Pith Number

pith:VDSUBEEG

pith:2026:VDSUBEEG553OQFM2TYCDXDT6Q5

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Neural Point-Forms

Bruno Trentini, Ekaterina S. Ivshina, Jacob Hume, Kelly Maggs, Philipp Misof, Vincenzo Antonio Isoldi

Neural point-forms represent point clouds as learned comparison matrices of differential forms.

arxiv:2605.15524 v1 · 2026-05-15 · cs.LG · cs.AI · math.DG · math.ST · stat.TH

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4 Citations open

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Claims

C1strongest claim

We introduce a new family of principled learnable geometric features for point clouds called neural point-forms (NPFs). [...] We make this intuition precise by proving the long-run consistency of comparison matrices under standard sampling, bandwidth, density, and manifold-hypothesis assumptions. This yields a compact, efficient and permutation-invariant neural layer whose output is a learned form-comparison matrix.

C2weakest assumption

The long-run consistency of comparison matrices holds under standard sampling, bandwidth, density, and manifold-hypothesis assumptions, as invoked to justify the theoretical foundation for the neural layer.

C3one line summary

Neural point-forms are introduced as permutation-invariant neural layers that output learned form-comparison matrices for point clouds, with a claimed consistency proof under sampling and manifold assumptions and competitive results on synthetic and biological data.

References

106 extracted · 106 resolved · 7 Pith anchors

[1] Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges 2021 · arXiv:2104.13478

[2] Justin Gilmer, Samuel S. Schoenholz, Patrick F. Riley, Oriol Vinyals, and George E. Dahl. Neural message passing for quantum chemistry. InICML, 2017 2017

[3] Relational inductive biases, deep learning, and graph networks 2018 · arXiv:1806.01261

[4] Hamilton, Rex Ying, and Jure Leskovec

[5] Inductive Representation Learning on Large Graphs · arXiv:1706.02216

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:03.222127Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8e5409086ef76e8159a9e043b8e7e87677df9e8ac70248b6a95bf67386f3a04

Aliases

arxiv: 2605.15524 · arxiv_version: 2605.15524v1 · doi: 10.48550/arxiv.2605.15524 · pith_short_12: VDSUBEEG553O · pith_short_16: VDSUBEEG553OQFM2 · pith_short_8: VDSUBEEG

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/VDSUBEEG553OQFM2TYCDXDT6Q5 \
  | 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: a8e5409086ef76e8159a9e043b8e7e87677df9e8ac70248b6a95bf67386f3a04

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9a6f0e73ef6f02df1ed8e331a11b4649b4cb3bdc9796823f6351f6dc1eade060",
    "cross_cats_sorted": [
      "cs.AI",
      "math.DG",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-15T01:44:31Z",
    "title_canon_sha256": "1b53ccf7bc06c20ccd63b3fe6d60025f765de79c5fc13f1d6c0e8f9f175648b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15524",
    "kind": "arxiv",
    "version": 1
  }
}