{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:WLHRIBAH3DYMGMERIFTGUEZ55E","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":"f207017e84eba76e13ca89b46999d502465026d2bd92af37aa7ef85871f4b700","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-05-28T15:31:51Z","title_canon_sha256":"d693d6fdc3c0dcdb35d3dc0b77853ccd2129d3b64057c12d1e42b03666d530c0"},"schema_version":"1.0","source":{"id":"1905.11887","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.11887","created_at":"2026-05-17T23:44:50Z"},{"alias_kind":"arxiv_version","alias_value":"1905.11887v1","created_at":"2026-05-17T23:44:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.11887","created_at":"2026-05-17T23:44:50Z"},{"alias_kind":"pith_short_12","alias_value":"WLHRIBAH3DYM","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"WLHRIBAH3DYMGMER","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"WLHRIBAH","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:3ecde38e2e21c6778656a1c00eb5fc907b6305b5eef9795e852a9574fdca05da","target":"graph","created_at":"2026-05-17T23:44:50Z","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":"We give a formal and complete characterization of the explicit regularizer induced by dropout in deep linear networks with squared loss. We show that (a) the explicit regularizer is composed of an $\\ell_2$-path regularizer and other terms that are also re-scaling invariant, (b) the convex envelope of the induced regularizer is the squared nuclear norm of the network map, and (c) for a sufficiently large dropout rate, we characterize the global optima of the dropout objective. We validate our theoretical findings with empirical results.","authors_text":"Poorya Mianjy, Raman Arora","cross_cats":["cs.AI","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-05-28T15:31:51Z","title":"On Dropout and Nuclear Norm Regularization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.11887","kind":"arxiv","version":1},"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:d1d64d76d651a676b5b5e34846b788408c5e52074673998f8fca1038cad605b3","target":"record","created_at":"2026-05-17T23:44:50Z","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":"f207017e84eba76e13ca89b46999d502465026d2bd92af37aa7ef85871f4b700","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-05-28T15:31:51Z","title_canon_sha256":"d693d6fdc3c0dcdb35d3dc0b77853ccd2129d3b64057c12d1e42b03666d530c0"},"schema_version":"1.0","source":{"id":"1905.11887","kind":"arxiv","version":1}},"canonical_sha256":"b2cf140407d8f0c3309141666a133de926e33ff634877b95cb093384eb2549b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2cf140407d8f0c3309141666a133de926e33ff634877b95cb093384eb2549b8","first_computed_at":"2026-05-17T23:44:50.027124Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:50.027124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0Ol8em8i/08f9urUnAlECm665HKSf9E0Q2BAHm90XkXCEHyc/0Jy4bVNuFGoA+r1ZhOM3//abqZVrUw5XbUXBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:50.027662Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.11887","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1d64d76d651a676b5b5e34846b788408c5e52074673998f8fca1038cad605b3","sha256:3ecde38e2e21c6778656a1c00eb5fc907b6305b5eef9795e852a9574fdca05da"],"state_sha256":"1bb49ab0ee6c0f2292d6a7a5dd68c77e4faf5b0c69adfeca737f542c05da0731"}