Pith Number

pith:OIPHSS7T

pith:2026:OIPHSS7TJ6NNB6YXGDEQE3Q5KZ

not attested not anchored not stored refs resolved

Scaling Laws from Sequential Feature Recovery: A Solvable Hierarchical Model

Arie Wortsman-Zurich, Bruno Loureiro, Florent Krzakala, Hugo Tabanelli, Yatin Dandi

A layer-wise spectral algorithm on a hierarchical target with power-law feature weights recovers latent directions sequentially and aggregates their sharp thresholds into an explicit power-law decay of prediction error.

arxiv:2605.14567 v1 · 2026-05-14 · stat.ML · cs.LG · math.PR · math.ST · stat.TH

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\usepackage{pith}
\pithnumber{OIPHSS7TJ6NNB6YXGDEQE3Q5KZ}

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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

aggregating these transitions yields an explicit power-law decay of the prediction error

C2weakest assumption

the high-dimensional target admits a representation as a combination of latent compositional features whose weights decrease as a power law, and that the layer-wise spectral algorithm is specifically adapted to this compositional structure

C3one line summary

A solvable hierarchical model with power-law feature strengths yields explicit power-law scaling of prediction error through sequential recovery of latent directions by a layer-wise spectral algorithm.

References

187 extracted · 187 resolved · 7 Pith anchors

[1] Random matrix methods for machine learning , author=. 2022 , publisher= 2022

[2] Introduction to the non-asymptotic analysis of random matrices · arXiv:1011.3027

[3] Applied and Computational Harmonic Analysis , volume= 2022

[4] Bert: Pre-training of deep bidirectional transformers for language understanding , author=. Proceedings of the 2019 conference of the North American chapter of the association for computational lingui 2019

[5] arXiv preprint arXiv:2305.15501 , year=

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:05.519254Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

721e794bf34f9ad0fb1730c9026e1d56748be3ba441a947fe8f544ba55b7f10a

Aliases

arxiv: 2605.14567 · arxiv_version: 2605.14567v1 · doi: 10.48550/arxiv.2605.14567 · pith_short_12: OIPHSS7TJ6NN · pith_short_16: OIPHSS7TJ6NNB6YX · pith_short_8: OIPHSS7T

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/OIPHSS7TJ6NNB6YXGDEQE3Q5KZ \
  | 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: 721e794bf34f9ad0fb1730c9026e1d56748be3ba441a947fe8f544ba55b7f10a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4f5e35460f433f2770a89e63256e4742a2edfbeeb4ba2ed24fd0929891281947",
    "cross_cats_sorted": [
      "cs.LG",
      "math.PR",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-05-14T08:37:28Z",
    "title_canon_sha256": "ec3bf8972b912f87282da59ffb84651525cf10c2cfbddf538ad7584caffec381"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14567",
    "kind": "arxiv",
    "version": 1
  }
}