.AI","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-10-11T19:16:35Z","title":"Optimal Linear Decay Learning Rate Schedules and Further Refinements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.07831","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":"sha256:1487371dae4165beea701ac13543335085c421b1e7e9c58d9699cb413ebb858b","target":"record","created_at":"2026-07-05T09:28:09Z","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":"106fa98131f18ef3b2ef73b1c7c9ca453ed1face29f9bee8d4a5baa19285d8c5","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-10-11T19:16:35Z","title_canon_sha256":"498a187027c6a815409477cb36d00ec5349faa9e68d5816cebf1f550d20592aa"},"schema_version":"1.0","source":{"id":"2310.07831","kind":"arxiv","version":2}},"canonical_sha256":"4e65a63f62303ac6f796d98389f58cc9f2bf780cae6bf50d7d260ab6440e76db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e65a63f62303ac6f796d98389f58cc9f2bf780cae6bf50d7d260ab6440e76db","first_computed_at":"2026-07-05T09:28:09.559987Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:28:09.559987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R1oWWqs5nL/C1Taxck625I+9O4QKK9uKxMtBjRgC2ryRD4PfWk75Exd3+LJwrHJcgAlVNPsgz0vqXU0M1le7CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:28:09.560461Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.07831","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1487371dae4165beea701ac13543335085c421b1e7e9c58d9699cb413ebb858b","sha256:23b9c5b711bf428973276bd3fea2ee9a812d0598480a1b8048dab3698217caec"],"state_sha256":"18b161a7a79f6f6554ce921671833ffb9ffe9c39c63c0c6ec7688c4656b0760b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J2mZ/7j2D67eyc9HgEkRn11CJVHv374SCw527m6Me9swlYIS4tUHBlkAmNdRrGjWgvsy16yhE1cRH82r7RsOBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T02:25:02.784462Z","bundle_sha256":"7d309d22d69807b3d6dab84d65b3474e3ee973c4a99d4f4bb9aa3cb568903696"}}