{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:QWY6EUJ33NRPVGJSIWT7DLLIPC","short_pith_number":"pith:QWY6EUJ3","canonical_record":{"source":{"id":"1906.11417","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-27T03:08:21Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"cbad1ad14e39d66b1e1098a8d2d9f4fcef5012e04ceb4f702308c67c4ff35e52","abstract_canon_sha256":"7fa0f18fb2e85ace1f438cc14dc5a2f4ea6c3bf6dba6c86ae6a3aa8604df92c0"},"schema_version":"1.0"},"canonical_sha256":"85b1e2513bdb62fa993245a7f1ad6878991c6e541845bf6e9e1aad7f5b211020","source":{"kind":"arxiv","id":"1906.11417","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.11417","created_at":"2026-05-17T23:42:07Z"},{"alias_kind":"arxiv_version","alias_value":"1906.11417v1","created_at":"2026-05-17T23:42:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.11417","created_at":"2026-05-17T23:42:07Z"},{"alias_kind":"pith_short_12","alias_value":"QWY6EUJ33NRP","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"QWY6EUJ33NRPVGJS","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"QWY6EUJ3","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:QWY6EUJ33NRPVGJSIWT7DLLIPC","target":"record","payload":{"canonical_record":{"source":{"id":"1906.11417","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-27T03:08:21Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"cbad1ad14e39d66b1e1098a8d2d9f4fcef5012e04ceb4f702308c67c4ff35e52","abstract_canon_sha256":"7fa0f18fb2e85ace1f438cc14dc5a2f4ea6c3bf6dba6c86ae6a3aa8604df92c0"},"schema_version":"1.0"},"canonical_sha256":"85b1e2513bdb62fa993245a7f1ad6878991c6e541845bf6e9e1aad7f5b211020","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:07.180984Z","signature_b64":"9ztpYGpfA4fdkbVE9IkjoyCehDbdDTvZ+jNorwAYzWfMjRwglFysXnsEplGSydCH1s/rmAC7PhosK/zRoapECQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85b1e2513bdb62fa993245a7f1ad6878991c6e541845bf6e9e1aad7f5b211020","last_reissued_at":"2026-05-17T23:42:07.180267Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:07.180267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.11417","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:42:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RNNO1P9uyP6IPPuoA2ATL1WTi34Q+kZzSQnxJ6oUSHqB+WBssxl7y0UeFJPy8sOozxh5FA7InPVoPr2/fO38AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:41:17.179118Z"},"content_sha256":"f6afea0eab4ee4a9bba581ed5472d98c2e0e602faec05b6af23cc4539844e303","schema_version":"1.0","event_id":"sha256:f6afea0eab4ee4a9bba581ed5472d98c2e0e602faec05b6af23cc4539844e303"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:QWY6EUJ33NRPVGJSIWT7DLLIPC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Combining Stochastic Adaptive Cubic Regularization with Negative Curvature for Nonconvex Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Panos M. Pardalos, Seonho Park, Seung Hyun Jung","submitted_at":"2019-06-27T03:08:21Z","abstract_excerpt":"We focus on minimizing nonconvex finite-sum functions that typically arise in machine learning problems. In an attempt to solve this problem, the adaptive cubic regularized Newton method has shown its strong global convergence guarantees and ability to escape from strict saddle points. This method uses a trust region-like scheme to determine if an iteration is successful or not, and updates only when it is successful. In this paper, we suggest an algorithm combining negative curvature with the adaptive cubic regularized Newton method to update even at unsuccessful iterations. We call this new "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.11417","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:42:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NbDT5vk0blHYYJ1c63RbEuA/d4YhbE8f1yorspd996ydb7oK/4z904vxL5f+M1Qj84HYO/G7pjEoSV17SPobBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:41:17.179814Z"},"content_sha256":"583d251fa9ff5c4bd9949647c6ed637254549274fba5a52fdeae6dc3a0acfa96","schema_version":"1.0","event_id":"sha256:583d251fa9ff5c4bd9949647c6ed637254549274fba5a52fdeae6dc3a0acfa96"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QWY6EUJ33NRPVGJSIWT7DLLIPC/bundle.json","state_url":"https://pith.science