{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:UQIJ2CZL5CLIBXJ3B5RLRMUB4O","short_pith_number":"pith:UQIJ2CZL","canonical_record":{"source":{"id":"1907.01849","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MA","submitted_at":"2019-07-03T11:06:43Z","cross_cats_sorted":["cs.LG","eess.SP","math.OC"],"title_canon_sha256":"cb3e03c0dbc7cff257929f4e9f218e625618e35e8736c5caaf771c2eb90bd542","abstract_canon_sha256":"736425e96beff47fbd69e689e677b6572264a4cad3cf1d2b1849d4287ea94e7f"},"schema_version":"1.0"},"canonical_sha256":"a4109d0b2be89680dd3b0f62b8b281e3b43ab72bf679dc20df0feb3c7ccf29d8","source":{"kind":"arxiv","id":"1907.01849","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.01849","created_at":"2026-05-17T23:41:34Z"},{"alias_kind":"arxiv_version","alias_value":"1907.01849v1","created_at":"2026-05-17T23:41:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.01849","created_at":"2026-05-17T23:41:34Z"},{"alias_kind":"pith_short_12","alias_value":"UQIJ2CZL5CLI","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"UQIJ2CZL5CLIBXJ3","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"UQIJ2CZL","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:UQIJ2CZL5CLIBXJ3B5RLRMUB4O","target":"record","payload":{"canonical_record":{"source":{"id":"1907.01849","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MA","submitted_at":"2019-07-03T11:06:43Z","cross_cats_sorted":["cs.LG","eess.SP","math.OC"],"title_canon_sha256":"cb3e03c0dbc7cff257929f4e9f218e625618e35e8736c5caaf771c2eb90bd542","abstract_canon_sha256":"736425e96beff47fbd69e689e677b6572264a4cad3cf1d2b1849d4287ea94e7f"},"schema_version":"1.0"},"canonical_sha256":"a4109d0b2be89680dd3b0f62b8b281e3b43ab72bf679dc20df0feb3c7ccf29d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:34.813073Z","signature_b64":"hqYxr6v/B9+Bu0yMy9WyHkfjpb0mQMymzPdrxOlKQdyeeyTxdeCQk3GR15UP+a05SV6T7OKJcAXrS3rDUo3aCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4109d0b2be89680dd3b0f62b8b281e3b43ab72bf679dc20df0feb3c7ccf29d8","last_reissued_at":"2026-05-17T23:41:34.812435Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:34.812435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.01849","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:41:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y0nhJICoMUKeKFxEbnNGbWhQ6C5zj79jTx73YhJuznaM8FXVSHylbs59V1jjwvcJ4GfUcS9mLysnKUpa8AehDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T09:26:20.001105Z"},"content_sha256":"e4a4ee1601d6bc31284d5a270a05208174d59e7acb14d531c738c08285996fe7","schema_version":"1.0","event_id":"sha256:e4a4ee1601d6bc31284d5a270a05208174d59e7acb14d531c738c08285996fe7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:UQIJ2CZL5CLIBXJ3B5RLRMUB4O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","eess.SP","math.OC"],"primary_cat":"cs.MA","authors_text":"Ali H. Sayed, Stefan Vlaski","submitted_at":"2019-07-03T11:06:43Z","abstract_excerpt":"The diffusion strategy for distributed learning from streaming data employs local stochastic gradient updates along with exchange of iterates over neighborhoods. In Part I [2] of this work we established that agents cluster around a network centroid and proceeded to study the dynamics of this point. We established expected descent in non-convex environments in the large-gradient regime and introduced a short-term model to examine the dynamics over finite-time horizons. Using this model, we establish in this work that the diffusion strategy is able to escape from strict saddle-points in O(1/$\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.01849","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-17T23:41:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QL69VSEcckh8V49i63T32XoWWH9gJLR3GgNnV2no+mBJvHSQc+mPKS13XV2FMyCzZ/3fqHZokqKO+Q3HUcsVCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T09:26:20.001788Z"},"content_sha256":"e1a485692af0890547d84af857812e0cff85e5cb519cfabe676aeb731f2ae132","schema_version":"1.0","event_id":"sha256:e1a485692af0890547d84af857812e0cff85e5cb519cfabe676aeb731f2ae132"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UQIJ2CZL5CLIBXJ3B5RLRMUB4O/bundle.json","state_url":"https://pith.science/pith/UQIJ2CZL5CLIBXJ3B5RLRMUB4O