{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:4BMGNDNJYGDIJWEYEDXC3PSUSH","short_pith_number":"pith:4BMGNDNJ","canonical_record":{"source":{"id":"2410.08395","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-10-10T22:02:10Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"b42d817cb3c918dd6ddbab7f2897606e5cf4611145bd2948601796772bf9e6d6","abstract_canon_sha256":"553196d7ceae5b52dd7b52b353c13a4d0d699cf41bcec1d70d57cf5d1240b216"},"schema_version":"1.0"},"canonical_sha256":"e058668da9c18684d89820ee2dbe5491d640ffba6112bbb5d3c6ca12eb519735","source":{"kind":"arxiv","id":"2410.08395","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.08395","created_at":"2026-07-05T11:02:13Z"},{"alias_kind":"arxiv_version","alias_value":"2410.08395v3","created_at":"2026-07-05T11:02:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.08395","created_at":"2026-07-05T11:02:13Z"},{"alias_kind":"pith_short_12","alias_value":"4BMGNDNJYGDI","created_at":"2026-07-05T11:02:13Z"},{"alias_kind":"pith_short_16","alias_value":"4BMGNDNJYGDIJWEY","created_at":"2026-07-05T11:02:13Z"},{"alias_kind":"pith_short_8","alias_value":"4BMGNDNJ","created_at":"2026-07-05T11:02:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:4BMGNDNJYGDIJWEYEDXC3PSUSH","target":"record","payload":{"canonical_record":{"source":{"id":"2410.08395","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-10-10T22:02:10Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"b42d817cb3c918dd6ddbab7f2897606e5cf4611145bd2948601796772bf9e6d6","abstract_canon_sha256":"553196d7ceae5b52dd7b52b353c13a4d0d699cf41bcec1d70d57cf5d1240b216"},"schema_version":"1.0"},"canonical_sha256":"e058668da9c18684d89820ee2dbe5491d640ffba6112bbb5d3c6ca12eb519735","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:02:13.348209Z","signature_b64":"uFQmsXkRyudjhAGPmC++zQQH3dEOC6l1M6ZfU3eGyIWJTnyJ5X47hiF836GWCeSi2C42OW/3fDgI0gQJGCUfBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e058668da9c18684d89820ee2dbe5491d640ffba6112bbb5d3c6ca12eb519735","last_reissued_at":"2026-07-05T11:02:13.347772Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:02:13.347772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.08395","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":"2026-07-05T11:02:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Bpw/72gQcxpsjeJOWNc8GHoTdwH5UmTr5kV92m2oi9w7Fj5NOta5xYYODYNaQF2R0AAeGthwuNKiNzuT+f7Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T07:21:35.669423Z"},"content_sha256":"c08a56153fa159031c5efcb2248fa2f08a7d6db29cd193e09746155db2480551","schema_version":"1.0","event_id":"sha256:c08a56153fa159031c5efcb2248fa2f08a7d6db29cd193e09746155db2480551"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:4BMGNDNJYGDIJWEYEDXC3PSUSH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nesterov acceleration in benignly non-convex landscapes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"math.OC","authors_text":"Kanan Gupta, Stephan Wojtowytsch","submitted_at":"2024-10-10T22:02:10Z","abstract_excerpt":"While momentum-based optimization algorithms are commonly used in the notoriously non-convex optimization problems of deep learning, their analysis has historically been restricted to the convex and strongly convex setting. In this article, we partially close this gap between theory and practice and demonstrate that virtually identical guarantees can be obtained in optimization problems with a `benign' non-convexity. We show that these weaker geometric assumptions are well justified in overparametrized deep learning, at least locally. Variations of this result are obtained for a continuous tim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.08395","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/2410.08395/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":"2026-07-05T11:02:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zmF1SqstKpJUjlWlMll52V5u0tk9UUUOad1xNsIC37E3mYvbTC4XvMt2kT94n0Ly6X3dYr6Xcvaye5Sgr46xCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T07:21:35.669954Z"},"content_sha256":"26c8c47b54ddf8d5bd5ea7cc6e62db37ccd96980862cd7b2b5637d87080f4307","schema_version":"1.0","event_id":"sha256:26c8c47b54ddf8d5bd5ea7cc6e62db37ccd96980862cd7b2b5637d87080f4307"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4BMGNDNJYGDIJWEYEDXC3PSUSH/bundle.json","state_url":"https