{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GCPROQ5TZHAPVYRJY3NTA3HHTF","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":"c955e7c86c68e05bacd8ac9851858d4ebf62ce7d237c2a26d838aad977dfcfa4","cross_cats_sorted":["cs.DS","cs.NE","math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-10-29T11:45:02Z","title_canon_sha256":"8acdab021c5d00eba6619711a5ce7a4cecfdcf7877cef0671edd2ada0210c7c6"},"schema_version":"1.0","source":{"id":"1810.12065","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.12065","created_at":"2026-05-17T23:45:04Z"},{"alias_kind":"arxiv_version","alias_value":"1810.12065v4","created_at":"2026-05-17T23:45:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.12065","created_at":"2026-05-17T23:45:04Z"},{"alias_kind":"pith_short_12","alias_value":"GCPROQ5TZHAP","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GCPROQ5TZHAPVYRJ","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GCPROQ5T","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:7f0d3c3a20f91184540ecb1b31843a0fb392f70b4a04b7d355a43152c69bdea8","target":"graph","created_at":"2026-05-17T23:45:04Z","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":"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","authors_text":"Yuanzhi Li, Zeyuan Allen-Zhu, Zhao Song","cross_cats":["cs.DS","cs.NE","math.OC","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-10-29T11:45:02Z","title":"On the Convergence Rate of Training Recurrent Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12065","kind":"arxiv","version":4},"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":"sha256:089aef48a5aa76bea7cd6664de2965fd026280fd6cb93dbce207da5bd682af26","target":"record","created_at":"2026-05-17T23:45:04Z","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":"c955e7c86c68e05bacd8ac9851858d4ebf62ce7d237c2a26d838aad977dfcfa4","cross_cats_sorted":["cs.DS","cs.NE","math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-10-29T11:45:02Z","title_canon_sha256":"8acdab021c5d00eba6619711a5ce7a4cecfdcf7877cef0671edd2ada0210c7c6"},"schema_version":"1.0","source":{"id":"1810.12065","kind":"arxiv","version":4}},"canonical_sha256":"309f1743b3c9c0fae229c6db306ce79943fb2af9c332782c40df3a586eb58f1c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"309f1743b3c9c0fae229c6db306ce79943fb2af9c332782c40df3a586eb58f1c","first_computed_at":"2026-05-17T23:45:04.331165Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:04.331165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AZqDT+i/sk56+qQObBpXaVLvkK7/GT+5FroH+PRAWkr52uvnhX0w2rcQ1o/GyhophtlYxKhmAId/Btcb6lHJCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:04.331822Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.12065","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:089aef48a5aa76bea7cd6664de2965fd026280fd6cb93dbce207da5bd682af26","sha256:7f0d3c3a20f91184540ecb1b31843a0fb392f70b4a04b7d355a43152c69bdea8"],"state_sha256":"04c687e15dc8fbacd741f6c485e2719ffef5cfca50270d5bf0757376e831f165"}