Pith Number

pith:W7ZVCLE2

pith:2026:W7ZVCLE22AVKXHL7VKSASRGIPE

not attested not anchored not stored refs resolved

Beyond Oversquashing: Understanding Signal Propagation in GNNs Via Observables

Eden Nagar, Ron Levie, Ya-Wei Eileen Lin

Standard spectral GNNs diffuse signals broadly instead of routing them to specific regions, while Schrödinger GNNs maintain better directed propagation.

arxiv:2605.13383 v1 · 2026-05-13 · cs.LG

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\usepackage{pith}
\pithnumber{W7ZVCLE22AVKXHL7VKSASRGIPE}

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Record completeness

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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

We prove that standard spectral GNNs have poor signal propagation capabilities. We then propose a new type of spectral GNN, termed Schrödinger GNN, which we show has a superior capacity to route the signal across the graph.

C2weakest assumption

That the quantum-mechanics-inspired definitions of signal location, concentration, and propagation to a location of interest faithfully capture the discrete, finite-layer behavior of message passing in GNNs.

C3one line summary

Quantum-inspired observables reveal poor signal routing in standard spectral GNNs and motivate Schrödinger GNNs with superior propagation capacity.

References

20 extracted · 20 resolved · 2 Pith anchors

[1] Oversquashing in gnns through the lens of information contraction and graph expansion

[2] A generalization of transformer networks to graphs 2012

[3] doi: 10.1002/mana.202100466 · doi:10.1002/mana.202100466

[4] Adam: A Method for Stochastic Optimization · arXiv:1412.6980

[5] Semi-Supervised Classification with Graph Convolutional Networks · arXiv:1609.02907

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:47.811738Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7f3512c9ad02aab9d7faaa40944c879097a9238fd4677c1fb901190c822b822

Aliases

arxiv: 2605.13383 · arxiv_version: 2605.13383v1 · doi: 10.48550/arxiv.2605.13383 · pith_short_12: W7ZVCLE22AVK · pith_short_16: W7ZVCLE22AVKXHL7 · pith_short_8: W7ZVCLE2

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/W7ZVCLE22AVKXHL7VKSASRGIPE \
  | 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: b7f3512c9ad02aab9d7faaa40944c879097a9238fd4677c1fb901190c822b822

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b752c8442ff87d15a1d0de3ac7a0b50938aa40c01c7ffb78850565773b37c607",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-13T11:38:35Z",
    "title_canon_sha256": "de105de8017823c6187a4faaacdb4d9ff19d527a74759c32f065756f6a3aeeff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13383",
    "kind": "arxiv",
    "version": 1
  }
}