{"paper":{"title":"NOFE - Neural Operator Function Embedding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Neural Operator Function Embedding learns function-to-function mappings to reduce dimensionality while preserving continuous domain structures.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Arnt-B{\\o}rre Salberg, Georgios Leontidis, Harald L. Joakimsen, Kristoffer K. Wickstr{\\o}m, Lars Uebbing, Michael C. Kampffmeyer, Robert Jenssen, S\\'ebastien Lef\\`evre, Siyan Chen","submitted_at":"2026-05-12T11:25:52Z","abstract_excerpt":"Most dimensionality reduction methods treat data as discrete point clouds, ignoring the continuous domain structure inherent to many real-world processes. To bridge this gap, we introduce Neural Operator Function Embedding (NOFE), a domain-aware framework for continuous dimensionality reduction. NOFE learns function-to-function mappings via a Graph Kernel Operator, enabling mesh-free evaluation at arbitrary query locations independent of input discretization. We establish NOFE as approximation of sheaf-to-sheaf mappings, generalizing Sheaf Neural Networks to continuous domains. We evaluate NOF"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Our results demonstrate that NOFE significantly outperforms baselines in local structure preservation, achieving a local Stress of 0.111 compared to 0.398 for PCA, 0.773 for t-SNE, and 0.791 for UMAP for the ERA5 climate reanalysis dataset. NOFE also exhibits robust sampling independence, reducing the Patch Stitching Error by up to 20.0× relative to UMAP.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That real-world processes possess an inherent continuous domain structure that can be faithfully captured by function-to-function mappings via the Graph Kernel Operator, and that this operator provides a valid approximation to sheaf-to-sheaf mappings on continuous domains.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"NOFE learns continuous function-to-function embeddings via graph kernel operators, outperforming PCA, t-SNE, and UMAP in local structure preservation on function-valued datasets like ERA5 while remaining robust to sampling changes.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Neural Operator Function Embedding learns function-to-function mappings to reduce dimensionality while preserving continuous domain structures.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"92f35656a1840eea98f3c3b68485f97f5a9b38217a18a069843d263d520177e3"},"source":{"id":"2605.11970","kind":"arxiv","version":2},"verdict":{"id":"e1b08a44-a975-4438-87fb-3f5c8c4f06e9","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-13T07:34:06.090061Z","strongest_claim":"Our results demonstrate that NOFE significantly outperforms baselines in local structure preservation, achieving a local Stress of 0.111 compared to 0.398 for PCA, 0.773 for t-SNE, and 0.791 for UMAP for the ERA5 climate reanalysis dataset. NOFE also exhibits robust sampling independence, reducing the Patch Stitching Error by up to 20.0× relative to UMAP.","one_line_summary":"NOFE learns continuous function-to-function embeddings via graph kernel operators, outperforming PCA, t-SNE, and UMAP in local structure preservation on function-valued datasets like ERA5 while remaining robust to sampling changes.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That real-world processes possess an inherent continuous domain structure that can be faithfully captured by function-to-function mappings via the Graph Kernel Operator, and that this operator provides a valid approximation to sheaf-to-sheaf mappings on continuous domains.","pith_extraction_headline":"Neural Operator Function Embedding learns function-to-function mappings to reduce dimensionality while preserving continuous domain structures."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.11970/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T11:34:53.459275Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T09:01:17.217313Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T08:03:06.842907Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"3f31397d51720e410a78d8c70fdb0e6817a255deb1b88fc23d65a63eb53935a2"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"a4b7a0a3cea26bb5695ea5fb22f4128a314b2c5bccee35f8babf33f2315209ca"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}