This paper shows a Min–Max property existing in the connection weights of the convolutional layers in a neural network structure, i.e., the LeNet. Specifically, the Min–Max property means that, during the back propagation-based training for LeNet, the weights of the convolutional layers will become far away from their centers of intervals, i.e., decreasing to their minimum or increasing to their maximum. From the perspective of uncertainty, we demonstrate that the Min–Max property corresponds to minimizing the fuzziness of the model parameters through a simplified formulation of convolution. It is experimentally confirmed that the model with the Min–Max property has a stronger adversarial robustness, thus this property can be incorporated into the design of loss function. This paper points out a changing tendency of uncertainty in the convolutional layers of LeNet structure, and gives some insights to the interpretability of convolution.

本文显示了神经网络结构（即LeNet）中卷积层的连接权重中存在的Min-Max属性。特别是，Min-Max属性意味着，在对LeNet进行基于反向传播的训练时，卷积层的权重将远离其间隔中心，即减小至其最小值或增大至其最大值。从不确定性的角度来看，我们证明了Min-Max属性对应于通过简化卷积公式使模型参数的模糊性最小化。实验证明，具有Min-Max属性的模型具有更强的对抗鲁棒性，因此可以将该属性纳入损失函数的设计中。