Local Stability and Gaussian Smoothing of Quantized Neural Networks

Source

Source name: arXiv
Source kind: paper
Authors / organization: Sergey Salishev, Anton Makarov, Oleg Granichin
Venue: arXiv: cs.LG
Published: 2026-07-22
Collected: 2026-07-23
URL: http://arxiv.org/abs/2607.20153v1
PDF: https://arxiv.org/pdf/2607.20153v1
DOI: UNKNOWN

Plain-Language Brief

The authors study the use of Gaussian averaging as a smoother alternative for quantized neural networks. They derive a bound on the difference between the original function and the smoothed version under certain conditions, compute closed-form Gaussian averages for ReLU and sign activation functions, and demonstrate the mechanism using a high-dimensional binary perceptron.

What the Document Says

The paper investigates Gaussian smoothing as an alternative to quantized neural networks under bounded local oscillation.
They derive a local dimension-dependent bound for |f-g|, linking Gaussian smoothing to the stability analysis of discontinuous networks.
The authors compute closed-form Gaussian averages for rectified linear unit (ReLU) and sign activation functions.
They illustrate their method on a high-dimensional binary perceptron using layer-preactivation aggregation with an explicit quantization-noise surrogate.

Key Concepts Mentioned

Gaussian smoothing
quantized neural networks
bounded local oscillation
stability analysis
discontinuous networks
ReLU activation function
sign activation function
high-dimensional binary perceptron
layer-preactivation aggregation
quantization-noise surrogate

Claims Made by the Document

Under bounded local oscillation, a local dimension-dependent bound can be derived for |f-g|.
Gaussian smoothing can be linked to the stability analysis of discontinuous networks.

Evidence Used

The authors derive this bound in the paper.

Methods / Approach

UNKNOWN

Limitations Stated by the Authors

UNKNOWN

Limitations Noted by the Agent

Agent interpretation — not from the source.

UNKNOWN

Open Questions

UNKNOWN

Notes for Future Q&A

May include interpretation. Labeled where it does.

UNKNOWN

Raw Abstract / Excerpt

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.