{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GPFGM6ZUQIQ3YRNEOOIYGXO5BH","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":"6f7dd97217e9ad474cde3ae434f90a919750fdccb2ad2a1f468cdd6718e5c06e","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-12-11T17:26:43Z","title_canon_sha256":"3e94216cc64e977fc0aaaecdd71688a7c72ef9b14b8b83ea27ba1d6773cb67f0"},"schema_version":"1.0","source":{"id":"1612.03441","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.03441","created_at":"2026-05-18T00:54:52Z"},{"alias_kind":"arxiv_version","alias_value":"1612.03441v1","created_at":"2026-05-18T00:54:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.03441","created_at":"2026-05-18T00:54:52Z"},{"alias_kind":"pith_short_12","alias_value":"GPFGM6ZUQIQ3","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GPFGM6ZUQIQ3YRNE","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GPFGM6ZU","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:781dc6e124da49c558b40af791a6e49ae3b9eaa33825f1223c5809e7a36e9ed2","target":"graph","created_at":"2026-05-18T00:54:52Z","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":"Stochastic gradient descent~(SGD) and its variants have attracted much attention in machine learning due to their efficiency and effectiveness for optimization. To handle large-scale problems, researchers have recently proposed several lock-free strategy based parallel SGD~(LF-PSGD) methods for multi-core systems. However, existing works have only proved the convergence of these LF-PSGD methods for convex problems. To the best of our knowledge, no work has proved the convergence of the LF-PSGD methods for non-convex problems. In this paper, we provide the theoretical proof about the convergenc","authors_text":"Gong-Duo Zhang, Shen-Yi Zhao, Wu-Jun Li","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-12-11T17:26:43Z","title":"Lock-Free Optimization for Non-Convex Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03441","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:f0942aae44112ada77519a0ea117201e4e5960f5355b9efa67d29741cd4ef20e","target":"record","created_at":"2026-05-18T00:54:52Z","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":"6f7dd97217e9ad474cde3ae434f90a919750fdccb2ad2a1f468cdd6718e5c06e","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-12-11T17:26:43Z","title_canon_sha256":"3e94216cc64e977fc0aaaecdd71688a7c72ef9b14b8b83ea27ba1d6773cb67f0"},"schema_version":"1.0","source":{"id":"1612.03441","kind":"arxiv","version":1}},"canonical_sha256":"33ca667b348221bc45a47391835ddd09c8cc39397cb6d5e432e55b30894972bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33ca667b348221bc45a47391835ddd09c8cc39397cb6d5e432e55b30894972bf","first_computed_at":"2026-05-18T00:54:52.383725Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:52.383725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JLYqKKqmWSOrTwaDS+SUxodWhf2X5uZrGzeNbBuEV8m1J7B0NzJ6qwEC2Lg4Rwh9hAqGa4EhRjCRLxZ+kceYDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:52.384180Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.03441","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0942aae44112ada77519a0ea117201e4e5960f5355b9efa67d29741cd4ef20e","sha256:781dc6e124da49c558b40af791a6e49ae3b9eaa33825f1223c5809e7a36e9ed2"],"state_sha256":"b50f998a4ceebc6eab1da702a70644dd72b19279c32d7bc5f0f753024e470541"}