{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:GHXNPK2JGRG25EM65KLFFBHLNV","short_pith_number":"pith:GHXNPK2J","schema_version":"1.0","canonical_sha256":"31eed7ab49344dae919eea965284eb6d775747c1e3c467dc189301c52d093418","source":{"kind":"arxiv","id":"1907.01848","version":1},"attestation_state":"computed","paper":{"title":"Distributed Learning in Non-Convex Environments -- Part I: Agreement at a Linear Rate","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.MA","eess.SP"],"primary_cat":"math.OC","authors_text":"Ali H. Sayed, Stefan Vlaski","submitted_at":"2019-07-03T11:06:11Z","abstract_excerpt":"Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, there has been increasing interest in understanding the behavior of gradient-descent algorithms in non-convex environments. Most available works on distributed non-convex optimization problems focus on the deterministic setting where exact gradients are available at each agent. In this work and its Part II, we consider stochastic cost functions, where exact gradients are replaced by stochastic approximations and the resulting gradient noise persistently seeps into the dynamics of t"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1907.01848","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-07-03T11:06:11Z","cross_cats_sorted":["cs.MA","eess.SP"],"title_canon_sha256":"753d1b6b1eceebdbb5cd6fd58c53636c3caf9c35720bc0b0a53d821bd4d71b30","abstract_canon_sha256":"ca63384cfea139a96e17c7354b0c6007c529baeb7e15ef2c15ef4b114e58b459"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:34.821588Z","signature_b64":"lY0SlCR8rM1G0aRgAoDcY0CK3efK9oFTym53sJpOB8J1RWOc6J7Tc1u9FMPUIuNOtkGGTUSBqt9bAaf59vlFBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31eed7ab49344dae919eea965284eb6d775747c1e3c467dc189301c52d093418","last_reissued_at":"2026-05-17T23:41:34.820776Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:34.820776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Distributed Learning in Non-Convex Environments -- Part I: Agreement at a Linear Rate","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.MA","eess.SP"],"primary_cat":"math.OC","authors_text":"Ali H. Sayed, Stefan Vlaski","submitted_at":"2019-07-03T11:06:11Z","abstract_excerpt":"Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, there has been increasing interest in understanding the behavior of gradient-descent algorithms in non-convex environments. Most available works on distributed non-convex optimization problems focus on the deterministic setting where exact gradients are available at each agent. In this work and its Part II, we consider stochastic cost functions, where exact gradients are replaced by stochastic approximations and the resulting gradient noise persistently seeps into the dynamics of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.01848","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1907.01848","created_at":"2026-05-17T23:41:34.820906+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.01848v1","created_at":"2026-05-17T23:41:34.820906+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.01848","created_at":"2026-05-17T23:41:34.820906+00:00"},{"alias_kind":"pith_short_12","alias_value":"GHXNPK2JGRG2","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"GHXNPK2JGRG25EM6","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"GHXNPK2J","created_at":"2026-05-18T12:33:18.533446+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GHXNPK2JGRG25EM65KLFFBHLNV","json":"https://pith.science/pith/GHXNPK2JGRG25EM65KLFFBHLNV.json","graph_json":"https://pith.science/api/pith-number/GHXNPK2JGRG25EM65KLFFBHLNV/graph.json","events_json":"https://pith.science/api/pith-number/GHXNPK2JGRG25EM65KLFFBHLNV/events.json","paper":"https://pith.science/paper/GHXNPK2J"},"agent_actions":{"view_html":"https://pith.science/pith/GHXNPK2JGRG25EM65KLFFBHLNV","download_json":"https://pith.science/pith/GHXNPK2JGRG25EM65KLFFBHLNV.json","view_paper":"https://pith.science/paper/GHXNPK2J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.01848&json=true","fetch_graph":"https://pith.science/api/pith-number/GHXNPK2JGRG25EM65KLFFBHLNV/graph.json","fetch_events":"https://pith.science/api/pith-number/GHXNPK2JGRG25EM65KLFFBHLNV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GHXNPK2JGRG25EM65KLFFBHLNV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GHXNPK2JGRG25EM65KLFFBHLNV/action/storage_attestation","attest_author":"https://pith.science/pith/GHXNPK2JGRG25EM65KLFFBHLNV/action/author_attestation","sign_citation":"https://pith.science/pith/GHXNPK2JGRG25EM65KLFFBHLNV/action/citation_signature","submit_replication":"https://pith.science/pith/GHXNPK2JGRG25EM65KLFFBHLNV/action/replication_record"}},"created_at":"2026-05-17T23:41:34.820906+00:00","updated_at":"2026-05-17T23:41:34.820906+00:00"}