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Local Stability and Gaussian Smoothing of Quantized Neural Networks

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Computer Science > Machine Learning

arXiv:2607.20153 (cs)
[Submitted on 22 Jul 2026]

Title:Local Stability and Gaussian Smoothing of Quantized Neural Networks

View a PDF of the paper titled Local Stability and Gaussian Smoothing of Quantized Neural Networks, by Sergey Salishev and 2 other authors
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Abstract:We study Gaussian averaging as a smooth surrogate for quantized neural models. Under bounded local oscillation, we derive a local dimension-dependent bound on |f-g|, linking Gaussian smoothing to the stability analysis of discontinuous networks. We compute closed-form Gaussian averages of the rectified linear unit (ReLU) and sign activation functions, and illustrate the mechanism on a high-dimensional binary perceptron, where layer-preactivation aggregation under an explicit quantization-noise surrogate yields the Gaussian envelope used in inference-side smoothing and training-side smooth surrogate gradients.
Comments: Accepted at the 23rd IFAC World Congress (IFAC WC 2026), Busan, Republic of Korea, 2026; 6 pages, 2 figures
Subjects: Machine Learning (cs.LG); Systems and Control (eess.SY); Optimization and Control (math.OC)
MSC classes: 68T07 (Primary) 41A25, 60F05, 62M45 (Secondary)
ACM classes: I.2.6; I.5.1; I.2.8; G.1.2
Cite as: arXiv:2607.20153 [cs.LG]
  (or arXiv:2607.20153v1 [cs.LG] for this version)
  https://doi.org/10.48550/arXiv.2607.20153
arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Sergey Salishev [view email]
[v1] Wed, 22 Jul 2026 13:52:42 UTC (40 KB)
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