{"_canonicalization":{"envelope_id":"axm_ + sha256(envelope minus {signature, axiom_id, anchors})","envelope_signature":"ed25519(envelope minus {signature, axiom_id})","json":"sort_keys=True, separators=(',',':'), ensure_ascii=False, allow_nan=False, utf-8","leaf_hash":"sha256(0x00 || canonical_json(envelope_full))","seal_signature":"ed25519(seal minus {signature, sig_algorithm})"},"axiom_id":"axm_7ae16de233dd62f63850dcdf16476894cb380cacd4d90aaac190f1748a41f3e3","bitcoin_anchor":{"bitcoin_attestations":[],"calendar_attestations":[],"ots_url":"","stamped_at":"","status":"pending_next_stamp"},"envelope":{"anchors":[{"chain":"crovia.axiom_graph","height":0,"merkle_proof":"spider_vendor_press_v1","root_at_anchor":"spider_vendor_press_v1"}],"axiom_id":"axm_7ae16de233dd62f63850dcdf16476894cb380cacd4d90aaac190f1748a41f3e3","axiom_type":"AX.OBS","body":{"axiom_subtype":"news.vendor_press.v1","category":"news","fingerprint":"2dd1e8de309631631d0efccebd44bcf4c2dcae998ab95e8caf21c9c536a328a6","published":"Tue, 14 Jul 2026 00:00:00 -0400","receipt_hash":"2dd1e8de309631631d0efccebd44bcf4c2dcae998ab95e8caf21c9c536a328a6","schema":"spider.news.vendor_press.v1","spider":"vendor_press","spider_record":{"axiom_subtype":"news.vendor_press.v1","category":"news","decision_hint":"POSITIVE","envelope_target":"AX.OBS","fingerprint":"2dd1e8de309631631d0efccebd44bcf4c2dcae998ab95e8caf21c9c536a328a6","observed_at":"2026-07-14T04:43:37.834979Z","parent_run_hash":"66b89520a448b8d9fe7d8f602ef38b82b6c95e57f532ce72de51375b41870477","published":"Tue, 14 Jul 2026 00:00:00 -0400","runtime_version":"0.1.0","schema":"spider.news.vendor_press.v1","source_status":200,"source_url":"https://export.arxiv.org/rss/cs.AI","spider":"vendor_press","summary_excerpt":"arXiv:2511.22331v3 Announce Type: replace-cross \nAbstract: Bilevel optimization minimizes an objective function, defined by an upper-level problem whose feasible region is the solution of a lower-level problem. We study the oracle complexity of finding an $\\epsilon$-stationary point with first-order methods when the upper-level problem is nonconvex, and the lower-level problem is strongly convex. Recent works (Ji et al., ICML 2021; Arbel and Mairal, ICLR 2022; Chen et al., JMLR 2025) achieve a $\\tilde{\\mathcal{O}}(\\bar \\kappa_y^4 \\epsilon^{-2})$ upper bound that is near-optimal in $\\epsilon$, which can be reduced to $\\tilde{\\mathcal{O}}(\\bar \\kappa_y^{7/2} \\epsilon^{-2})$ by a naive application of Nesterov acceleration in the inner loop, where $\\bar \\kappa_y$ is the global condition number. However, the optimal dependency on the condition number is unknown. In this work, we establish a new $\\Omega(\\kappa_y^{5/2} \\epsilon^{-2})$ lower bound, where $\\kappa_y < \\bar \\kappa_y$ is the lower","title":"On the Condition Number Dependency in Bilevel Optimization","url":"https://arxiv.org/abs/2511.22331","vendor":"arxiv_cs_ai"},"summary":"arXiv:2511.22331v3 Announce Type: replace-cross \nAbstract: Bilevel optimization minimizes an objective function, defined by an upper-level problem whose feasible region is the solution of a lower-level problem. We study the oracle complexity of finding an $\\epsilon$-stationary point with first-order methods when the upper-level problem is nonconvex, and the lower-level problem is strongly convex. Recent works (Ji et al., ICML 2021; Arbel and Mairal, ICLR 2022; Chen et al., JMLR 2025) achieve a $\\tilde{\\mathcal{O}}(\\bar \\kappa_y^4 \\epsilon^{-2})$ upper