Pith Number

pith:LY6PQ5M3

pith:2026:LY6PQ5M3CSJK5Q4JACPDVWJQBF

not attested not anchored not stored refs pending

Mechanistic Evidence for Spectral Structures in Prior-Data Fitted Networks

Kaustubh Sharma, Ojasva Nema, Parikshit Pareek, Srijan Tiwari

PFNs encode spectral information in attention scores that is causally used for predictions and extractable as explicit kernels.

arxiv:2601.21731 v2 · 2026-01-29 · cs.LG

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\pithnumber{LY6PQ5M3CSJK5Q4JACPDVWJQBF}

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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

Probing, activation patching, and subspace interventions establish that spectral information is linearly decodable from PFN latent attention scores, causally used for prediction, concentrated in a low-dimensional subspace, and extractable via a Filter Bank Decoder as explicit stationary kernels that support competitive GP regression in a single forward pass.

C2weakest assumption

That the linearly decodable spectral directions identified by probing and interventions are the actual mechanism driving the PFN's Bayesian predictions rather than a correlated side effect of training on continuous regression tasks.

C3one line summary

PFNs learn linearly decodable spectral information in attention latents that is causally used for prediction and extractable as explicit kernels via a Filter Bank Decoder supporting competitive one-pass GP regression.

Receipt and verification

First computed	2026-05-18T03:09:24.118112Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e3cf8759b1492aec389009e3ad9300975d9cb2a8113ea8cf86e031f303fe230

Aliases

arxiv: 2601.21731 · arxiv_version: 2601.21731v2 · doi: 10.48550/arxiv.2601.21731 · pith_short_12: LY6PQ5M3CSJK · pith_short_16: LY6PQ5M3CSJK5Q4J · pith_short_8: LY6PQ5M3

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/LY6PQ5M3CSJK5Q4JACPDVWJQBF \
  | 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: 5e3cf8759b1492aec389009e3ad9300975d9cb2a8113ea8cf86e031f303fe230

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5fbf04465a93c6ba16c6d132c13f342ab55f5a780b29a04ded37b2e7d4b731f6",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-01-29T13:51:26Z",
    "title_canon_sha256": "42153520386bf76a0bd4e24f28e20ccc51f0c504cebf39a24a2524f09f5730f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.21731",
    "kind": "arxiv",
    "version": 2
  }
}