Stable and symmetric filter convolutional neural network

First we present a proof that convolutional neural networks (CNN) with max-norm regularization, max-pooling, and Relu non-linearity are stable to additive noise. Second, we explore the use of symmetric and antisymmetric filters in a baseline CNN model on digit classification, which enjoys the stability to additive noise. Experimental results indicate that the symmetric CNN outperforms the baseline model for nearly all training sizes and matches the state-of-the-art deep-net in the cases of limited training examples.