{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:DV5JSGR2ICEKKBTT56VHDLIKNC","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":"79eef1d802f2b15f93cc656d5a06a4d350e9a5dd37bda1bdfbc7c94292c2d946","cross_cats_sorted":["cs.NA","math.NA","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-21T16:57:33Z","title_canon_sha256":"7767bcc5476d19e0e2c273db73eab76b47c7b0c58ab2e0ef39e137506400b7a3"},"schema_version":"1.0","source":{"id":"2605.22724","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.22724","created_at":"2026-05-22T02:04:52Z"},{"alias_kind":"arxiv_version","alias_value":"2605.22724v1","created_at":"2026-05-22T02:04:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.22724","created_at":"2026-05-22T02:04:52Z"},{"alias_kind":"pith_short_12","alias_value":"DV5JSGR2ICEK","created_at":"2026-05-22T02:04:52Z"},{"alias_kind":"pith_short_16","alias_value":"DV5JSGR2ICEKKBTT","created_at":"2026-05-22T02:04:52Z"},{"alias_kind":"pith_short_8","alias_value":"DV5JSGR2","created_at":"2026-05-22T02:04:52Z"}],"graph_snapshots":[{"event_id":"sha256:cd0401120ac99ae41203707df1b36eb8221f49c9b467d5e6f35df0318cb2032b","target":"graph","created_at":"2026-05-22T02:04:52Z","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/2605.22724/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the approximation and statistical complexity of learning collections of operators in a shared multi-task setting, with a focus on the Multiple Neural Operators (MNO) architecture. For broad classes of Lipschitz multiple operator maps, we derive near-optimal upper bounds for approximation and statistical generalization. On the lower-bound side, we establish a curse of parametric complexity and prove corresponding minimax rates. Together, these results show that shared representations across tasks do not increase the overall cost: multi-task operator learning follows the same scaling la","authors_text":"Adrien Weihs, Hayden Schaeffer","cross_cats":["cs.NA","math.NA","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-21T16:57:33Z","title":"Multiple Neural Operators Achieve Near-Optimal Rates for Multi-Task Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22724","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":"sha256:4cd0f727b11ce308886fad6d168d780e77958cbcafb269f9b1cee8affaa4be19","target":"record","created_at":"2026-05-22T02:04:52Z","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":"79eef1d802f2b15f93cc656d5a06a4d350e9a5dd37bda1bdfbc7c94292c2d946","cross_cats_sorted":["cs.NA","math.NA","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-21T16:57:33Z","title_canon_sha256":"7767bcc5476d19e0e2c273db73eab76b47c7b0c58ab2e0ef39e137506400b7a3"},"schema_version":"1.0","source":{"id":"2605.22724","kind":"arxiv","version":1}},"canonical_sha256":"1d7a991a3a4088a50673efaa71ad0a689a781c1171ca23a6c4f770c0666af422","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d7a991a3a4088a50673efaa71ad0a689a781c1171ca23a6c4f770c0666af422","first_computed_at":"2026-05-22T02:04:52.043411Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T02:04:52.043411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"av8ddQoTVzLJHKIyqkLP7EokmwxkLu0ft+gr4kh/p18Sy5vcfe830gYW4krdnAWY6AVT1968O/wfp9f/xdZoDg==","signature_status":"signed_v1","signed_at":"2026-05-22T02:04:52.044010Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.22724","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4cd0f727b11ce308886fad6d168d780e77958cbcafb269f9b1cee8affaa4be19","sha256:cd0401120ac99ae41203707df1b36eb8221f49c9b467d5e6f35df0318cb2032b"],"state_sha256":"23421d2aa9f3839fef609c46c310fbf2d82c41bc604c1067f7f926760168b01d"}