{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:XWYDLJFCHE2K4Y6XWPDH5K5NXE","short_pith_number":"pith:XWYDLJFC","schema_version":"1.0","canonical_sha256":"bdb035a4a23934ae63d7b3c67eabadb91430aba022b6d4fb0dbd1b19ce55ce12","source":{"kind":"arxiv","id":"2501.18471","version":1},"attestation_state":"computed","paper":{"title":"Computing AD-compatible subgradients of convex relaxations of implicit functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.OC","authors_text":"Kamil A. Khan, Yingkai Song","submitted_at":"2025-01-30T16:46:26Z","abstract_excerpt":"Automatic generation of convex relaxations and subgradients is critical in global optimization, and is typically carried out using variants of automatic/algorithmic differentiation (AD). At previous AD conferences, variants of the forward and reverse AD modes were presented to evaluate accurate subgradients for convex relaxations of supplied composite functions. In a recent approach for generating convex relaxations of implicit functions, these relaxations are constructed as optimal-value functions; this formulation is versatile but complicates sensitivity analysis. We present the first subgra"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2501.18471","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-01-30T16:46:26Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"3ea1ea2c7b74c5427730ba9c35ac65ac8b8c9307e2e95a699d57afaf361ee69c","abstract_canon_sha256":"44b24301c7b36cd3f5f55fda0bf06bfcb0c0be25de94b6fed8c64cfe31ae9f6d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:07:34.513924Z","signature_b64":"VbI3jVI4pVKzJjp+JCCjehS8SZLNPeCg+ttr7sBZeunf6Mfzm0zfzJH7vHyfeQSdFopnJsTWj/OF8EFExxS9Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bdb035a4a23934ae63d7b3c67eabadb91430aba022b6d4fb0dbd1b19ce55ce12","last_reissued_at":"2026-07-05T10:07:34.513467Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:07:34.513467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computing AD-compatible subgradients of convex relaxations of implicit functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.OC","authors_text":"Kamil A. Khan, Yingkai Song","submitted_at":"2025-01-30T16:46:26Z","abstract_excerpt":"Automatic generation of convex relaxations and subgradients is critical in global optimization, and is typically carried out using variants of automatic/algorithmic differentiation (AD). At previous AD conferences, variants of the forward and reverse AD modes were presented to evaluate accurate subgradients for convex relaxations of supplied composite functions. In a recent approach for generating convex relaxations of implicit functions, these relaxations are constructed as optimal-value functions; this formulation is versatile but complicates sensitivity analysis. We present the first subgra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.18471","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.18471/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2501.18471","created_at":"2026-07-05T10:07:34.513524+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.18471v1","created_at":"2026-07-05T10:07:34.513524+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.18471","created_at":"2026-07-05T10:07:34.513524+00:00"},{"alias_kind":"pith_short_12","alias_value":"XWYDLJFCHE2K","created_at":"2026-07-05T10:07:34.513524+00:00"},{"alias_kind":"pith_short_16","alias_value":"XWYDLJFCHE2K4Y6X","created_at":"2026-07-05T10:07:34.513524+00:00"},{"alias_kind":"pith_short_8","alias_value":"XWYDLJFC","created_at":"2026-07-05T10:07:34.513524+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XWYDLJFCHE2K4Y6XWPDH5K5NXE","json":"https://pith.science/pith/XWYDLJFCHE2K4Y6XWPDH5K5NXE.json","graph_json":"https://pith.science/api/pith-number/XWYDLJFCHE2K4Y6XWPDH5K5NXE/graph.json","events_json":"https://pith.science/api/pith-number/XWYDLJFCHE2K4Y6XWPDH5K5NXE/events.json","paper":"https://pith.science/paper/XWYDLJFC"},"agent_actions":{"view_html":"https://pith.science/pith/XWYDLJFCHE2K4Y6XWPDH5K5NXE","download_json":"https://pith.science/pith/XWYDLJFCHE2K4Y6XWPDH5K5NXE.json","view_paper":"https://pith.science/paper/XWYDLJFC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.18471&json=true","fetch_graph":"https://pith.science/api/pith-number/XWYDLJFCHE2K4Y6XWPDH5K5NXE/graph.json","fetch_events":"https://pith.science/api/pith-number/XWYDLJFCHE2K4Y6XWPDH5K5NXE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XWYDLJFCHE2K4Y6XWPDH5K5NXE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XWYDLJFCHE2K4Y6XWPDH5K5NXE/action/storage_attestation","attest_author":"https://pith.science/pith/XWYDLJFCHE2K4Y6XWPDH5K5NXE/action/author_attestation","sign_citation":"https://pith.science/pith/XWYDLJFCHE2K4Y6XWPDH5K5NXE/action/citation_signature","submit_replication":"https://pith.science/pith/XWYDLJFCHE2K4Y6XWPDH5K5NXE/action/replication_record"}},"created_at":"2026-07-05T10:07:34.513524+00:00","updated_at":"2026-07-05T10:07:34.513524+00:00"}