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arXiv · 2607.20153

Local Stability and Gaussian Smoothing of Quantized Neural Networks

Sergey Salishev·Anton Makarov·Oleg Granichin
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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.

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Sergey Salishev, Anton Makarov, Oleg Granichin. 2026-07-22. Local Stability and Gaussian Smoothing of Quantized Neural Networks. https://arxiv.org/abs/2607.20153

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