  In this paper we discuss the stability properties of convolutional neural
networks. Convolutional neural networks are widely used in machine learning. In
classification they are mainly used as feature extractors. Ideally, we expect
similar features when the inputs are from the same class. That is, we hope to
see a small change in the feature vector with respect to a deformation on the
input signal. This can be established mathematically, and the key step is to
derive the Lipschitz properties. Further, we establish that the stability
results can be extended for more general networks. We give a formula for
computing the Lipschitz bound, and compare it with other methods to show it is
closer to the optimal value.
