用高斯平滑分析量化神经网络的局部稳定性，揭示其与梯度训练的关系。
Local Stability and Gaussian Smoothing of Quantized Neural Networks
- 基于局部震荡有界性，推导出依赖维度的|f-g|局部界
- 解析计算ReLU和符号激活函数的高斯平均，获得闭式解
- 在高维二值感知机上验证平滑机制，适用于量化模型优化
我们研究了高斯平均作为量化神经模型的平滑替代方法。在局部振荡有界的条件下，推导出|f-g|的局部维度相关上界，将高斯平滑与不连续网络的稳定性分析联系起来。本文计算了修正线性单元（ReLU）和符号激活函数的闭式高斯平均，并在高维二值感知机上展示该机制：层前激活聚合在显式量化噪声替代下产生推理阶段使用的高斯包络，以及训练阶段的平滑梯度替代。
原文摘要 · Abstract (English)
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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