Pith Number

pith:VYTKFDUT

pith:2026:VYTKFDUTU36YRB5UQQLEV64VQN

not attested not anchored not stored refs pending

Convergence Analysis of Newton's Method for Neural Networks in the Overparameterized Limit

Justin Sirignano, Konstantinos Spiliopoulos, Konstantin Riedl

Regularized Newton's method for neural networks converges exponentially to zero loss in the infinite-width limit uniformly across frequencies.

arxiv:2605.08352 v2 · 2026-05-08 · cs.LG · math.PR · stat.ML

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VYTKFDUTU36YRB5UQQLEV64VQN}

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.

Claims

C1strongest claim

in the infinite-width limit, we prove that the NN converges exponentially fast to the target data (i.e., a global minimizer with zero loss). We show that this convergence is uniform across the frequency spectrum, addressing the spectral bias inherent in gradient descent.

C2weakest assumption

The regularization parameter can be chosen via a scaling formula that vanishes at a suitable rate as the number of hidden units grows, ensuring the regularized Hessian remains positive definite for sufficiently large widths during training.

C3one line summary

In the infinite-width limit, regularized Newton's method for neural networks converges exponentially to global minimizers with uniform rates across the frequency spectrum using the Newton neural tangent kernel.

Receipt and verification

First computed	2026-05-21T02:05:04.806156Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae26a28e93a6fd8887b484164afb95836f906ed86c316ed3060a032c06ea99d2

Aliases

arxiv: 2605.08352 · arxiv_version: 2605.08352v2 · doi: 10.48550/arxiv.2605.08352 · pith_short_12: VYTKFDUTU36Y · pith_short_16: VYTKFDUTU36YRB5U · pith_short_8: VYTKFDUT

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/VYTKFDUTU36YRB5UQQLEV64VQN \
  | 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: ae26a28e93a6fd8887b484164afb95836f906ed86c316ed3060a032c06ea99d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "99515b2b2f5d1f52f3697959431d65f6a38e26548e2d9251e7f985ffcf779346",
    "cross_cats_sorted": [
      "math.PR",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-08T18:02:37Z",
    "title_canon_sha256": "84e6314d565c0160b7e80e372d99f57b5d903d62c81c316e3a99dbe81d497087"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.08352",
    "kind": "arxiv",
    "version": 2
  }
}