  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.
