{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:GCPROQ5TZHAPVYRJY3NTA3HHTF","short_pith_number":"pith:GCPROQ5T","schema_version":"1.0","canonical_sha256":"309f1743b3c9c0fae229c6db306ce79943fb2af9c332782c40df3a586eb58f1c","source":{"kind":"arxiv","id":"1810.12065","version":4},"attestation_state":"computed","paper":{"title":"On the Convergence Rate of Training Recurrent Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.NE","math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Yuanzhi Li, Zeyuan Allen-Zhu, Zhao Song","submitted_at":"2018-10-29T11:45:02Z","abstract_excerpt":"How can local-search methods such as stochastic gradient descent (SGD) avoid bad local minima in training multi-layer neural networks? Why can they fit random labels even given non-convex and non-smooth architectures? Most existing theory only covers networks with one hidden layer, so can we go deeper?\n  In this paper, we focus on recurrent neural networks (RNNs) which are multi-layer networks widely used in natural language processing. They are harder to analyze than feedforward neural networks, because the $\\textit{same}$ recurrent unit is repeatedly applied across the entire time horizon of"},"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":"1810.12065","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-10-29T11:45:02Z","cross_cats_sorted":["cs.DS","cs.NE","math.OC","stat.ML"],"title_canon_sha256":"8acdab021c5d00eba6619711a5ce7a4cecfdcf7877cef0671edd2ada0210c7c6","abstract_canon_sha256":"c955e7c86c68e05bacd8ac9851858d4ebf62ce7d237c2a26d838aad977dfcfa4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:04.331822Z","signature_b64":"AZqDT+i/sk56+qQObBpXaVLvkK7/GT+5FroH+PRAWkr52uvnhX0w2rcQ1o/GyhophtlYxKhmAId/Btcb6lHJCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"309f1743b3c9c0fae229c6db306ce79943fb2af9c332782c40df3a586eb58f1c","last_reissued_at":"2026-05-17T23:45:04.331165Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:04.331165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Convergence Rate of Training Recurrent Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.NE","math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Yuanzhi Li, Zeyuan Allen-Zhu, Zhao Song","submitted_at":"2018-10-29T11:45:02Z","abstract_excerpt":"How can local-search methods such as stochastic gradient descent (SGD) avoid bad local minima in training multi-layer neural networks? Why can they fit random labels even given non-convex and non-smooth architectures? Most existing theory only covers networks with one hidden layer, so can we go deeper?\n  In this paper, we focus on recurrent neural networks (RNNs) which are multi-layer networks widely used in natural language processing. They are harder to analyze than feedforward neural networks, because the $\\textit{same}$ recurrent unit is repeatedly applied across the entire time horizon of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12065","kind":"arxiv","version":4},"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":"1810.12065","created_at":"2026-05-17T23:45:04.331268+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.12065v4","created_at":"2026-05-17T23:45:04.331268+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.12065","created_at":"2026-05-17T23:45:04.331268+00:00"},{"alias_kind":"pith_short_12","alias_value":"GCPROQ5TZHAP","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_16","alias_value":"GCPROQ5TZHAPVYRJ","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_8","alias_value":"GCPROQ5T","created_at":"2026-05-18T12:32:25.280505+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1907.10732","citing_title":"Hessian based analysis of SGD for Deep Nets: Dynamics and Generalization","ref_index":1,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GCPROQ5TZHAPVYRJY3NTA3HHTF","json":"https://pith.science/pith/GCPROQ5TZHAPVYRJY3NTA3HHTF.json","graph_json":"https://pith.science/api/pith-number/GCPROQ5TZHAPVYRJY3NTA3HHTF/graph.json","events_json":"https://pith.science/api/pith-number/GCPROQ5TZHAPVYRJY3NTA3HHTF/events.json","paper":"https://pith.science/paper/GCPROQ5T"},"agent_actions":{"view_html":"https://pith.science/pith/GCPROQ5TZHAPVYRJY3NTA3HHTF","download_json":"https://pith.science/pith/GCPROQ5TZHAPVYRJY3NTA3HHTF.json","view_paper":"https://pith.science/paper/GCPROQ5T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.12065&json=true","fetch_graph":"https://pith.science/api/pith-number/GCPROQ5TZHAPVYRJY3NTA3HHTF/graph.json","fetch_events":"https://pith.science/api/pith-number/GCPROQ5TZHAPVYRJY3NTA3HHTF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GCPROQ5TZHAPVYRJY3NTA3HHTF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GCPROQ5TZHAPVYRJY3NTA3HHTF/action/storage_attestation","attest_author":"https://pith.science/pith/GCPROQ5TZHAPVYRJY3NTA3HHTF/action/author_attestation","sign_citation":"https://pith.science/pith/GCPROQ5TZHAPVYRJY3NTA3HHTF/action/citation_signature","submit_replication":"https://pith.science/pith/GCPROQ5TZHAPVYRJY3NTA3HHTF/action/replication_record"}},"created_at":"2026-05-17T23:45:04.331268+00:00","updated_at":"2026-05-17T23:45:04.331268+00:00"}