{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:SYV4PQ3HGCHMB6LLRGTWUIR6OM","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":"61426c44d74e489cc25492bfb936c2c060c605077a3d2cd85924986f6aeb39ee","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-05-01T23:44:26Z","title_canon_sha256":"77631a262078a8c4d5bd8d4f3c0a6893f711fc9201c3ce46ae570477af13d8fb"},"schema_version":"1.0","source":{"id":"1905.00529","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.00529","created_at":"2026-05-17T23:47:11Z"},{"alias_kind":"arxiv_version","alias_value":"1905.00529v1","created_at":"2026-05-17T23:47:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.00529","created_at":"2026-05-17T23:47:11Z"},{"alias_kind":"pith_short_12","alias_value":"SYV4PQ3HGCHM","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"SYV4PQ3HGCHMB6LL","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"SYV4PQ3H","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:c134d6bcae4eac470752b306acafc83e4cfa3e5957b3add8ccf74f2e4c01b609","target":"graph","created_at":"2026-05-17T23:47:11Z","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":"Variance reduction techniques like SVRG provide simple and fast algorithms for optimizing a convex finite-sum objective. For nonconvex objectives, these techniques can also find a first-order stationary point (with small gradient). However, in nonconvex optimization it is often crucial to find a second-order stationary point (with small gradient and almost PSD hessian). In this paper, we show that Stabilized SVRG (a simple variant of SVRG) can find an $\\epsilon$-second-order stationary point using only $\\widetilde{O}(n^{2/3}/\\epsilon^2+n/\\epsilon^{1.5})$ stochastic gradients. To our best knowl","authors_text":"Rong Ge, Weiyao Wang, Xiang Wang, Zhize Li","cross_cats":["math.OC","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-05-01T23:44:26Z","title":"Stabilized SVRG: Simple Variance Reduction for Nonconvex Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.00529","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":"sha256:3b5523a5c023a1a44ebe45f0e5abf8ed7dac57e2b3a2d2ce59dc5fe179c18fc7","target":"record","created_at":"2026-05-17T23:47:11Z","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":"61426c44d74e489cc25492bfb936c2c060c605077a3d2cd85924986f6aeb39ee","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-05-01T23:44:26Z","title_canon_sha256":"77631a262078a8c4d5bd8d4f3c0a6893f711fc9201c3ce46ae570477af13d8fb"},"schema_version":"1.0","source":{"id":"1905.00529","kind":"arxiv","version":1}},"canonical_sha256":"962bc7c367308ec0f96b89a76a223e732b236d754bc6fb8df35fe1c67e9fcb95","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"962bc7c367308ec0f96b89a76a223e732b236d754bc6fb8df35fe1c67e9fcb95","first_computed_at":"2026-05-17T23:47:11.623207Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:11.623207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rIN0DsorUyqgfyqXpFpmsVfQPiRrYA0m6ldTN36UlF3YinE4SpvPfGAyKTInwuuz5Psbq5rDNBmRxwJla4GDDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:11.623570Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.00529","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b5523a5c023a1a44ebe45f0e5abf8ed7dac57e2b3a2d2ce59dc5fe179c18fc7","sha256:c134d6bcae4eac470752b306acafc83e4cfa3e5957b3add8ccf74f2e4c01b609"],"state_sha256":"f1546f84b917e5f5d6b4bc824ca37e413a46678fc6245e939e5dc136912e6144"}