{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:QU4LQL5RGD34UB2HFPR5IKKBAG","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":"716f88f1bc197d9b7558103019fe53091d161241695aaf167f06451eb8572521","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-12-09T12:26:26Z","title_canon_sha256":"a61a9fa86d28484b1752e6439aa823266040113af3a3978046cc126ca372f93f"},"schema_version":"1.0","source":{"id":"2412.06436","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.06436","created_at":"2026-07-05T11:17:38Z"},{"alias_kind":"arxiv_version","alias_value":"2412.06436v3","created_at":"2026-07-05T11:17:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.06436","created_at":"2026-07-05T11:17:38Z"},{"alias_kind":"pith_short_12","alias_value":"QU4LQL5RGD34","created_at":"2026-07-05T11:17:38Z"},{"alias_kind":"pith_short_16","alias_value":"QU4LQL5RGD34UB2H","created_at":"2026-07-05T11:17:38Z"},{"alias_kind":"pith_short_8","alias_value":"QU4LQL5R","created_at":"2026-07-05T11:17:38Z"}],"graph_snapshots":[{"event_id":"sha256:81eb19b7f495c9a929824b8e970d9b087c057f5ac7c1f5414912c7d4772af64e","target":"graph","created_at":"2026-07-05T11:17:38Z","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/2412.06436/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a bilevel learning framework for learning linear operators. In this framework, the learnable parameters are optimized via a loss function that also depends on the minimizer of a convex optimization problem (denoted lower-level problem). We utilize an iterative algorithm called `piggyback' to compute the gradient of the loss and minimizer of the lower-level problem. Given that the lower-level problem is solved numerically, the loss function and thus its gradient can only be computed inexactly. To estimate the accuracy of the computed hypergradient, we derive an a-posteriori error bo","authors_text":"Hok Shing Wong, Lea Bogensperger, Matthias J. Ehrhardt, Mohammad Sadegh Salehi, Thomas Pock","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-12-09T12:26:26Z","title":"An Adaptively Inexact Method for Bilevel Learning Using Primal-Dual Style Differentiation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.06436","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":"sha256:6c3041d742794068edd81ea20e53d099cedb710d52dd8b7b7fd75e2b964694b2","target":"record","created_at":"2026-07-05T11:17:38Z","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":"716f88f1bc197d9b7558103019fe53091d161241695aaf167f06451eb8572521","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-12-09T12:26:26Z","title_canon_sha256":"a61a9fa86d28484b1752e6439aa823266040113af3a3978046cc126ca372f93f"},"schema_version":"1.0","source":{"id":"2412.06436","kind":"arxiv","version":3}},"canonical_sha256":"8538b82fb130f7ca07472be3d4294101a211ff982516c8966724cb593610819d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8538b82fb130f7ca07472be3d4294101a211ff982516c8966724cb593610819d","first_computed_at":"2026-07-05T11:17:38.714045Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:17:38.714045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GmJAoJHyQPH9sBxvR91fn5K75fOFBs9u68GUSQxu1jGi5cw9q+cvo8IMauuFVMScEvxn/L4YtAHsirsdAp4UAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:17:38.714617Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.06436","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c3041d742794068edd81ea20e53d099cedb710d52dd8b7b7fd75e2b964694b2","sha256:81eb19b7f495c9a929824b8e970d9b087c057f5ac7c1f5414912c7d4772af64e"],"state_sha256":"e9176092f40c300e986b07783f3185fa041d2fd15a2ad2a119dec9a69e8b9ef8"}