{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:G2BSPFFDXR2DZJUMEIZUGBE3CU","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":"4999a88f71e27625d43acd47b1d2adbc1a43f623baec614bcc06b52cbe564bd8","cross_cats_sorted":["cs.NA","math.NA","stat.ML"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2019-10-14T00:50:55Z","title_canon_sha256":"922dc83827836562e3cd3725bb9da3e52262916bf9220c6cd346da09d5bda923"},"schema_version":"1.0","source":{"id":"1910.05874","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.05874","created_at":"2026-07-05T01:33:34Z"},{"alias_kind":"arxiv_version","alias_value":"1910.05874v2","created_at":"2026-07-05T01:33:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.05874","created_at":"2026-07-05T01:33:34Z"},{"alias_kind":"pith_short_12","alias_value":"G2BSPFFDXR2D","created_at":"2026-07-05T01:33:34Z"},{"alias_kind":"pith_short_16","alias_value":"G2BSPFFDXR2DZJUM","created_at":"2026-07-05T01:33:34Z"},{"alias_kind":"pith_short_8","alias_value":"G2BSPFFD","created_at":"2026-07-05T01:33:34Z"}],"graph_snapshots":[{"event_id":"sha256:bbdb324351648cb0fbc7f3bcf391edef67e80a5b6413062678490026de870dbf","target":"graph","created_at":"2026-07-05T01:33:34Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1910.05874/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Deep neural networks have been used in various machine learning applications and achieved tremendous empirical successes. However, training deep neural networks is a challenging task. Many alternatives have been proposed in place of end-to-end back-propagation. Layer-wise training is one of them, which trains a single layer at a time, rather than trains the whole layers simultaneously. In this paper, we study a layer-wise training using a block coordinate gradient descent (BCGD) for deep linear networks. We establish a general convergence analysis of BCGD and found the optimal learning rate, w","authors_text":"Yeonjong Shin","cross_cats":["cs.NA","math.NA","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2019-10-14T00:50:55Z","title":"Effects of Depth, Width, and Initialization: A Convergence Analysis of Layer-wise Training for Deep Linear Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.05874","kind":"arxiv","version":2},"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:b41df6b91430136e9bead6334b6efa668fd23fe85a8fc4f9cf83ce35474d7f56","target":"record","created_at":"2026-07-05T01:33:34Z","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":"4999a88f71e27625d43acd47b1d2adbc1a43f623baec614bcc06b52cbe564bd8","cross_cats_sorted":["cs.NA","math.NA","stat.ML"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2019-10-14T00:50:55Z","title_canon_sha256":"922dc83827836562e3cd3725bb9da3e52262916bf9220c6cd346da09d5bda923"},"schema_version":"1.0","source":{"id":"1910.05874","kind":"arxiv","version":2}},"canonical_sha256":"36832794a3bc743ca68c223343049b1533369fab52a82c839a491609dd292e3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36832794a3bc743ca68c223343049b1533369fab52a82c839a491609dd292e3e","first_computed_at":"2026-07-05T01:33:34.186929Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:33:34.186929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BktkQxbWbAzdnV3UJb0Ed7DWbB+VJuw+WZ6LuByolfNZvv1zizwE0ky44EL8VNmQeFkaAck+rAd2RW4hWOIACA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:33:34.187276Z","signed_message":"canonical_sha256_bytes"},"source_id":"1910.05874","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b41df6b91430136e9bead6334b6efa668fd23fe85a8fc4f9cf83ce35474d7f56","sha256:bbdb324351648cb0fbc7f3bcf391edef67e80a5b6413062678490026de870dbf"],"state_sha256":"3909e81a85731eac3525b274346cdcfd0062976a64dcb947fc3d2390b88a744a"}