{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LWUWXZHTBEUU5B4ZXGWZ3FE54S","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":"b3d5fd968b7521c2f455ff09fe36a3aa3db61b71d4ec36e81c94caf598ac6e84","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-12-18T18:57:44Z","title_canon_sha256":"554398fda0e10ebda10dff93609113bd33d21e6766200901aa54a55e3d4e21dd"},"schema_version":"1.0","source":{"id":"1712.06585","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.06585","created_at":"2026-05-18T00:27:47Z"},{"alias_kind":"arxiv_version","alias_value":"1712.06585v1","created_at":"2026-05-18T00:27:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.06585","created_at":"2026-05-18T00:27:47Z"},{"alias_kind":"pith_short_12","alias_value":"LWUWXZHTBEUU","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LWUWXZHTBEUU5B4Z","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LWUWXZHT","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:a7e757aa439c6ef2a9dda7d38a1a836577b014d5fcf7533c1f2f5d8e21734993","target":"graph","created_at":"2026-05-18T00:27:47Z","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"},"paper":{"abstract_excerpt":"We propose stochastic optimization algorithms that can find local minima faster than existing algorithms for nonconvex optimization problems, by exploiting the third-order smoothness to escape non-degenerate saddle points more efficiently. More specifically, the proposed algorithm only needs $\\tilde{O}(\\epsilon^{-10/3})$ stochastic gradient evaluations to converge to an approximate local minimum $\\mathbf{x}$, which satisfies $\\|\\nabla f(\\mathbf{x})\\|_2\\leq\\epsilon$ and $\\lambda_{\\min}(\\nabla^2 f(\\mathbf{x}))\\geq -\\sqrt{\\epsilon}$ in the general stochastic optimization setting, where $\\tilde{O}","authors_text":"Pan Xu, Quanquan Gu, Yaodong Yu","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-12-18T18:57:44Z","title":"Third-order Smoothness Helps: Even Faster Stochastic Optimization Algorithms for Finding Local Minima"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06585","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":"sha256:72d78cd47ecb399e711bc4efc737dc4429b6ffa787c495ec69b382d1ad7c8586","target":"record","created_at":"2026-05-18T00:27:47Z","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":"b3d5fd968b7521c2f455ff09fe36a3aa3db61b71d4ec36e81c94caf598ac6e84","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-12-18T18:57:44Z","title_canon_sha256":"554398fda0e10ebda10dff93609113bd33d21e6766200901aa54a55e3d4e21dd"},"schema_version":"1.0","source":{"id":"1712.06585","kind":"arxiv","version":1}},"canonical_sha256":"5da96be4f309294e8799b9ad9d949de488604441a4ebad5e6ada266b9c98b9a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5da96be4f309294e8799b9ad9d949de488604441a4ebad5e6ada266b9c98b9a7","first_computed_at":"2026-05-18T00:27:47.533060Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:47.533060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"96lrHRInkwYZ9jhWMwb9Luii7vOakmctL1oMNU9meSdX2hd0sXDDRaKgisW8xAFskRYPspKYA9UtsoEQubKZAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:47.533501Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.06585","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72d78cd47ecb399e711bc4efc737dc4429b6ffa787c495ec69b382d1ad7c8586","sha256:a7e757aa439c6ef2a9dda7d38a1a836577b014d5fcf7533c1f2f5d8e21734993"],"state_sha256":"81ab6fc045696090e5a045ed8d5cf5b8d17e883a63bdcc20cc67930943809b24"}