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pith:WMNEPMVC

pith:2026:WMNEPMVC4VKSL3J5VJ7Z4OEHQB

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Optimization, Generalization and Differential Privacy Bounds for Gradient Descent on Kolmogorov-Arnold Networks

Junyu Zhou, Marius Kloft, Philipp Liznerski, Puyu Wang

Gradient descent on two-layer Kolmogorov-Arnold networks reaches optimization and generalization rates of order 1/T and 1/n with polylogarithmic width, and differential privacy makes that width necessary.

arxiv:2601.22409 v3 · 2026-01-29 · cs.LG · cs.AI · stat.ML

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Claims

C1strongest claim

we show that polylogarithmic network width suffices for GD to achieve an optimization rate of order 1/T and a generalization rate of order 1/n ... obtain a utility bound of order √d/(nε) ... polylogarithmic width is not only sufficient but also necessary under differential privacy

C2weakest assumption

NTK-separable assumption for the data under logistic loss, used to specialize the general analysis to achieve the stated rates

C3one line summary

For two-layer KANs trained with gradient descent under logistic loss and NTK-separable assumption, polylogarithmic width suffices for 1/T optimization and 1/n generalization rates, while differential privacy requires the same width and yields √d/(nε) utility.

References

73 extracted · 73 resolved · 0 Pith anchors

[1] Deep learning with differential privacy 2016

[2] A convergence theory for deep learning via over- parameterization 2019

[3] On functions of three variables 1957

[4] Fine-grained analysis of optimization and generalization for overparameterized two-layer neural networks 2019

[5] Spectrally-normalized margin bounds for neural networks.Advances in Neural Information Processing Systems, 30, 2017 2017

Receipt and verification

First computed	2026-05-18T03:09:24.079935Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b31a47b2a2e55525ed3daa7f9e3887806bc7ad91be6cda14327d0a0e556be6c2

Aliases

arxiv: 2601.22409 · arxiv_version: 2601.22409v3 · doi: 10.48550/arxiv.2601.22409 · pith_short_12: WMNEPMVC4VKS · pith_short_16: WMNEPMVC4VKSL3J5 · pith_short_8: WMNEPMVC

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/WMNEPMVC4VKSL3J5VJ7Z4OEHQB \
  | 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: b31a47b2a2e55525ed3daa7f9e3887806bc7ad91be6cda14327d0a0e556be6c2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "47141e9eda08d6d56882e919e1ff514db52efcd61ed096650281dff17c08c4ce",
    "cross_cats_sorted": [
      "cs.AI",
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-01-29T23:43:26Z",
    "title_canon_sha256": "a67079889d6ae0d1988e286ae7cff6a247eba891ada557e62dfe9ea129636f3e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.22409",
    "kind": "arxiv",
    "version": 3
  }
}