AI 中文总结
研究高斯平均替代量化神经模型，推导其与不连续网络稳定性分析的联系，计算特定激活函数的闭式高斯平均，并在高维二元感知器上说明机制，通过层预激活聚合产生高斯包络用于推理和训练。
AI 中文摘要
我们研究高斯平均作为量化神经模型的平滑替代。在有界局部振荡下，我们推导了关于|f - g|的局部维度相关界，将高斯平滑与不连续网络的稳定性分析联系起来。我们计算了整流线性单元（ReLU）和符号激活函数的闭式高斯平均，并在高维二元感知器上说明了该机制。在显式量化噪声替代下的层预激活聚合产生了推理侧平滑和训练侧平滑替代梯度中使用的高斯包络。
英文摘要
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.
CommentsAccepted at the 23rd IFAC World Congress (IFAC WC 2026), Busan, Republic of Korea, 2026; 6 pages, 2 figures
