{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:G76MQFNTALORMWFUYSMW5POTL6","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":"614cc686b1b995dee466a8ffea7e0840d204af1b97a89aa5528f975ae9bd20b1","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-08-11T07:05:58Z","title_canon_sha256":"75733f87afb1c90cde70344549e06efdc16088f0e9f2cb5fc98372921645c8b8"},"schema_version":"1.0","source":{"id":"2008.04555","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.04555","created_at":"2026-07-05T01:26:26Z"},{"alias_kind":"arxiv_version","alias_value":"2008.04555v1","created_at":"2026-07-05T01:26:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.04555","created_at":"2026-07-05T01:26:26Z"},{"alias_kind":"pith_short_12","alias_value":"G76MQFNTALOR","created_at":"2026-07-05T01:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"G76MQFNTALORMWFU","created_at":"2026-07-05T01:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"G76MQFNT","created_at":"2026-07-05T01:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:e200140b2ea50dbce40ff478cab7963616f5daeaffb216c967afced5837b247c","target":"graph","created_at":"2026-07-05T01:26:26Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2008.04555/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a stochastic recursive momentum method for Riemannian non-convex optimization that achieves a near-optimal complexity of $\\tilde{\\mathcal{O}}(\\epsilon^{-3})$ to find $\\epsilon$-approximate solution with one sample. That is, our method requires $\\mathcal{O}(1)$ gradient evaluations per iteration and does not require restarting with a large batch gradient, which is commonly used to obtain the faster rate. Extensive experiment results demonstrate the superiority of our proposed algorithm.","authors_text":"Andi Han, Junbin Gao","cross_cats":["cs.LG","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-08-11T07:05:58Z","title":"Riemannian stochastic recursive momentum method for non-convex optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.04555","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":"sha256:8d18903046d9261b4db11ddfc4cc9bfb1a6c379df0dec17518a05c305e443c7f","target":"record","created_at":"2026-07-05T01:26:26Z","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":"614cc686b1b995dee466a8ffea7e0840d204af1b97a89aa5528f975ae9bd20b1","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-08-11T07:05:58Z","title_canon_sha256":"75733f87afb1c90cde70344549e06efdc16088f0e9f2cb5fc98372921645c8b8"},"schema_version":"1.0","source":{"id":"2008.04555","kind":"arxiv","version":1}},"canonical_sha256":"37fcc815b302dd1658b4c4996ebdd35fae1b2e3d79f613d2cd347072456805df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37fcc815b302dd1658b4c4996ebdd35fae1b2e3d79f613d2cd347072456805df","first_computed_at":"2026-07-05T01:26:26.370151Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:26:26.370151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6motJCij5Av0m9M1YmCJUHpoP8npckzKteDNkgSMkCWWOK2JUpxclZiaNod+KMHp8oxDc7FTpH0AjWT+Ej0LCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:26:26.370532Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.04555","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d18903046d9261b4db11ddfc4cc9bfb1a6c379df0dec17518a05c305e443c7f","sha256:e200140b2ea50dbce40ff478cab7963616f5daeaffb216c967afced5837b247c"],"state_sha256":"828daf0f2abeaf0cc7655873bfc4627abf49c28d86344b9f12cd719ef5e45491"}