{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:6DNBSWNTVRIPMG5MSA26MD5LXA","short_pith_number":"pith:6DNBSWNT","canonical_record":{"source":{"id":"2008.04195","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-08-10T15:29:13Z","cross_cats_sorted":["cs.LG","cs.MA","cs.SY","eess.SY","stat.ML"],"title_canon_sha256":"15eb53f36b87133de067e8992a905f4f6601e46138dd5eed06915c83b832e5db","abstract_canon_sha256":"d012b8e77982a00aff017dab51a03e77b4744371b5c38cbe271db97b0d4be955"},"schema_version":"1.0"},"canonical_sha256":"f0da1959b3ac50f61bac9035e60fabb807ac9e2d291b6e344752bb87f23d25d2","source":{"kind":"arxiv","id":"2008.04195","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.04195","created_at":"2026-07-05T02:33:19Z"},{"alias_kind":"arxiv_version","alias_value":"2008.04195v2","created_at":"2026-07-05T02:33:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.04195","created_at":"2026-07-05T02:33:19Z"},{"alias_kind":"pith_short_12","alias_value":"6DNBSWNTVRIP","created_at":"2026-07-05T02:33:19Z"},{"alias_kind":"pith_short_16","alias_value":"6DNBSWNTVRIPMG5M","created_at":"2026-07-05T02:33:19Z"},{"alias_kind":"pith_short_8","alias_value":"6DNBSWNT","created_at":"2026-07-05T02:33:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:6DNBSWNTVRIPMG5MSA26MD5LXA","target":"record","payload":{"canonical_record":{"source":{"id":"2008.04195","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-08-10T15:29:13Z","cross_cats_sorted":["cs.LG","cs.MA","cs.SY","eess.SY","stat.ML"],"title_canon_sha256":"15eb53f36b87133de067e8992a905f4f6601e46138dd5eed06915c83b832e5db","abstract_canon_sha256":"d012b8e77982a00aff017dab51a03e77b4744371b5c38cbe271db97b0d4be955"},"schema_version":"1.0"},"canonical_sha256":"f0da1959b3ac50f61bac9035e60fabb807ac9e2d291b6e344752bb87f23d25d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:33:19.604238Z","signature_b64":"be2f/8O47DOKPCi5xzV//xceeXzEOtpT6RQtl4WXhHrTBuxBNCOArrW9JRluSOiWeOgIdfkg/etKkLlel4L9Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0da1959b3ac50f61bac9035e60fabb807ac9e2d291b6e344752bb87f23d25d2","last_reissued_at":"2026-07-05T02:33:19.603816Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:33:19.603816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2008.04195","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":"2026-07-05T02:33:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mZ7/4NLXJJ5ogcK/wYJSASBy3yFJrfIIUd648Ig6OCa/6glwcBxAInfTlUXa87yf5qWXOgh3mgbxrrWDYTiyCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T07:31:34.047997Z"},"content_sha256":"222e727859a6e503959f458f222f764a55f6eedee4a3ca7fdcbf866758f49d69","schema_version":"1.0","event_id":"sha256:222e727859a6e503959f458f222f764a55f6eedee4a3ca7fdcbf866758f49d69"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:6DNBSWNTVRIPMG5MSA26MD5LXA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An improved convergence analysis for decentralized online stochastic non-convex optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.MA","cs.SY","eess.SY","stat.ML"],"primary_cat":"math.OC","authors_text":"Ran Xin, Soummya Kar, Usman A. Khan","submitted_at":"2020-08-10T15:29:13Z","abstract_excerpt":"In this paper, we study decentralized online stochastic non-convex optimization over a network of nodes. Integrating a technique called gradient tracking in decentralized stochastic gradient descent, we show that the resulting algorithm, GT-DSGD, enjoys certain desirable characteristics towards minimizing a sum of smooth non-convex functions. In particular, for general smooth non-convex functions, we establish non-asymptotic characterizations of GT-DSGD and derive the conditions under which it achieves network-independent performances that match the centralized minibatch SGD. In contrast, the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.04195","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/2008.04195/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":"2026-07-05T02:33:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fs67V+t+rzqsQIFz4K+J6wZ1a0Fm6wKrD5oMQqfGdIcHLWGObC/ea0AOacezhMTUvv+jVDW/44oD1B+x+WGxCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T07:31:34.048508Z"},"content_sha256":"612a664edd3ac90299e8ea2eebeb23b5c627f9cda66e1f4c27571b3444984955","schema_version":"1.0","event_id":"sha256:612a664edd3ac90299e8ea2eebeb23b5c627f9cda66e1f4c27571b3444984955"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6DNBSWNTVRIPMG5MSA26MD5LXA/bundle.json","state_url":"https://