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UQIJ2CZL5CLIBXJ3B5RLRMUB4O/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":"2026-05-25T09:26:20Z","links":{"resolver":"https://pith.science/pith/UQIJ2CZL5CLIBXJ3B5RLRMUB4O","bundle":"https://pith.science/pith/UQIJ2CZL5CLIBXJ3B5RLRMUB4O/bundle.json","state":"https://pith.science/pith/UQIJ2CZL5CLIBXJ3B5RLRMUB4O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UQIJ2CZL5CLIBXJ3B5RLRMUB4O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:UQIJ2CZL5CLIBXJ3B5RLRMUB4O","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":"736425e96beff47fbd69e689e677b6572264a4cad3cf1d2b1849d4287ea94e7f","cross_cats_sorted":["cs.LG","eess.SP","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MA","submitted_at":"2019-07-03T11:06:43Z","title_canon_sha256":"cb3e03c0dbc7cff257929f4e9f218e625618e35e8736c5caaf771c2eb90bd542"},"schema_version":"1.0","source":{"id":"1907.01849","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.01849","created_at":"2026-05-17T23:41:34Z"},{"alias_kind":"arxiv_version","alias_value":"1907.01849v1","created_at":"2026-05-17T23:41:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.01849","created_at":"2026-05-17T23:41:34Z"},{"alias_kind":"pith_short_12","alias_value":"UQIJ2CZL5CLI","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"UQIJ2CZL5CLIBXJ3","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"UQIJ2CZL","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:e1a485692af0890547d84af857812e0cff85e5cb519cfabe676aeb731f2ae132","target":"graph","created_at":"2026-05-17T23:41:34Z","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":"The diffusion strategy for distributed learning from streaming data employs local stochastic gradient updates along with exchange of iterates over neighborhoods. In Part I [2] of this work we established that agents cluster around a network centroid and proceeded to study the dynamics of this point. We established expected descent in non-convex environments in the large-gradient regime and introduced a short-term model to examine the dynamics over finite-time horizons. Using this model, we establish in this work that the diffusion strategy is able to escape from strict saddle-points in O(1/$\\m","authors_text":"Ali H. Sayed, Stefan Vlaski","cross_cats":["cs.LG","eess.SP","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MA","submitted_at":"2019-07-03T11:06:43Z","title":"Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.01849","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:e4a4ee1601d6bc31284d5a270a05208174d59e7acb14d531c738c08285996fe7","target":"record","created_at":"2026-05-17T23:41:34Z","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":"736425e96beff47fbd69e689e677b6572264a4cad3cf1d2b1849d4287ea94e7f","cross_cats_sorted":["cs.LG","eess.SP","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MA","submitted_at":"2019-07-03T11:06:43Z","title_canon_sha256":"cb3e03c0dbc7cff257929f4e9f218e625618e35e8736c5caaf771c2eb90bd542"},"schema_version":"1.0","source":{"id":"1907.01849","kind":"arxiv","version":1}},"canonical_sha256":"a4109d0b2be89680dd3b0f62b8b281e3b43ab72bf679dc20df0feb3c7ccf29d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4109d0b2be89680dd3b0f62b8b281e3b43ab72bf679dc20df0feb3c7ccf29d8","first_computed_at":"2026-05-17T23:41:34.812435Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:34.812435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hqYxr6v/B9+Bu0yMy9WyHkfjpb0mQMymzPdrxOlKQdyeeyTxdeCQk3GR15UP+a05SV6T7OKJcAXrS3rDUo3aCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:34.813073Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.01849","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4a4ee1601d6bc31284d5a270a05208174d59e7acb14d531c738c08285996fe7","sha256:e1a485692af0890547d84af857812e0cff85e5cb519cfabe676aeb731f2ae132"],"state_sha256":"fdfd8cab0180518e5769d33b7f3356711f93738d85aafac74d748d3791456cb7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lHwVg4vfXxmrfwgltPsKomXPhN/OVXJJOlgTV79k9tsg8oJnryRT0PrBzgUyUIUHiwAWOaRPaGxNmnfKI+HqBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T09:26:20.005408Z","bundle_sha256":"252488a9e8ee52caf63b858bf613d4c0f7f4b73456a8d772ac2f723185424eb3"}}