Pith Number

pith:SAH3XESM

pith:2026:SAH3XESM4CCNNG6KAWXAXF5D5H

not attested not anchored not stored refs pending

Laplacian Heads Improve Transformers by Smoothing Token Representations

Vardan Papyan, Yuchong Zhang

Replacing some attention heads with Laplacian operators improves Transformer performance by enabling beneficial smoothing of token representations.

arxiv:2602.09297 v3 · 2026-02-10 · cs.LG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SAH3XESM4CCNNG6KAWXAXF5D5H}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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

We show that this simple modification improves performance across supervised learning, language modeling, and self-supervised learning tasks.

C2weakest assumption

That the performance gains are caused by the smoothing mechanism of the Laplacian heads rather than incidental changes in optimization dynamics or capacity.

C3one line summary

Laplacian heads replace some attention matrices with I minus P in Transformers, improving performance by smoothing tokens and challenging the view that oversmoothing is always detrimental.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:00:34.094185Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

900fbb924ce084d69bca05ae0b97a3e9df2ab81f3a0b8f856e9663f8b3fedd12

Aliases

arxiv: 2602.09297 · arxiv_version: 2602.09297v3 · doi: 10.48550/arxiv.2602.09297 · pith_short_12: SAH3XESM4CCN · pith_short_16: SAH3XESM4CCNNG6K · pith_short_8: SAH3XESM

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/SAH3XESM4CCNNG6KAWXAXF5D5H \
  | 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: 900fbb924ce084d69bca05ae0b97a3e9df2ab81f3a0b8f856e9663f8b3fedd12

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dc3fd782ca89fbf7dced4a2c33c9570a63fc9516e542b48be878274c8040a072",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-02-10T00:27:45Z",
    "title_canon_sha256": "81ee95e16ae3ba4d92318d7139e17d4b6c70c2ebeaa1fef635dd73709e30eed4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.09297",
    "kind": "arxiv",
    "version": 3
  }
}