bound that is near-optimal in $\\epsilon$, which can be reduced to $\\tilde{\\mathcal{O}}(\\bar \\kappa_y^{7/2} \\epsilon^{-2})$ by a naive application of Nesterov acceleration in the inner loop, where $\\bar \\kappa_y$ is the global condition number. However, the optimal dependency on the condition number is unknown. In this work, we establish a new $\\Omega(\\kappa_y^{5/2} \\epsilon^{-2})$ lower bound, where $\\kappa_y < \\bar \\kappa_y$ is the lower","title":"On the Condition Number Dependency in Bilevel Optimization","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-14T04:43:37Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2511.22331"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:2801d6256433723a2ee43183e1f17a0dea29500b515da9af69386502cee513f902c2f497142f0d95b664c91597e0b9f9c336f613b693984bea2ea7e2dd09bc02","signer":"crovia.substrate","subject":{"observed_at":"2026-07-14T04:43:37Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2511.22331"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"463872a27a3b47978886bd1674a3c769eaddedeb7ae2b4c8e492f8d3255a7a9b","leaf_index":313184,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"62c0fe15d1fe3776444af8cfabd12ad58424f4e2d44e063d1feda4cedd465c56","side":"right"},{"sibling":"ae828835f67ad26180bdadc1605ad5501a7718bed51b0d695495140431373e1a","side":"right"},{"sibling":"df5ced943419dbe88213ca29af2129d8ec3184a8b77c858440fa9ebd04b9562e","side":"right"},{"sibling":"02cf0343d5718ebc38cb6f711e11a80394bca8408a0b2959a480781ddedc906d","side":"right"},{"sibling":"e3efb21b407a8a3cd925f0e4bd04ae259fa3cb3a6ca2bfd971d3e1bc5001b378","side":"right"},{"sibling":"8aada29eba3e9c831319c79336b0d83c3c9d322066309633aa9f715da7e5ca28","side":"left"},{"sibling":"242ec9ba910918e34f549c2e0edeb1bb80f79a3991e32c51c92f262711ff9ed9","side":"left"},{"sibling":"edf133a890c50dc04a7d212f979f1424434d765ec9a191894fda402b340d9450","side":"right"},{"sibling":"ae8fbfdec46ce02d0a92359c6a034f0439394d13e731da90290f5ca7192e6da4","side":"left"},{"sibling":"8393dc03644000353c5d503b6ec261c022cd2aa85a649223916153bc8af2dc75","side":"left"},{"sibling":"1627ce6908965f2e5fbc7c16bc8e247867478c587014561d0de1359dc2dc0afc","side":"left"},{"sibling":"74e1ba9fd48bdd0f52777dd5b56c10706e73f42629013748eca13ef113cd59db","side":"right"},{"sibling":"682fd39539db5bce908d0ab6f180374728fed6b34a9a8c87c7b4eb5a726e30b8","side":"right"},{"sibling":"184927f71d667ac0c6ebeadb33394626973738b9107c6dc3c0c4949b44acf295","side":"right"},{"sibling":"f302542c38ba7c3aab7c9280dd60259ecec777dca6e6f71b6f0729b0b8791b72","side":"left"},{"sibling":"d8b9143917b539c543cf4448cec00131f8b807bd8004979c54ebe09798748c66","side":"left"},{"sibling":"c4c189d79669979b59d9aa976ee249c54a7e065b4a05bf49463459cc7f37428e","side":"right"},{"sibling":"19475e206bdf2698769a286db2c97c4d3f089741319f9b29a139038c6e511975","side":"right"},{"sibling":"1cecb7f447febd025aac272837c80de218aecc6485d2395a509b2a1f1b9c746e","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":313381,"merkle_root":"5f7d48580373d0ab0bc6bdf34f26de442f9a86d130946f7ee45addd1a55cb9f4","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260714T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-14T05:38:23Z","sig_algorithm":"ed25519","signature":"97364224142ed1b2a8925fed1bfba2e0a8a6a15f8ca0999b934846ad83584a78c7f0f5cd09dbc1c938b35383fcc5c8fa4b723118e30916628879d1c5fd3a9908","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_7ae16de233dd62f63850dcdf16476894cb380cacd4d90aaac190f1748a41f3e3"}}