{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:XU4OPDBE4HCJFHZU5THCQ4DICJ","short_pith_number":"pith:XU4OPDBE","schema_version":"1.0","canonical_sha256":"bd38e78c24e1c4929f34ecce287068124b4dec3827da0d3fbf8783764d1ac1d9","source":{"kind":"arxiv","id":"1809.10858","version":2},"attestation_state":"computed","paper":{"title":"Efficiently testing local optimality and escaping saddles for ReLU networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"math.OC","authors_text":"Ali Jadbabaie, Chulhee Yun, Suvrit Sra","submitted_at":"2018-09-28T04:53:03Z","abstract_excerpt":"We provide a theoretical algorithm for checking local optimality and escaping saddles at nondifferentiable points of empirical risks of two-layer ReLU networks. Our algorithm receives any parameter value and returns: local minimum, second-order stationary point, or a strict descent direction. The presence of $M$ data points on the nondifferentiability of the ReLU divides the parameter space into at most $2^M$ regions, which makes analysis difficult. By exploiting polyhedral geometry, we reduce the total computation down to one convex quadratic program (QP) for each hidden node, $O(M)$ (in)equa"},"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":"1809.10858","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-09-28T04:53:03Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"76624da48bd8f02f1c271cfff90f644cf8a489729b22fc44a510da592d03effc","abstract_canon_sha256":"0c671be2df6d5bc1f4604eab050768a71d59167223eee6a1672e6b261023dec6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:49.553558Z","signature_b64":"IefZrJppwU1YOveWw3GrGbNkXaxIRc/KgCxoTOnTvhjx9oGqEFHKAqp9+7eS2J3Gh3O/jhj05a1b7LTTb+eOBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd38e78c24e1c4929f34ecce287068124b4dec3827da0d3fbf8783764d1ac1d9","last_reissued_at":"2026-05-17T23:44:49.552807Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:49.552807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Efficiently testing local optimality and escaping saddles for ReLU networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"math.OC","authors_text":"Ali Jadbabaie, Chulhee Yun, Suvrit Sra","submitted_at":"2018-09-28T04:53:03Z","abstract_excerpt":"We provide a theoretical algorithm for checking local optimality and escaping saddles at nondifferentiable points of empirical risks of two-layer ReLU networks. Our algorithm receives any parameter value and returns: local minimum, second-order stationary point, or a strict descent direction. The presence of $M$ data points on the nondifferentiability of the ReLU divides the parameter space into at most $2^M$ regions, which makes analysis difficult. By exploiting polyhedral geometry, we reduce the total computation down to one convex quadratic program (QP) for each hidden node, $O(M)$ (in)equa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10858","kind":"arxiv","version":2},"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":"1809.10858","created_at":"2026-05-17T23:44:49.552909+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.10858v2","created_at":"2026-05-17T23:44:49.552909+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10858","created_at":"2026-05-17T23:44:49.552909+00:00"},{"alias_kind":"pith_short_12","alias_value":"XU4OPDBE4HCJ","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_16","alias_value":"XU4OPDBE4HCJFHZU","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_8","alias_value":"XU4OPDBE","created_at":"2026-05-18T12:33:01.666342+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XU4OPDBE4HCJFHZU5THCQ4DICJ","json":"https://pith.science/pith/XU4OPDBE4HCJFHZU5THCQ4DICJ.json","graph_json":"https://pith.science/api/pith-number/XU4OPDBE4HCJFHZU5THCQ4DICJ/graph.json","events_json":"https://pith.science/api/pith-number/XU4OPDBE4HCJFHZU5THCQ4DICJ/events.json","paper":"https://pith.science/paper/XU4OPDBE"},"agent_actions":{"view_html":"https://pith.science/pith/XU4OPDBE4HCJFHZU5THCQ4DICJ","download_json":"https://pith.science/pith/XU4OPDBE4HCJFHZU5THCQ4DICJ.json","view_paper":"https://pith.science/paper/XU4OPDBE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.10858&json=true","fetch_graph":"https://pith.science/api/pith-number/XU4OPDBE4HCJFHZU5THCQ4DICJ/graph.json","fetch_events":"https://pith.science/api/pith-number/XU4OPDBE4HCJFHZU5THCQ4DICJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XU4OPDBE4HCJFHZU5THCQ4DICJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XU4OPDBE4HCJFHZU5THCQ4DICJ/action/storage_attestation","attest_author":"https://pith.science/pith/XU4OPDBE4HCJFHZU5THCQ4DICJ/action/author_attestation","sign_citation":"https://pith.science/pith/XU4OPDBE4HCJFHZU5THCQ4DICJ/action/citation_signature","submit_replication":"https://pith.science/pith/XU4OPDBE4HCJFHZU5THCQ4DICJ/action/replication_record"}},"created_at":"2026-05-17T23:44:49.552909+00:00","updated_at":"2026-05-17T23:44:49.552909+00:00"}