{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:4R2PHNVAFGPIEOOATZP4XDSJIM","short_pith_number":"pith:4R2PHNVA","schema_version":"1.0","canonical_sha256":"e474f3b6a0299e8239c09e5fcb8e49433388f887364ec697c19663c49e50f56b","source":{"kind":"arxiv","id":"1812.03934","version":3},"attestation_state":"computed","paper":{"title":"Stagewise Training Accelerates Convergence of Testing Error Over SGD","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.OC"],"primary_cat":"stat.ML","authors_text":"Rong Jin, Tianbao Yang, Yan Yan, Zhuoning Yuan","submitted_at":"2018-12-10T17:34:00Z","abstract_excerpt":"Stagewise training strategy is widely used for learning neural networks, which runs a stochastic algorithm (e.g., SGD) starting with a relatively large step size (aka learning rate) and geometrically decreasing the step size after a number of iterations. It has been observed that the stagewise SGD has much faster convergence than the vanilla SGD with a polynomially decaying step size in terms of both training error and testing error. {\\it But how to explain this phenomenon has been largely ignored by existing studies.} This paper provides some theoretical evidence for explaining this faster co"},"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":"1812.03934","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-12-10T17:34:00Z","cross_cats_sorted":["cs.LG","math.OC"],"title_canon_sha256":"684ea7b9b9e56b56f7286d7be92fba83ef5020e6e0b6131cea5a334c5125fd4b","abstract_canon_sha256":"39086f920288cac30e989afe95c5d98b90ae91fd14556dbc7e4aab1fa35a3ee9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:53.292649Z","signature_b64":"MqfK5sL/HGLGPgOap+L0hHGGJSEELVrLXLBVodfiFbbgsU7ktRtlNEtGhQ6JaFFogNm5qPOx58yyvoz1ihvYBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e474f3b6a0299e8239c09e5fcb8e49433388f887364ec697c19663c49e50f56b","last_reissued_at":"2026-05-17T23:54:53.292171Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:53.292171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stagewise Training Accelerates Convergence of Testing Error Over SGD","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.OC"],"primary_cat":"stat.ML","authors_text":"Rong Jin, Tianbao Yang, Yan Yan, Zhuoning Yuan","submitted_at":"2018-12-10T17:34:00Z","abstract_excerpt":"Stagewise training strategy is widely used for learning neural networks, which runs a stochastic algorithm (e.g., SGD) starting with a relatively large step size (aka learning rate) and geometrically decreasing the step size after a number of iterations. It has been observed that the stagewise SGD has much faster convergence than the vanilla SGD with a polynomially decaying step size in terms of both training error and testing error. {\\it But how to explain this phenomenon has been largely ignored by existing studies.} This paper provides some theoretical evidence for explaining this faster co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03934","kind":"arxiv","version":3},"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":"1812.03934","created_at":"2026-05-17T23:54:53.292239+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.03934v3","created_at":"2026-05-17T23:54:53.292239+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.03934","created_at":"2026-05-17T23:54:53.292239+00:00"},{"alias_kind":"pith_short_12","alias_value":"4R2PHNVAFGPI","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_16","alias_value":"4R2PHNVAFGPIEOOA","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_8","alias_value":"4R2PHNVA","created_at":"2026-05-18T12:32:05.422762+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1907.09547","citing_title":"Stochastic algorithms with geometric step decay converge linearly on sharp functions","ref_index":68,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4R2PHNVAFGPIEOOATZP4XDSJIM","json":"https://pith.science/pith/4R2PHNVAFGPIEOOATZP4XDSJIM.json","graph_json":"https://pith.science/api/pith-number/4R2PHNVAFGPIEOOATZP4XDSJIM/graph.json","events_json":"https://pith.science/api/pith-number/4R2PHNVAFGPIEOOATZP4XDSJIM/events.json","paper":"https://pith.science/paper/4R2PHNVA"},"agent_actions":{"view_html":"https://pith.science/pith/4R2PHNVAFGPIEOOATZP4XDSJIM","download_json":"https://pith.science/pith/4R2PHNVAFGPIEOOATZP4XDSJIM.json","view_paper":"https://pith.science/paper/4R2PHNVA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.03934&json=true","fetch_graph":"https://pith.science/api/pith-number/4R2PHNVAFGPIEOOATZP4XDSJIM/graph.json","fetch_events":"https://pith.science/api/pith-number/4R2PHNVAFGPIEOOATZP4XDSJIM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4R2PHNVAFGPIEOOATZP4XDSJIM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4R2PHNVAFGPIEOOATZP4XDSJIM/action/storage_attestation","attest_author":"https://pith.science/pith/4R2PHNVAFGPIEOOATZP4XDSJIM/action/author_attestation","sign_citation":"https://pith.science/pith/4R2PHNVAFGPIEOOATZP4XDSJIM/action/citation_signature","submit_replication":"https://pith.science/pith/4R2PHNVAFGPIEOOATZP4XDSJIM/action/replication_record"}},"created_at":"2026-05-17T23:54:53.292239+00:00","updated_at":"2026-05-17T23:54:53.292239+00:00"}