**"Exponential decay of scattering neural networks with tensor wavelet frames"**
#### K Z, NAJIYAConvolutional neural networks involving two-dimensional input signals occur in many applications such as facial recognition, image processing, etc. Since the complexity of the network increases with the number of layers in the hidden network, it is important to analyze the energy propagation in these layers. Motivated by this, in this work, we prove that the decay rate of energy propagation is exponential for scattering convolutional neural networks with tensor wavelet frames in two dimension. We also provide a handy estimate for the number of layers needed to have feature vectors that contain a certain percentage of the energy of the input signal. |