Pith Number

pith:QDRDPX6V

pith:2026:QDRDPX6VG2XO2EQ7GT4NP2GWOH

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Residual Stream Duality in Modern Transformer Architectures

Yifan Zhang

The residual stream in Transformers is equivalent to causal short sliding-window attention when interpreted over layer depth instead of sequence positions.

arxiv:2603.16039 v2 · 2026-03-17 · cs.LG · cs.AI · cs.CL

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Record completeness

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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

a causal depth-wise residual attention read is exactly the same local operator as causal short sliding-window attention (ShortSWA), except written over depth rather than over sequence. This is the core residual stream duality behind Transformer².

C2weakest assumption

That treating layer index as an ordered variable and reinterpreting fixed residual addition as causal depth-wise attention produces a meaningful and actionable operator equivalence, even though the paper states operator-level duality does not imply systems-level symmetry.

C3one line summary

Residual stream addition over depth is the same local operator as causal short sliding-window attention over sequence positions.

Formal links

1 machine-checked theorem link

Cited by

1 paper in Pith

Delta Attention Residuals

Receipt and verification

First computed	2026-05-17T23:38:59.635560Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80e237dfd536aeed121f34f8d7e8d671f4b78230b02122d902ca88241561836d

Aliases

arxiv: 2603.16039 · arxiv_version: 2603.16039v2 · doi: 10.48550/arxiv.2603.16039 · pith_short_12: QDRDPX6VG2XO · pith_short_16: QDRDPX6VG2XO2EQ7 · pith_short_8: QDRDPX6V

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/QDRDPX6VG2XO2EQ7GT4NP2GWOH \
  | 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: 80e237dfd536aeed121f34f8d7e8d671f4b78230b02122d902ca88241561836d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7effd2bd771efce4f30668994ead6c42326b4f138da9003c7778af433e90101c",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.CL"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-03-17T00:56:29Z",
    "title_canon_sha256": "ed2e4cdef73dafbdc8737d75e9c4617db3fe6195084c68ffb224e6e5ca58a20c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.16039",
    "kind": "arxiv",
    "version": 2
  }
}