pith.science/pith/6DNBSWNTVRIPMG5MSA26MD5LXA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6DNBSWNTVRIPMG5MSA26MD5LXA/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":"2026-08-18T07:31:34Z","links":{"resolver":"https://pith.science/pith/6DNBSWNTVRIPMG5MSA26MD5LXA","bundle":"https://pith.science/pith/6DNBSWNTVRIPMG5MSA26MD5LXA/bundle.json","state":"https://pith.science/pith/6DNBSWNTVRIPMG5MSA26MD5LXA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6DNBSWNTVRIPMG5MSA26MD5LXA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:6DNBSWNTVRIPMG5MSA26MD5LXA","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":"d012b8e77982a00aff017dab51a03e77b4744371b5c38cbe271db97b0d4be955","cross_cats_sorted":["cs.LG","cs.MA","cs.SY","eess.SY","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-08-10T15:29:13Z","title_canon_sha256":"15eb53f36b87133de067e8992a905f4f6601e46138dd5eed06915c83b832e5db"},"schema_version":"1.0","source":{"id":"2008.04195","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.04195","created_at":"2026-07-05T02:33:19Z"},{"alias_kind":"arxiv_version","alias_value":"2008.04195v2","created_at":"2026-07-05T02:33:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.04195","created_at":"2026-07-05T02:33:19Z"},{"alias_kind":"pith_short_12","alias_value":"6DNBSWNTVRIP","created_at":"2026-07-05T02:33:19Z"},{"alias_kind":"pith_short_16","alias_value":"6DNBSWNTVRIPMG5M","created_at":"2026-07-05T02:33:19Z"},{"alias_kind":"pith_short_8","alias_value":"6DNBSWNT","created_at":"2026-07-05T02:33:19Z"}],"graph_snapshots":[{"event_id":"sha256:612a664edd3ac90299e8ea2eebeb23b5c627f9cda66e1f4c27571b3444984955","target":"graph","created_at":"2026-07-05T02:33:19Z","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/2008.04195/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study decentralized online stochastic non-convex optimization over a network of nodes. Integrating a technique called gradient tracking in decentralized stochastic gradient descent, we show that the resulting algorithm, GT-DSGD, enjoys certain desirable characteristics towards minimizing a sum of smooth non-convex functions. In particular, for general smooth non-convex functions, we establish non-asymptotic characterizations of GT-DSGD and derive the conditions under which it achieves network-independent performances that match the centralized minibatch SGD. In contrast, the ","authors_text":"Ran Xin, Soummya Kar, Usman A. Khan","cross_cats":["cs.LG","cs.MA","cs.SY","eess.SY","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-08-10T15:29:13Z","title":"An improved convergence analysis for decentralized online stochastic non-convex optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.04195","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":"sha256:222e727859a6e503959f458f222f764a55f6eedee4a3ca7fdcbf866758f49d69","target":"record","created_at":"2026-07-05T02:33:19Z","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":"d012b8e77982a00aff017dab51a03e77b4744371b5c38cbe271db97b0d4be955","cross_cats_sorted":["cs.LG","cs.MA","cs.SY","eess.SY","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-08-10T15:29:13Z","title_canon_sha256":"15eb53f36b87133de067e8992a905f4f6601e46138dd5eed06915c83b832e5db"},"schema_version":"1.0","source":{"id":"2008.04195","kind":"arxiv","version":2}},"canonical_sha256":"f0da1959b3ac50f61bac9035e60fabb807ac9e2d291b6e344752bb87f23d25d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0da1959b3ac50f61bac9035e60fabb807ac9e2d291b6e344752bb87f23d25d2","first_computed_at":"2026-07-05T02:33:19.603816Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:33:19.603816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"be2f/8O47DOKPCi5xzV//xceeXzEOtpT6RQtl4WXhHrTBuxBNCOArrW9JRluSOiWeOgIdfkg/etKkLlel4L9Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:33:19.604238Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.04195","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:222e727859a6e503959f458f222f764a55f6eedee4a3ca7fdcbf866758f49d69","sha256:612a664edd3ac90299e8ea2eebeb23b5c627f9cda66e1f4c27571b3444984955"],"state_sha256":"a5a9db7097e4a807e063652d299aa80e46efcb58a45e06d4c5f9531a3d56a3a8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JygdXlOkJhtUTTrZTfq7TO8wkxtoF3B6jW5BgAOzgZXEsdSduurXu1F4XUDi6SWBXZHIN+DjXsskx7reDs+iAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T07:31:34.052210Z","bundle_sha256":"a163c843cfdc59d8a3581c1a871f39e5051c747f8bc727fa381f3891e420a9c8"}}