Pith Number

pith:LZ3D3G46

pith:2026:LZ3D3G46VLETAWS6EXEPKPGQD6

not attested not anchored not stored refs resolved

A Unified Framework for Critical Scaling of Inverse Temperature in Self-Attention

Ryo Karakida, Tomohiro Hayase

The critical inverse-temperature scale for self-attention concentration is fixed by an upper-tail accumulation scale derived from the gap-counting function of each attention row.

arxiv:2605.12697 v1 · 2026-05-12 · stat.ML · cs.LG · math.PR

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Claims

C1strongest claim

we define an upper-tail accumulation scale and prove that it gives the critical inverse-temperature scale for softmax concentration: below this scale, the top competitors remain unseparated, whereas above it, the attention entropy collapses.

C2weakest assumption

That the gap-counting function N_n of each attention row fully determines the critical scale and that the attention-score distributions admit well-defined successive gaps from the maximum.

C3one line summary

The upper-tail accumulation scale derived from the gap-counting function N_n sets the critical inverse temperature for softmax attention concentration, unifying prior conflicting laws as special cases of different N_n.

References

32 extracted · 32 resolved · 3 Pith anchors

[1] Attention is all you need 2017

[2] Infinite attention: NNGP and NTK for deep attention networks 2020

[3] Infinite limits of multi-head transformer dynamics 2024

[4] Infinite-width limit of a single attention layer: Analysis via tensor programs 2025

[5] A mathematical perspective on transformers 2025

Formal links

3 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:09:49.753423Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e763d9b9eaac9305a5e25c8f53cd01fa6b455df36ea251d7facbc29d4bf7732

Aliases

arxiv: 2605.12697 · arxiv_version: 2605.12697v1 · doi: 10.48550/arxiv.2605.12697 · pith_short_12: LZ3D3G46VLET · pith_short_16: LZ3D3G46VLETAWS6 · pith_short_8: LZ3D3G46

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/LZ3D3G46VLETAWS6EXEPKPGQD6 \
  | 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: 5e763d9b9eaac9305a5e25c8f53cd01fa6b455df36ea251d7facbc29d4bf7732

Canonical record JSON

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    "abstract_canon_sha256": "c8eee8d2dfea4f8b5dcebcadbf84a54bb0b23d3731d813dcc701e3dc1b3884d1",
    "cross_cats_sorted": [
      "cs.LG",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-05-12T19:48:36Z",
    "title_canon_sha256": "e7e7361a6b0dd8924ec2cb1a074f514b5271392991d61c7399ec9260db43d215"
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  "source": {
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    "kind": "arxiv",
    "version": 1
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