{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XU4OPDBE4HCJFHZU5THCQ4DICJ","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":"0c671be2df6d5bc1f4604eab050768a71d59167223eee6a1672e6b261023dec6","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-09-28T04:53:03Z","title_canon_sha256":"76624da48bd8f02f1c271cfff90f644cf8a489729b22fc44a510da592d03effc"},"schema_version":"1.0","source":{"id":"1809.10858","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.10858","created_at":"2026-05-17T23:44:49Z"},{"alias_kind":"arxiv_version","alias_value":"1809.10858v2","created_at":"2026-05-17T23:44:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10858","created_at":"2026-05-17T23:44:49Z"},{"alias_kind":"pith_short_12","alias_value":"XU4OPDBE4HCJ","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XU4OPDBE4HCJFHZU","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XU4OPDBE","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:2b1ccae7001eac3de1ce5714a3e798196fb76f4ed8c1e9ab4319d88f76eabdbf","target":"graph","created_at":"2026-05-17T23:44:49Z","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 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","authors_text":"Ali Jadbabaie, Chulhee Yun, Suvrit Sra","cross_cats":["cs.LG","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-09-28T04:53:03Z","title":"Efficiently testing local optimality and escaping saddles for ReLU networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10858","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:fe8615a89ed3c405fbc322dc671ef5ba49d49fc10b3ebeaa8e35615855834fa0","target":"record","created_at":"2026-05-17T23:44:49Z","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":"0c671be2df6d5bc1f4604eab050768a71d59167223eee6a1672e6b261023dec6","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-09-28T04:53:03Z","title_canon_sha256":"76624da48bd8f02f1c271cfff90f644cf8a489729b22fc44a510da592d03effc"},"schema_version":"1.0","source":{"id":"1809.10858","kind":"arxiv","version":2}},"canonical_sha256":"bd38e78c24e1c4929f34ecce287068124b4dec3827da0d3fbf8783764d1ac1d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd38e78c24e1c4929f34ecce287068124b4dec3827da0d3fbf8783764d1ac1d9","first_computed_at":"2026-05-17T23:44:49.552807Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:49.552807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IefZrJppwU1YOveWw3GrGbNkXaxIRc/KgCxoTOnTvhjx9oGqEFHKAqp9+7eS2J3Gh3O/jhj05a1b7LTTb+eOBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:49.553558Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.10858","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe8615a89ed3c405fbc322dc671ef5ba49d49fc10b3ebeaa8e35615855834fa0","sha256:2b1ccae7001eac3de1ce5714a3e798196fb76f4ed8c1e9ab4319d88f76eabdbf"],"state_sha256":"355b4a22348ba12f89bd1ddefdda2ec46448dd726bcbef1068950bc4a0fba16f"}