Pith Number

pith:SWD5I3U3

pith:2026:SWD5I3U33XUBSWJED4HXLJLXIL

not attested not anchored not stored refs pending

NOFE - Neural Operator Function Embedding

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

Neural Operator Function Embedding learns function-to-function mappings to reduce dimensionality while preserving continuous domain structures.

arxiv:2605.11970 v2 · 2026-05-12 · cs.LG

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\usepackage{pith}
\pithnumber{SWD5I3U33XUBSWJED4HXLJLXIL}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest 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.

C2weakest 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.

C3one 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.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:18.085976Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9587d46e9bdde81959241f0f75a57742e77eb68a9ff523614b91adf39f6802bd

Aliases

arxiv: 2605.11970 · arxiv_version: 2605.11970v2 · doi: 10.48550/arxiv.2605.11970 · pith_short_12: SWD5I3U33XUB · pith_short_16: SWD5I3U33XUBSWJE · pith_short_8: SWD5I3U3

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/SWD5I3U33XUBSWJED4HXLJLXIL \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 9587d46e9bdde81959241f0f75a57742e77eb68a9ff523614b91adf39f6802bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "62fe93ef10cecfd29d3e3a40efcce730f4aa2847715d7f86d2b04b569892cc91",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-12T11:25:52Z",
    "title_canon_sha256": "6311e7d430ac304d737dcfcfc4390dfc869d3f1c0711e2824688bb05b0b2968b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.11970",
    "kind": "arxiv",
    "version": 2
  }
}