://pith.science/pith/4BMGNDNJYGDIJWEYEDXC3PSUSH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4BMGNDNJYGDIJWEYEDXC3PSUSH/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":"2026-08-12T07:21:35Z","links":{"resolver":"https://pith.science/pith/4BMGNDNJYGDIJWEYEDXC3PSUSH","bundle":"https://pith.science/pith/4BMGNDNJYGDIJWEYEDXC3PSUSH/bundle.json","state":"https://pith.science/pith/4BMGNDNJYGDIJWEYEDXC3PSUSH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4BMGNDNJYGDIJWEYEDXC3PSUSH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:4BMGNDNJYGDIJWEYEDXC3PSUSH","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":"553196d7ceae5b52dd7b52b353c13a4d0d699cf41bcec1d70d57cf5d1240b216","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-10-10T22:02:10Z","title_canon_sha256":"b42d817cb3c918dd6ddbab7f2897606e5cf4611145bd2948601796772bf9e6d6"},"schema_version":"1.0","source":{"id":"2410.08395","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.08395","created_at":"2026-07-05T11:02:13Z"},{"alias_kind":"arxiv_version","alias_value":"2410.08395v3","created_at":"2026-07-05T11:02:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.08395","created_at":"2026-07-05T11:02:13Z"},{"alias_kind":"pith_short_12","alias_value":"4BMGNDNJYGDI","created_at":"2026-07-05T11:02:13Z"},{"alias_kind":"pith_short_16","alias_value":"4BMGNDNJYGDIJWEY","created_at":"2026-07-05T11:02:13Z"},{"alias_kind":"pith_short_8","alias_value":"4BMGNDNJ","created_at":"2026-07-05T11:02:13Z"}],"graph_snapshots":[{"event_id":"sha256:26c8c47b54ddf8d5bd5ea7cc6e62db37ccd96980862cd7b2b5637d87080f4307","target":"graph","created_at":"2026-07-05T11:02:13Z","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/2410.08395/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"While momentum-based optimization algorithms are commonly used in the notoriously non-convex optimization problems of deep learning, their analysis has historically been restricted to the convex and strongly convex setting. In this article, we partially close this gap between theory and practice and demonstrate that virtually identical guarantees can be obtained in optimization problems with a `benign' non-convexity. We show that these weaker geometric assumptions are well justified in overparametrized deep learning, at least locally. Variations of this result are obtained for a continuous tim","authors_text":"Kanan Gupta, Stephan Wojtowytsch","cross_cats":["cs.LG","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-10-10T22:02:10Z","title":"Nesterov acceleration in benignly non-convex landscapes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.08395","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:c08a56153fa159031c5efcb2248fa2f08a7d6db29cd193e09746155db2480551","target":"record","created_at":"2026-07-05T11:02:13Z","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":"553196d7ceae5b52dd7b52b353c13a4d0d699cf41bcec1d70d57cf5d1240b216","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-10-10T22:02:10Z","title_canon_sha256":"b42d817cb3c918dd6ddbab7f2897606e5cf4611145bd2948601796772bf9e6d6"},"schema_version":"1.0","source":{"id":"2410.08395","kind":"arxiv","version":3}},"canonical_sha256":"e058668da9c18684d89820ee2dbe5491d640ffba6112bbb5d3c6ca12eb519735","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e058668da9c18684d89820ee2dbe5491d640ffba6112bbb5d3c6ca12eb519735","first_computed_at":"2026-07-05T11:02:13.347772Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:02:13.347772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uFQmsXkRyudjhAGPmC++zQQH3dEOC6l1M6ZfU3eGyIWJTnyJ5X47hiF836GWCeSi2C42OW/3fDgI0gQJGCUfBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:02:13.348209Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.08395","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c08a56153fa159031c5efcb2248fa2f08a7d6db29cd193e09746155db2480551","sha256:26c8c47b54ddf8d5bd5ea7cc6e62db37ccd96980862cd7b2b5637d87080f4307"],"state_sha256":"00901f1554b08190a75200fd15676b80ff5cfe4873a10cebb1d3d1950ede4bef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QeSGM5uqW7in7dVxVD7OauxKJLbuPkBI0vhOPeDqwE4w2JnyKK8jJ3b7QC53/2F2QZXLrS4XLxv4UhzPSGFqCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T07:21:35.674653Z","bundle_sha256":"21e8825a50077375da35e9d69a13c23d72b8e7450356ae59efb37fa49581a2c4"}}