Pith Number

pith:KXHWQWJR

pith:2026:KXHWQWJROEYUERR656X7RQJWGM

not attested not anchored not stored refs resolved

Discretizing Group-Convolutional Neural Networks for 3D Geometry in Feature Space

Daniel Franzen, Jean Philip Filling, Michael Wand

Sampling transformations in feature space preserves accuracy in group-convolutional networks for 3D geometry while reducing costs.

arxiv:2605.15368 v1 · 2026-05-14 · cs.CV · cs.GR · cs.LG

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\usepackage{pith}
\pithnumber{KXHWQWJROEYUERR656X7RQJWGM}

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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

A coarse feature-space sampling already preserves classification accuracy remarkably well, which permits precomputation based on geometric similarity, accelerating the training of equivariant 3D classifiers substantially.

C2weakest assumption

That representative samples selected purely by feature similarity are sufficient to maintain the equivariance properties and accuracy that dense geometric sampling would have provided.

C3one line summary

Feature-space sampling in GCNNs preserves 3D classification accuracy with coarse discretization, enabling precomputation and faster training of equivariant models.

References

68 extracted · 68 resolved · 3 Pith anchors

[1] Matan Atzmon, Haggai Maron, and Yaron Lipman. 2018. Point Convolutional Neural Networks by Extension Operators. Issue 4 2018

[2] Erik J. Bekkers. 2020. B-Spline CNNs on Lie Groups. InInternational Conference on Learning Representations (ICLR). https://openreview.net/forum?id=H1gBhkBFDH 2020

[3] Bekkers, Sharvaree Vadgama, Rob D 2024

[4] Daniel Bolya, Cheng-Yang Fu, Xiaoliang Dai, Peizhao Zhang, Christoph Fe- ichtenhofer, and Judy Hoffman. 2023. Token Merging: Your ViT But Faster. InThe Eleventh International Conference on Learning Re 2023

[5] Johann Brehmer, Sönke Behrends, Pim de Haan, and Taco Cohen. 2024. Does Equivariance Matter at Scale?arXiv preprint arXiv:2410.23179(2024). arXiv:2410.23179 [cs.LG] 2024

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-20T00:00:54.888534Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

55cf685931713142463eefaff8c13633174cebb0bd6166335110dea30f2991e0

Aliases

arxiv: 2605.15368 · arxiv_version: 2605.15368v1 · doi: 10.48550/arxiv.2605.15368 · pith_short_12: KXHWQWJROEYU · pith_short_16: KXHWQWJROEYUERR6 · pith_short_8: KXHWQWJR

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/KXHWQWJROEYUERR656X7RQJWGM \
  | 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: 55cf685931713142463eefaff8c13633174cebb0bd6166335110dea30f2991e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c0f100e5e99f85d79c8d4149393bb5424a90de0bb430ab70f9e95d56f323c53d",
    "cross_cats_sorted": [
      "cs.GR",
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CV",
    "submitted_at": "2026-05-14T19:47:43Z",
    "title_canon_sha256": "162b02cc3b151bf4c89920e7f54cde2d10b42dce221172b02e51fc07416ff144"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15368",
    "kind": "arxiv",
    "version": 1
  }
}