{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:H5L52ALDSOV3VVQ23MT74TVNT2","short_pith_number":"pith:H5L52ALD","canonical_record":{"source":{"id":"2410.10800","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-10-14T17:57:33Z","cross_cats_sorted":[],"title_canon_sha256":"16aeec52314f18a551f5fc957f4d64d3aa769417f1b6ce2b7438b1101a4b6d9b","abstract_canon_sha256":"532aea0402354f60a5e059082a2af7675260bce90ee0c154901d38d2fd934eb5"},"schema_version":"1.0"},"canonical_sha256":"3f57dd016393abbad61adb27fe4ead9eba53641938e12cf6cd88f1b70a8bbd60","source":{"kind":"arxiv","id":"2410.10800","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.10800","created_at":"2026-07-05T10:26:40Z"},{"alias_kind":"arxiv_version","alias_value":"2410.10800v3","created_at":"2026-07-05T10:26:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.10800","created_at":"2026-07-05T10:26:40Z"},{"alias_kind":"pith_short_12","alias_value":"H5L52ALDSOV3","created_at":"2026-07-05T10:26:40Z"},{"alias_kind":"pith_short_16","alias_value":"H5L52ALDSOV3VVQ2","created_at":"2026-07-05T10:26:40Z"},{"alias_kind":"pith_short_8","alias_value":"H5L52ALD","created_at":"2026-07-05T10:26:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:H5L52ALDSOV3VVQ23MT74TVNT2","target":"record","payload":{"canonical_record":{"source":{"id":"2410.10800","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-10-14T17:57:33Z","cross_cats_sorted":[],"title_canon_sha256":"16aeec52314f18a551f5fc957f4d64d3aa769417f1b6ce2b7438b1101a4b6d9b","abstract_canon_sha256":"532aea0402354f60a5e059082a2af7675260bce90ee0c154901d38d2fd934eb5"},"schema_version":"1.0"},"canonical_sha256":"3f57dd016393abbad61adb27fe4ead9eba53641938e12cf6cd88f1b70a8bbd60","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:26:40.825574Z","signature_b64":"BjOv/tJAHh+WKAQdNdtL7q4Uv1nNromLskdXbOUGDBFpT4xS/w9RJ4hNoiaG53fpXfJ8KgIPbojGIrEVvrwwBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f57dd016393abbad61adb27fe4ead9eba53641938e12cf6cd88f1b70a8bbd60","last_reissued_at":"2026-07-05T10:26:40.825086Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:26:40.825086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.10800","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:26:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V7k653g8QmAPdDlG3FERJJmmcPadwcnUbQtiUAbmFdOMZv4Nc6NBSCrv2Ee7rzGDpQ/YurbbKDl+x2bBakcVCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T01:04:49.599056Z"},"content_sha256":"b7cd99cf3c7155e6326546c10a2763b5b1a0b040deb2135d503ea791231c65fb","schema_version":"1.0","event_id":"sha256:b7cd99cf3c7155e6326546c10a2763b5b1a0b040deb2135d503ea791231c65fb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:H5L52ALDSOV3VVQ23MT74TVNT2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimizing $(L_0, L_1)$-Smooth Functions by Gradient Methods","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Angelia Nedich, Anton Rodomanov, Daniil Vankov, Lalitha Sankar, Sebastian U. Stich","submitted_at":"2024-10-14T17:57:33Z","abstract_excerpt":"We study gradient methods for optimizing $(L_0, L_1)$-smooth functions, a class that generalizes Lipschitz-smooth functions and has gained attention for its relevance in machine learning. We provide new insights into the structure of this function class and develop a principled framework for analyzing optimization methods in this setting. While our convergence rate estimates recover existing results for minimizing the gradient norm in nonconvex problems, our approach significantly improves the best-known complexity bounds for convex objectives. Moreover, we show that the gradient method with P"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.10800","kind":"arxiv","version":3},"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/2410.10800/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":"2026-07-05T10:26:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c2Gr5emS9ZRZGIigb3PDl0XTXkAXlp2s5/FZb+N70Am6XqdL+TgRb5nHctv9yp8XkpGiyrDoGmNL0bUt5DpWCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T01:04:49.599556Z"},"content_sha256":"0e632543ec0659103f0e00ca039b0adb78571f41ab94a7ebea0596b36393cc30","schema_version":"1.0","event_id":"sha256:0e632543ec0659103f0e00ca039b0adb78571f41ab94a7ebea0596b36393cc30"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H5L52ALDSOV3VVQ23MT74TVNT2/bundle.json","state_url":"https://pith.science