Pith Number

pith:WOOKY7V5

pith:2025:WOOKY7V5BJOB4RIWY7BHVSVJWT

not attested not anchored not stored refs pending

Statistical physics of deep learning: Optimal learning of a multi-layer perceptron near interpolation

Francesco Camilli, Jean Barbier, Mauro Pastore, Minh-Toan Nguyen, Rudy Skerk

arxiv:2510.24616 v4 · 2025-10-28 · stat.ML · cond-mat.dis-nn · cond-mat.stat-mech · cs.IT · cs.LG · math.IT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WOOKY7V5BJOB4RIWY7BHVSVJWT}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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.

Cited by

4 papers in Pith

Statistical Properties of Training & Generalization

Signal-to-Noise Ratio and Sample Size Govern Representational Alignment in Neural Networks

Asymmetric Scaling Laws from Sparse Features

There Will Be a Scientific Theory of Deep Learning

Receipt and verification

First computed	2026-07-24T01:24:04.509352Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b39cac7ebd0a5c1e4516c7c27acaa9b4f57d19aae10b201b157abe645055c55a

Aliases

arxiv: 2510.24616 · arxiv_version: 2510.24616v4 · doi: 10.48550/arxiv.2510.24616 · pith_short_12: WOOKY7V5BJOB · pith_short_16: WOOKY7V5BJOB4RIW · pith_short_8: WOOKY7V5

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/WOOKY7V5BJOB4RIWY7BHVSVJWT \
  | 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: b39cac7ebd0a5c1e4516c7c27acaa9b4f57d19aae10b201b157abe645055c55a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a51ae2281b735c03f3cf5ccccb8e4d3c323b66e76e90c10c5653c84cede1b9b8",
    "cross_cats_sorted": [
      "cond-mat.dis-nn",
      "cond-mat.stat-mech",
      "cs.IT",
      "cs.LG",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2025-10-28T16:44:34Z",
    "title_canon_sha256": "c76c1bbc96eb6dd8060e7d22e65a575dc2f1862440a190f3e2cb9b2290182bdd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.24616",
    "kind": "arxiv",
    "version": 4
  }
}