Pith Number

pith:EQ5GSC7X

pith:2025:EQ5GSC7X2PYIYUMXALC7XS2JRI

not attested not anchored not stored refs pending

Scaling Laws and Spectra of Shallow Neural Networks in the Feature Learning Regime

Bruno Loureiro, Emanuele Troiani, Florent Krzakala, Julius Girardin, Lenka Zdeborov\'a, Leonardo Defilippis, Vittorio Erba, Yizhou Xu

arxiv:2509.24882 v2 · 2025-09-29 · cs.LG · cond-mat.dis-nn · cs.AI · stat.ML

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\usepackage{pith}
\pithnumber{EQ5GSC7X2PYIYUMXALC7XS2JRI}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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.

Cited by

6 papers in Pith

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction

Asymmetric Scaling Laws from Sparse Features

Spectral Dynamics in Deep Networks: Feature Learning, Outlier Escape, and Learning Rate Transfer

A Fourier perspective on the learning dynamics of neural networks: from sample complexities to mechanistic insights

Sharp feature-learning transitions and Bayes-optimal neural scaling laws in extensive-width networks

Receipt and verification

First computed	2026-06-05T01:15:16.576800Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

243a690bf7d3f08c519702c5fbcb498a09cdf7f28cf3f4ee1d72be6312440e68

Aliases

arxiv: 2509.24882 · arxiv_version: 2509.24882v2 · doi: 10.48550/arxiv.2509.24882 · pith_short_12: EQ5GSC7X2PYI · pith_short_16: EQ5GSC7X2PYIYUMX · pith_short_8: EQ5GSC7X

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/EQ5GSC7X2PYIYUMXALC7XS2JRI \
  | 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: 243a690bf7d3f08c519702c5fbcb498a09cdf7f28cf3f4ee1d72be6312440e68

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "609e1ee9efe3cdaed0220f12e153e0fc0da0374630233f1a1f47ddc254c9aa85",
    "cross_cats_sorted": [
      "cond-mat.dis-nn",
      "cs.AI",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2025-09-29T14:58:13Z",
    "title_canon_sha256": "7c702dfb3b114423677ab889394327ecc73c6c4cf062de7640d36b9d26ba6635"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.24882",
    "kind": "arxiv",
    "version": 2
  }
}