Pith Number

pith:IPPKFWT7

pith:2026:IPPKFWT7OXIN3RNZ7DJ2POAB2G

not attested not anchored not stored refs pending

Sheaf Neural Networks on SPD Manifolds: Second-Order Geometric Representation Learning

Anna Wienhard, Ce Ju, Diaaeldin Taha, Hao Li, Huitao Feng, Junwen Dong, Kelin Xia, Yuhan Peng, Yuzhi Zeng

Sheaf neural networks defined on SPD manifolds represent second-order geometric features that Euclidean sheaves cannot.

arxiv:2604.20308 v2 · 2026-04-22 · cs.LG

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\usepackage{pith}
\pithnumber{IPPKFWT7OXIN3RNZ7DJ2POAB2G}

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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

SPD-valued sheaves are strictly more expressive than Euclidean sheaves: they admit consistent configurations (global sections) that vector-valued sheaves cannot represent, directly translating to richer learned representations.

C2weakest assumption

The SPD manifold admits a Lie group structure, enabling well-posed analogs of sheaf operators without projecting to Euclidean space.

C3one line summary

Sheaf neural networks on the SPD manifold enable strictly more expressive second-order geometric representations than Euclidean versions and achieve SOTA results on most MoleculeNet benchmarks.

Cited by

2 papers in Pith

Consistent Geometric Deep Learning via Hilbert Bundles and Cellular Sheaves

Receipt and verification

First computed	2026-06-02T01:04:16.374169Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

43dea2da7f75d0ddc5b9f8d3a7b801d1b619d19a2eb612d61b23e5b439bca9b6

Aliases

arxiv: 2604.20308 · arxiv_version: 2604.20308v2 · doi: 10.48550/arxiv.2604.20308 · pith_short_12: IPPKFWT7OXIN · pith_short_16: IPPKFWT7OXIN3RNZ · pith_short_8: IPPKFWT7

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/IPPKFWT7OXIN3RNZ7DJ2POAB2G \
  | 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: 43dea2da7f75d0ddc5b9f8d3a7b801d1b619d19a2eb612d61b23e5b439bca9b6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f5549ba833101d593dd239458d6397f2e4585a000a195db877d61efbc159d2af",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-04-22T08:09:04Z",
    "title_canon_sha256": "b5963ee4779632999bcc18c88b0af1e9e80484c837b5940b929e3a2fdae86fe5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.20308",
    "kind": "arxiv",
    "version": 2
  }
}