  Scattering network is a convolutional network, consisting of cascading
convolutions using pre-defined wavelets followed by the modulus operator. Since
its introduction in 2012, the scattering network is used as one of few
mathematical tools explaining components of the convolutional neural networks
(CNNs). However, a pooling operator, which is one of main components of
conventional CNNs, is not considered in the original scattering network. In
this paper, we propose a new network, called scattering-maxp network,
integrating the scattering network with the max-pooling operator. We model
continuous max-pooling, apply it to the scattering network, and get the
scattering-maxp network. We show that the scattering-maxp network shares many
useful properties of the scattering network including translation invariance,
but with much smaller number of parameters. Numerical experiments show that the
use of scattering-maxp does not degrade the performance too much and is much
faster than the original one, in image classification tasks.
