{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:VBV6IQNG32GIQN2UTOWYNXERBE","short_pith_number":"pith:VBV6IQNG","schema_version":"1.0","canonical_sha256":"a86be441a6de8c8837549bad86dc910931bc32f0c8ef3735607fc31d58645ae8","source":{"kind":"arxiv","id":"2110.00455","version":2},"attestation_state":"computed","paper":{"title":"Towards Gradient-based Bilevel Optimization with Non-convex Followers and Beyond","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Jin Zhang, Risheng Liu, Shangzhi Zeng, Yaohua Liu","submitted_at":"2021-10-01T14:41:17Z","abstract_excerpt":"In recent years, Bi-Level Optimization (BLO) techniques have received extensive attentions from both learning and vision communities. A variety of BLO models in complex and practical tasks are of non-convex follower structure in nature (a.k.a., without Lower-Level Convexity, LLC for short). However, this challenging class of BLOs is lack of developments on both efficient solution strategies and solid theoretical guarantees. In this work, we propose a new algorithmic framework, named Initialization Auxiliary and Pessimistic Trajectory Truncated Gradient Method (IAPTT-GM), to partially address t"},"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":"2110.00455","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-10-01T14:41:17Z","cross_cats_sorted":[],"title_canon_sha256":"2027af54e970cc387a2ac44026bba62fdfc0112c1425f9b935f232d74b2b859d","abstract_canon_sha256":"8548c0f18da111a8e5beff073464f2a1f0bfb1925554b3f833b3323c107ef29b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:26:44.517832Z","signature_b64":"0o1XDESexKysnxnHeWXtVfJZqEnAQMLZtb1Pjb4KqWpn2CuA1ChZIqRM+2rISG9NQAgMO8jJIBzSGUq+PvDUDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a86be441a6de8c8837549bad86dc910931bc32f0c8ef3735607fc31d58645ae8","last_reissued_at":"2026-07-05T03:26:44.517363Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:26:44.517363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Towards Gradient-based Bilevel Optimization with Non-convex Followers and Beyond","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Jin Zhang, Risheng Liu, Shangzhi Zeng, Yaohua Liu","submitted_at":"2021-10-01T14:41:17Z","abstract_excerpt":"In recent years, Bi-Level Optimization (BLO) techniques have received extensive attentions from both learning and vision communities. A variety of BLO models in complex and practical tasks are of non-convex follower structure in nature (a.k.a., without Lower-Level Convexity, LLC for short). However, this challenging class of BLOs is lack of developments on both efficient solution strategies and solid theoretical guarantees. In this work, we propose a new algorithmic framework, named Initialization Auxiliary and Pessimistic Trajectory Truncated Gradient Method (IAPTT-GM), to partially address t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.00455","kind":"arxiv","version":2},"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/2110.00455/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":"2110.00455","created_at":"2026-07-05T03:26:44.517426+00:00"},{"alias_kind":"arxiv_version","alias_value":"2110.00455v2","created_at":"2026-07-05T03:26:44.517426+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.00455","created_at":"2026-07-05T03:26:44.517426+00:00"},{"alias_kind":"pith_short_12","alias_value":"VBV6IQNG32GI","created_at":"2026-07-05T03:26:44.517426+00:00"},{"alias_kind":"pith_short_16","alias_value":"VBV6IQNG32GIQN2U","created_at":"2026-07-05T03:26:44.517426+00:00"},{"alias_kind":"pith_short_8","alias_value":"VBV6IQNG","created_at":"2026-07-05T03:26:44.517426+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/VBV6IQNG32GIQN2UTOWYNXERBE","json":"https://pith.science/pith/VBV6IQNG32GIQN2UTOWYNXERBE.json","graph_json":"https://pith.science/api/pith-number/VBV6IQNG32GIQN2UTOWYNXERBE/graph.json","events_json":"https://pith.science/api/pith-number/VBV6IQNG32GIQN2UTOWYNXERBE/events.json","paper":"https://pith.science/paper/VBV6IQNG"},"agent_actions":{"view_html":"https://pith.science/pith/VBV6IQNG32GIQN2UTOWYNXERBE","download_json":"https://pith.science/pith/VBV6IQNG32GIQN2UTOWYNXERBE.json","view_paper":"https://pith.science/paper/VBV6IQNG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2110.00455&json=true","fetch_graph":"https://pith.science/api/pith-number/VBV6IQNG32GIQN2UTOWYNXERBE/graph.json","fetch_events":"https://pith.science/api/pith-number/VBV6IQNG32GIQN2UTOWYNXERBE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VBV6IQNG32GIQN2UTOWYNXERBE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VBV6IQNG32GIQN2UTOWYNXERBE/action/storage_attestation","attest_author":"https://pith.science/pith/VBV6IQNG32GIQN2UTOWYNXERBE/action/author_attestation","sign_citation":"https://pith.science/pith/VBV6IQNG32GIQN2UTOWYNXERBE/action/citation_signature","submit_replication":"https://pith.science/pith/VBV6IQNG32GIQN2UTOWYNXERBE/action/replication_record"}},"created_at":"2026-07-05T03:26:44.517426+00:00","updated_at":"2026-07-05T03:26:44.517426+00:00"}