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pith:M7TGAC7U

pith:2026:M7TGAC7UO7ZV7SUF6T2MSAWQED

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Population Risk Bounds for Kolmogorov-Arnold Networks Trained by DP-SGD with Correlated Noise

Christoph Lampert, Jan Schuchardt, Junyu Zhou, Marius Kloft, Nikita Kalinin, Puyu Wang, Sophie Fellenz

Kolmogorov-Arnold Networks receive population risk bounds under mini-batch DP-SGD with correlated noise.

arxiv:2605.12648 v1 · 2026-05-12 · cs.LG · stat.ML

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Claims

C1strongest claim

We establish the first population risk bounds for Kolmogorov-Arnold Networks (KANs) trained by mini-batch SGD with gradient clipping, covering non-private SGD as well as differentially private SGD (DP-SGD) with Gaussian perturbations that interpolate between independent and temporally correlated noise.

C2weakest assumption

The new analysis route for correlated-noise DP training in the non-convex regime relies on an auxiliary unprojected dynamics, a shifted iterate absorbing noise, and a high-probability bootstrap certifying projection inactivity; if these constructs fail to control the temporal dependence or clipping effects under the paper's noise model, the population risk bounds do not hold.

C3one line summary

First population risk bounds for KANs under mini-batch DP-SGD with correlated noise, using a new non-convex optimization analysis combined with stability-based generalization.

References

70 extracted · 70 resolved · 2 Pith anchors

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

[2] A smooth binary mechanism for efficient private continual observation.Advances in Neural Information Processing Systems, 36:49133–49145, 2023 2023

[3] The hitchhiker’s guide to efficient, end-to-end, and tight dp auditing 2025

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

[5] Beyond differential privacy: Composition theorems and relational logic for f-divergences between probabilistic programs 2013

Receipt and verification

First computed	2026-05-18T03:09:59.801298Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

67e6600bf477f35fca85f4f4c902d020ed6526acc64b2a4ddb27a7ac38dcec77

Aliases

arxiv: 2605.12648 · arxiv_version: 2605.12648v1 · doi: 10.48550/arxiv.2605.12648 · pith_short_12: M7TGAC7UO7ZV · pith_short_16: M7TGAC7UO7ZV7SUF · pith_short_8: M7TGAC7U

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/M7TGAC7UO7ZV7SUF6T2MSAWQED \
  | 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: 67e6600bf477f35fca85f4f4c902d020ed6526acc64b2a4ddb27a7ac38dcec77

Canonical record JSON

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    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-12T18:44:47Z",
    "title_canon_sha256": "1e02e97f9e5ab34cc82f17c4dcd5e579a03a3da0c626e433ce3e42ac9befccff"
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