{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:CPI4LZG63NRVTLOJLJDOOCXUAD","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":"14331b3c24263177576599cf9bf31e5a59fd05e01ee34a6029a064c76122ec4c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-11-21T17:39:41Z","title_canon_sha256":"44e4fe997a1b7e89fcf824d93904fba0709ec9983479c858bc6edc21b517029a"},"schema_version":"1.0","source":{"id":"2411.14342","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.14342","created_at":"2026-07-05T09:38:45Z"},{"alias_kind":"arxiv_version","alias_value":"2411.14342v1","created_at":"2026-07-05T09:38:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.14342","created_at":"2026-07-05T09:38:45Z"},{"alias_kind":"pith_short_12","alias_value":"CPI4LZG63NRV","created_at":"2026-07-05T09:38:45Z"},{"alias_kind":"pith_short_16","alias_value":"CPI4LZG63NRVTLOJ","created_at":"2026-07-05T09:38:45Z"},{"alias_kind":"pith_short_8","alias_value":"CPI4LZG6","created_at":"2026-07-05T09:38:45Z"}],"graph_snapshots":[{"event_id":"sha256:8c960e721a2a10a660799e4728e0f4e4fcdd3b04b9f817347cc0a5e70b171904","target":"graph","created_at":"2026-07-05T09:38:45Z","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/2411.14342/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This note studies numerical methods for solving compositional optimization problems, where the inner function is smooth, and the outer function is Lipschitz continuous, non-smooth, and non-convex but exhibits one of two special structures that enable the design of efficient first-order methods. In the first structure, the outer function allows for an easily solvable proximal mapping. We demonstrate that, in this case, a smoothing compositional gradient method can find a $(\\delta,\\epsilon)$-stationary point--specifically defined for compositional optimization--in $O(1/(\\delta \\epsilon^2))$ iter","authors_text":"Qihang Lin, Tianbao Yang, Yao Yao","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-11-21T17:39:41Z","title":"A Note on Complexity for Two Classes of Structured Non-Smooth Non-Convex Compositional Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.14342","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:ee5109f32115ff225700b9563f261c2b55ea55faccd9d2004c409853d8be35a3","target":"record","created_at":"2026-07-05T09:38:45Z","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":"14331b3c24263177576599cf9bf31e5a59fd05e01ee34a6029a064c76122ec4c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-11-21T17:39:41Z","title_canon_sha256":"44e4fe997a1b7e89fcf824d93904fba0709ec9983479c858bc6edc21b517029a"},"schema_version":"1.0","source":{"id":"2411.14342","kind":"arxiv","version":1}},"canonical_sha256":"13d1c5e4dedb6359adc95a46e70af400c78862a51cbbad5bf00d6c7b28eb221d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13d1c5e4dedb6359adc95a46e70af400c78862a51cbbad5bf00d6c7b28eb221d","first_computed_at":"2026-07-05T09:38:45.457217Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:38:45.457217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z82LitLTKHU+sqo+8kzkx6n47iTzt6UXAEgrjJvYmF1+m9lSGMN/aTNBuNT9h3/gEFQXPo7WOpXmLryNKfrBDg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:38:45.457748Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.14342","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee5109f32115ff225700b9563f261c2b55ea55faccd9d2004c409853d8be35a3","sha256:8c960e721a2a10a660799e4728e0f4e4fcdd3b04b9f817347cc0a5e70b171904"],"state_sha256":"438c5169fce5c73b2e78c69ce32b059f50273276e1b2816b43242c79cccf20b7"}