Pith Number

pith:I3CPQ63N

pith:2026:I3CPQ63NKWO2XCMKN6PTMHPTIJ

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Beyond Linearity in Attention Projections: The Case for Nonlinear Queries

Marko Karbevski

Replacing the linear query projection with identity plus a small bottleneck MLP improves validation log-loss by 2.4 percent in GPT-style models.

arxiv:2603.13381 v3 · 2026-03-11 · cs.LG · cs.AI

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\pithnumber{I3CPQ63NKWO2XCMKN6PTMHPTIJ}

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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

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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

Experiments on GPT-3 small style models show consistent improvement over the baseline (2.40% lower validation log-loss, 6.81% lower perplexity), comfortably outperforming a model with 12.5% more non-embedding parameters.

C2weakest assumption

That the basis transformations absorbed by adjacent layers remain stable when the query projection is made nonlinear and that the small MLP does not introduce optimization instabilities at the tested scale.

C3one line summary

Nonlinear query projections of the form X + MLP(X) improve transformer performance on small models with only d² + O(d) added parameters.

Receipt and verification

First computed	2026-05-27T01:04:57.215379Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

46c4f87b6d559dab898a6f9f361df3427f32d746d42c902acd9afcbbdb567555

Aliases

arxiv: 2603.13381 · arxiv_version: 2603.13381v3 · doi: 10.48550/arxiv.2603.13381 · pith_short_12: I3CPQ63NKWO2 · pith_short_16: I3CPQ63NKWO2XCMK · pith_short_8: I3CPQ63N

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/I3CPQ63NKWO2XCMKN6PTMHPTIJ \
  | 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: 46c4f87b6d559dab898a6f9f361df3427f32d746d42c902acd9afcbbdb567555

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "08ed397f88febbe07b6a0ffb9f291c4479b617a901fa0ccc23215fbf80cc6831",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-03-11T03:13:10Z",
    "title_canon_sha256": "c078383ab9c6950b4a8b2163a0b527fe12d53317c4b9abde170fb63f272e271d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.13381",
    "kind": "arxiv",
    "version": 3
  }
}