/pith/H5L52ALDSOV3VVQ23MT74TVNT2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H5L52ALDSOV3VVQ23MT74TVNT2/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":"2026-08-04T01:04:49Z","links":{"resolver":"https://pith.science/pith/H5L52ALDSOV3VVQ23MT74TVNT2","bundle":"https://pith.science/pith/H5L52ALDSOV3VVQ23MT74TVNT2/bundle.json","state":"https://pith.science/pith/H5L52ALDSOV3VVQ23MT74TVNT2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H5L52ALDSOV3VVQ23MT74TVNT2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:H5L52ALDSOV3VVQ23MT74TVNT2","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":"532aea0402354f60a5e059082a2af7675260bce90ee0c154901d38d2fd934eb5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-10-14T17:57:33Z","title_canon_sha256":"16aeec52314f18a551f5fc957f4d64d3aa769417f1b6ce2b7438b1101a4b6d9b"},"schema_version":"1.0","source":{"id":"2410.10800","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.10800","created_at":"2026-07-05T10:26:40Z"},{"alias_kind":"arxiv_version","alias_value":"2410.10800v3","created_at":"2026-07-05T10:26:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.10800","created_at":"2026-07-05T10:26:40Z"},{"alias_kind":"pith_short_12","alias_value":"H5L52ALDSOV3","created_at":"2026-07-05T10:26:40Z"},{"alias_kind":"pith_short_16","alias_value":"H5L52ALDSOV3VVQ2","created_at":"2026-07-05T10:26:40Z"},{"alias_kind":"pith_short_8","alias_value":"H5L52ALD","created_at":"2026-07-05T10:26:40Z"}],"graph_snapshots":[{"event_id":"sha256:0e632543ec0659103f0e00ca039b0adb78571f41ab94a7ebea0596b36393cc30","target":"graph","created_at":"2026-07-05T10:26:40Z","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/2410.10800/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study gradient methods for optimizing $(L_0, L_1)$-smooth functions, a class that generalizes Lipschitz-smooth functions and has gained attention for its relevance in machine learning. We provide new insights into the structure of this function class and develop a principled framework for analyzing optimization methods in this setting. While our convergence rate estimates recover existing results for minimizing the gradient norm in nonconvex problems, our approach significantly improves the best-known complexity bounds for convex objectives. Moreover, we show that the gradient method with P","authors_text":"Angelia Nedich, Anton Rodomanov, Daniil Vankov, Lalitha Sankar, Sebastian U. Stich","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-10-14T17:57:33Z","title":"Optimizing $(L_0, L_1)$-Smooth Functions by Gradient Methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.10800","kind":"arxiv","version":3},"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:b7cd99cf3c7155e6326546c10a2763b5b1a0b040deb2135d503ea791231c65fb","target":"record","created_at":"2026-07-05T10:26:40Z","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":"532aea0402354f60a5e059082a2af7675260bce90ee0c154901d38d2fd934eb5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-10-14T17:57:33Z","title_canon_sha256":"16aeec52314f18a551f5fc957f4d64d3aa769417f1b6ce2b7438b1101a4b6d9b"},"schema_version":"1.0","source":{"id":"2410.10800","kind":"arxiv","version":3}},"canonical_sha256":"3f57dd016393abbad61adb27fe4ead9eba53641938e12cf6cd88f1b70a8bbd60","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f57dd016393abbad61adb27fe4ead9eba53641938e12cf6cd88f1b70a8bbd60","first_computed_at":"2026-07-05T10:26:40.825086Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:26:40.825086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BjOv/tJAHh+WKAQdNdtL7q4Uv1nNromLskdXbOUGDBFpT4xS/w9RJ4hNoiaG53fpXfJ8KgIPbojGIrEVvrwwBg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:26:40.825574Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.10800","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7cd99cf3c7155e6326546c10a2763b5b1a0b040deb2135d503ea791231c65fb","sha256:0e632543ec0659103f0e00ca039b0adb78571f41ab94a7ebea0596b36393cc30"],"state_sha256":"e608dd1cf6e4869d586d55692f2c279170f979b85c7121d4e201f4b52f1451fb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n0y5DVlthtYRd2nxdDvenPkxtcU6tAB0IzQOJynXZlQRVUFGwHb+vFbPISF6tBNGNWcCS4+V4bw/Novb6+eWBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T01:04:49.603184Z","bundle_sha256":"6772f9cc815fb981b2df6adcae938f46398117ea1843bb4ab4a7656ec0e55abc"}}