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pith:XRHRPY3V

pith:2026:XRHRPY3VXSASLXOMVLMFEM5MMZ

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Symmetry Reveals Layerwise Dynamics: How Transformers Perform In-Context Classification

Aditya Gangrade, Arjun Chandra, Patrick Lutz, Themistoklis Haris, Venkatesh Saligrama

By enforcing equivariance under feature and label permutations, transformer layers yield an explicit recursive update rule for in-context classification.

arxiv:2604.11613 v3 · 2026-04-13 · cs.LG · cs.AI

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Claims

C1strongest claim

From these models we extract an explicit depth-indexed recursion: an end-to-end identified, emergent update rule inside a softmax transformer, to our knowledge the first of its kind. Attention matrices formed from mixed feature-label Gram structure drive coupled updates of training points, labels, and the test probe. The resulting dynamics implement a geometry-driven algorithmic motif, which can provably amplify class separation and yields robust expected class alignment.

C2weakest assumption

Enforcing feature- and label-permutation equivariance at every layer maintains functional equivalence to the original transformer while enabling interpretability and yielding highly structured weights from which the recursion can be extracted.

C3one line summary

Enforcing feature- and label-permutation equivariance in transformers for in-context classification yields an identifiable emergent update rule driven by mixed feature-label Gram matrices that amplifies class separation.

Receipt and verification

First computed	2026-06-01T01:03:53.039044Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc4f17e375bc8125ddccaad85233ac667c9793ce5d922d32508e391f225bedb4

Aliases

arxiv: 2604.11613 · arxiv_version: 2604.11613v3 · doi: 10.48550/arxiv.2604.11613 · pith_short_12: XRHRPY3VXSAS · pith_short_16: XRHRPY3VXSASLXOM · pith_short_8: XRHRPY3V

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/XRHRPY3VXSASLXOMVLMFEM5MMZ \
  | 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: bc4f17e375bc8125ddccaad85233ac667c9793ce5d922d32508e391f225bedb4

Canonical record JSON

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      "cs.AI"
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    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-04-13T15:20:41Z",
    "title_canon_sha256": "d7d844326f0106221b2533883244b457176faf2669fcecfcda537d843886a475"
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