Pith Number

pith:QVL7Y3HR

pith:2026:QVL7Y3HRHQ6NMD3QS653LTLBEG

not attested not anchored not stored refs pending

Beyond Linear Attention: Softmax Transformers Implement In-Context Reinforcement Learning

Claire Chen, Rohan Chandra, Shangtong Zhang, Shuze Daniel Liu, Xinyu Liu, Zixuan Xie

Softmax attention in Transformers computes iterative updates of a weighted softmax TD learning algorithm across layers.

arxiv:2605.07333 v2 · 2026-05-08 · cs.LG

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\usepackage{pith}
\pithnumber{QVL7Y3HRHQ6NMD3QS653LTLBEG}

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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

with certain parameters, the layerwise forward pass of a Transformer with such softmax attention is equivalent to iterative updates of a weighted softmax temporal difference (TD) learning algorithm.

C2weakest assumption

The existence of specific parameters that simultaneously achieve the forward-pass equivalence, satisfy the contraction condition for error decay, and globally minimize the pretraining loss.

C3one line summary

Softmax Transformers with specific parameters implement iterative weighted softmax TD learning for in-context policy evaluation, with evaluation error decaying over layers and those parameters globally minimizing pretraining loss.

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-20T00:03:14.782992Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8557fc6cf13c3cd60f7097bbb5cd612188fd06e6c8d80549a64b31ee0c92bf21

Aliases

arxiv: 2605.07333 · arxiv_version: 2605.07333v2 · doi: 10.48550/arxiv.2605.07333 · pith_short_12: QVL7Y3HRHQ6N · pith_short_16: QVL7Y3HRHQ6NMD3Q · pith_short_8: QVL7Y3HR

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/QVL7Y3HRHQ6NMD3QS653LTLBEG \
  | 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: 8557fc6cf13c3cd60f7097bbb5cd612188fd06e6c8d80549a64b31ee0c92bf21

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef20c4785bfd3d0c313a012adf5467b17f16589b980a02ddc3620d5999e4a6c6",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-08T06:37:51Z",
    "title_canon_sha256": "f4cd6c6fff14e397f96992fe72b8137ed2309dbc9ab7077ac3511ebd71d95017"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.07333",
    "kind": "arxiv",
    "version": 2
  }
}