/pith/QWY6EUJ33NRPVGJSIWT7DLLIPC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QWY6EUJ33NRPVGJSIWT7DLLIPC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T04:41:17Z","links":{"resolver":"https://pith.science/pith/QWY6EUJ33NRPVGJSIWT7DLLIPC","bundle":"https://pith.science/pith/QWY6EUJ33NRPVGJSIWT7DLLIPC/bundle.json","state":"https://pith.science/pith/QWY6EUJ33NRPVGJSIWT7DLLIPC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QWY6EUJ33NRPVGJSIWT7DLLIPC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:QWY6EUJ33NRPVGJSIWT7DLLIPC","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":"7fa0f18fb2e85ace1f438cc14dc5a2f4ea6c3bf6dba6c86ae6a3aa8604df92c0","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-27T03:08:21Z","title_canon_sha256":"cbad1ad14e39d66b1e1098a8d2d9f4fcef5012e04ceb4f702308c67c4ff35e52"},"schema_version":"1.0","source":{"id":"1906.11417","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.11417","created_at":"2026-05-17T23:42:07Z"},{"alias_kind":"arxiv_version","alias_value":"1906.11417v1","created_at":"2026-05-17T23:42:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.11417","created_at":"2026-05-17T23:42:07Z"},{"alias_kind":"pith_short_12","alias_value":"QWY6EUJ33NRP","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"QWY6EUJ33NRPVGJS","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"QWY6EUJ3","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:583d251fa9ff5c4bd9949647c6ed637254549274fba5a52fdeae6dc3a0acfa96","target":"graph","created_at":"2026-05-17T23:42:07Z","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 focus on minimizing nonconvex finite-sum functions that typically arise in machine learning problems. In an attempt to solve this problem, the adaptive cubic regularized Newton method has shown its strong global convergence guarantees and ability to escape from strict saddle points. This method uses a trust region-like scheme to determine if an iteration is successful or not, and updates only when it is successful. In this paper, we suggest an algorithm combining negative curvature with the adaptive cubic regularized Newton method to update even at unsuccessful iterations. We call this new ","authors_text":"Panos M. Pardalos, Seonho Park, Seung Hyun Jung","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-27T03:08:21Z","title":"Combining Stochastic Adaptive Cubic Regularization with Negative Curvature for Nonconvex Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.11417","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:f6afea0eab4ee4a9bba581ed5472d98c2e0e602faec05b6af23cc4539844e303","target":"record","created_at":"2026-05-17T23:42:07Z","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":"7fa0f18fb2e85ace1f438cc14dc5a2f4ea6c3bf6dba6c86ae6a3aa8604df92c0","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-27T03:08:21Z","title_canon_sha256":"cbad1ad14e39d66b1e1098a8d2d9f4fcef5012e04ceb4f702308c67c4ff35e52"},"schema_version":"1.0","source":{"id":"1906.11417","kind":"arxiv","version":1}},"canonical_sha256":"85b1e2513bdb62fa993245a7f1ad6878991c6e541845bf6e9e1aad7f5b211020","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85b1e2513bdb62fa993245a7f1ad6878991c6e541845bf6e9e1aad7f5b211020","first_computed_at":"2026-05-17T23:42:07.180267Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:07.180267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9ztpYGpfA4fdkbVE9IkjoyCehDbdDTvZ+jNorwAYzWfMjRwglFysXnsEplGSydCH1s/rmAC7PhosK/zRoapECQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:07.180984Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.11417","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6afea0eab4ee4a9bba581ed5472d98c2e0e602faec05b6af23cc4539844e303","sha256:583d251fa9ff5c4bd9949647c6ed637254549274fba5a52fdeae6dc3a0acfa96"],"state_sha256":"1a1686a7f84080bb3e9ab1fedf4685ae42b2c05f65448b3ee55da0d04fe655d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pb+PTRJRE/SZsLQfmGO7SBGh/HhfkJEv56hobhDkW6hwce3unNuYJiU8jRc5SLL3mP23GsnVv48/i/5TtBAmAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T04:41:17.183394Z","bundle_sha256":"6e3a178192175e42fafe41dc8cafbe5bd7eeded622ea33cc86aa0122b2a106ca"}}