{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:2FNJUORZHB3GIPYC3OJUEBVSOD","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":"379051e74167ad5e212b8ff9218e2821d709f0c4909c71452a5322c9d9285edd","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-04-03T18:14:23Z","title_canon_sha256":"135a9368f5c90bbde295784f161ef7f6d0186b713cdb2d6d5dfc3143a91469af"},"schema_version":"1.0","source":{"id":"2404.02986","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.02986","created_at":"2026-07-05T09:40:56Z"},{"alias_kind":"arxiv_version","alias_value":"2404.02986v3","created_at":"2026-07-05T09:40:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.02986","created_at":"2026-07-05T09:40:56Z"},{"alias_kind":"pith_short_12","alias_value":"2FNJUORZHB3G","created_at":"2026-07-05T09:40:56Z"},{"alias_kind":"pith_short_16","alias_value":"2FNJUORZHB3GIPYC","created_at":"2026-07-05T09:40:56Z"},{"alias_kind":"pith_short_8","alias_value":"2FNJUORZ","created_at":"2026-07-05T09:40:56Z"}],"graph_snapshots":[{"event_id":"sha256:ea379824f301eb6b16d37b3cc5cfd121311887443c1a07258203eb8cee13e275","target":"graph","created_at":"2026-07-05T09:40:56Z","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/2404.02986/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Regression on function spaces is typically limited to models with Gaussian process priors. We introduce the notion of universal functional regression, in which we aim to learn a prior distribution over non-Gaussian function spaces that remains mathematically tractable for functional regression. To do this, we develop Neural Operator Flows (OpFlow), an infinite-dimensional extension of normalizing flows. OpFlow is an invertible operator that maps the (potentially unknown) data function space into a Gaussian process, allowing for exact likelihood estimation of functional point evaluations. OpFlo","authors_text":"Angela F. Gao, Kamyar Azizzadenesheli, Yaozhong Shi, Zachary E. Ross","cross_cats":["stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-04-03T18:14:23Z","title":"Universal Functional Regression with Neural Operator Flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.02986","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":"sha256:67f979b6a9bfc2a15f5a84055d289d1e6c4191876c67a45779dff1538eb0dd9c","target":"record","created_at":"2026-07-05T09:40:56Z","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":"379051e74167ad5e212b8ff9218e2821d709f0c4909c71452a5322c9d9285edd","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-04-03T18:14:23Z","title_canon_sha256":"135a9368f5c90bbde295784f161ef7f6d0186b713cdb2d6d5dfc3143a91469af"},"schema_version":"1.0","source":{"id":"2404.02986","kind":"arxiv","version":3}},"canonical_sha256":"d15a9a3a393876643f02db934206b270fed63ce95cb3aeb36ea07545f3eed939","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d15a9a3a393876643f02db934206b270fed63ce95cb3aeb36ea07545f3eed939","first_computed_at":"2026-07-05T09:40:56.343484Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:40:56.343484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wAd73Uueue/FQCMWGZUgVFoqZRXy+EW6QUNiNBtO8P9mJ5bPcfTIc/ZDAdy9QS2f68D0AFe6yoGO8d4z+ZLRAw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:40:56.344060Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.02986","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67f979b6a9bfc2a15f5a84055d289d1e6c4191876c67a45779dff1538eb0dd9c","sha256:ea379824f301eb6b16d37b3cc5cfd121311887443c1a07258203eb8cee13e275"],"state_sha256":"8a451846cf7a421597c7eafe3b594d4d6ba219790d2a424c69b912c7ed3db008"}