{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:CURLG4QYKVEBMBJ7BHRLRYXYDH","short_pith_number":"pith:CURLG4QY","canonical_record":{"source":{"id":"1705.05933","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-05-16T21:44:44Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"d8716d846573f6378b8d266bfffa986e8298113b524845619a50bc9666a51732","abstract_canon_sha256":"6bed4077b27d0b3708ac07fe32ffea0f9089a06008ba8a38ba64cbafda43ce87"},"schema_version":"1.0"},"canonical_sha256":"1522b37218554816053f09e2b8e2f819c3c1f495ab9afc88b2bba205a4a41611","source":{"kind":"arxiv","id":"1705.05933","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.05933","created_at":"2026-05-18T00:41:06Z"},{"alias_kind":"arxiv_version","alias_value":"1705.05933v3","created_at":"2026-05-18T00:41:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05933","created_at":"2026-05-18T00:41:06Z"},{"alias_kind":"pith_short_12","alias_value":"CURLG4QYKVEB","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CURLG4QYKVEBMBJ7","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CURLG4QY","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:CURLG4QYKVEBMBJ7BHRLRYXYDH","target":"record","payload":{"canonical_record":{"source":{"id":"1705.05933","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-05-16T21:44:44Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"d8716d846573f6378b8d266bfffa986e8298113b524845619a50bc9666a51732","abstract_canon_sha256":"6bed4077b27d0b3708ac07fe32ffea0f9089a06008ba8a38ba64cbafda43ce87"},"schema_version":"1.0"},"canonical_sha256":"1522b37218554816053f09e2b8e2f819c3c1f495ab9afc88b2bba205a4a41611","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:06.928969Z","signature_b64":"Hc2AHZXhR5W09tdXjVQmFQDrm+ivWvU90Aj22xMnd9AxX4SX5WRtmPqZ9ZKfVDQPBA69NFJSkri8DvvPEX+ADg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1522b37218554816053f09e2b8e2f819c3c1f495ab9afc88b2bba205a4a41611","last_reissued_at":"2026-05-18T00:41:06.928495Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:06.928495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.05933","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YU334UNXojoGPlymvvmMt37+v/THq13MQ3TcXUCViAQIExz9LWcHwrOI//FxIMrAOtBFs7u2D9wfyUBWcLDBAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T14:42:04.282842Z"},"content_sha256":"fd188d9009f8ad37e4c3531b6297e9d21e6c4a780d45b71b330d9c194fd18109","schema_version":"1.0","event_id":"sha256:fd188d9009f8ad37e4c3531b6297e9d21e6c4a780d45b71b330d9c194fd18109"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:CURLG4QYKVEBMBJ7BHRLRYXYDH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sub-sampled Cubic Regularization for Non-convex Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Aurelien Lucchi, Jonas Moritz Kohler","submitted_at":"2017-05-16T21:44:44Z","abstract_excerpt":"We consider the minimization of non-convex functions that typically arise in machine learning. Specifically, we focus our attention on a variant of trust region methods known as cubic regularization. This approach is particularly attractive because it escapes strict saddle points and it provides stronger convergence guarantees than first- and second-order as well as classical trust region methods. However, it suffers from a high computational complexity that makes it impractical for large-scale learning. Here, we propose a novel method that uses sub-sampling to lower this computational cost. B"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05933","kind":"arxiv","version":3},"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":"2026-05-18T00:41:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"soiiNS0GMniKQVMBdiZnd4c0cydbYoIIPWeQ9T389rmph73FvJ8ZerEehHPOxoG0MxC9eBv05C96Whp8O/DTBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T14:42:04.283579Z"},"content_sha256":"94cd3542d5871963385bd830b9a3d2d1e17a785cc0171de6c2b6734c8403aa65","schema_version":"1.0","event_id":"sha256:94cd3542d5871963385bd830b9a3d2d1e17a785cc0171de6c2b6734c8403aa65"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CURLG4QYKVEBMBJ7BHRLRYXYDH/bundle.json","state_url":"https://pith.science/pith/CURLG4QYKVEBMBJ7BHRLRYXYDH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CURLG4QYKVEBMBJ7BHRLRYXYDH/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":"2026-05-25T14:42:04Z","links":{"resolver":"https://pith.science/pith/CURLG4QYKVEBMBJ7BHRLRYXYDH","bundle":"https://pith.science/pith/CURLG4QYKVEBMBJ7BHRLRYXYDH/bundle.json","state":"https://pith.science/pith/CURLG4QYKVEBMBJ7BHRLRYXYDH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CURLG4QYKVEBMBJ7BHRLRYXYDH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CURLG4QYKVEBMBJ7BHRLRYXYDH","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":"6bed4077b27d0b3708ac07fe32ffea0f9089a06008ba8a38ba64cbafda43ce87","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-05-16T21:44:44Z","title_canon_sha256":"d8716d846573f6378b8d266bfffa986e8298113b524845619a50bc9666a51732"},"schema_version":"1.0","source":{"id":"1705.05933","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.05933","created_at":"2026-05-18T00:41:06Z"},{"alias_kind":"arxiv_version","alias_value":"1705.05933v3","created_at":"2026-05-18T00:41:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05933","created_at":"2026-05-18T00:41:06Z"},{"alias_kind":"pith_short_12","alias_value":"CURLG4QYKVEB","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CURLG4QYKVEBMBJ7","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CURLG4QY","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:94cd3542d5871963385bd830b9a3d2d1e17a785cc0171de6c2b6734c8403aa65","target":"graph","created_at":"2026-05-18T00:41:06Z","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 consider the minimization of non-convex functions that typically arise in machine learning. Specifically, we focus our attention on a variant of trust region methods known as cubic regularization. This approach is particularly attractive because it escapes strict saddle points and it provides stronger convergence guarantees than first- and second-order as well as classical trust region methods. However, it suffers from a high computational complexity that makes it impractical for large-scale learning. Here, we propose a novel method that uses sub-sampling to lower this computational cost. B","authors_text":"Aurelien Lucchi, Jonas Moritz Kohler","cross_cats":["math.OC","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-05-16T21:44:44Z","title":"Sub-sampled Cubic Regularization for Non-convex Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05933","kind":"arxiv","version":3},"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:fd188d9009f8ad37e4c3531b6297e9d21e6c4a780d45b71b330d9c194fd18109","target":"record","created_at":"2026-05-18T00:41:06Z","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":"6bed4077b27d0b3708ac07fe32ffea0f9089a06008ba8a38ba64cbafda43ce87","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-05-16T21:44:44Z","title_canon_sha256":"d8716d846573f6378b8d266bfffa986e8298113b524845619a50bc9666a51732"},"schema_version":"1.0","source":{"id":"1705.05933","kind":"arxiv","version":3}},"canonical_sha256":"1522b37218554816053f09e2b8e2f819c3c1f495ab9afc88b2bba205a4a41611","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1522b37218554816053f09e2b8e2f819c3c1f495ab9afc88b2bba205a4a41611","first_computed_at":"2026-05-18T00:41:06.928495Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:06.928495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hc2AHZXhR5W09tdXjVQmFQDrm+ivWvU90Aj22xMnd9AxX4SX5WRtmPqZ9ZKfVDQPBA69NFJSkri8DvvPEX+ADg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:06.928969Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.05933","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd188d9009f8ad37e4c3531b6297e9d21e6c4a780d45b71b330d9c194fd18109","sha256:94cd3542d5871963385bd830b9a3d2d1e17a785cc0171de6c2b6734c8403aa65"],"state_sha256":"b02a3c4bc7eedcbda77f4a9be44628f54437ba0da83c2514256164249197cd39"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o3N0+bJ5Q2lf4QrdHljGBfvZLex+8KC5BhLJ56EVYGyZZcCijSlHCbNFrLcBc+62pxOTDh7XVMyysZpAnfDcBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T14:42:04.287635Z","bundle_sha256":"d8a7bad9a95e11a957555fbe12a48a71b54f9de2885c28f73e1a1e26f71a32d7"}}