  We propose the introduction of nonlinear operation into the feature
generation process in convolutional neural networks. This nonlinearity can be
implemented in various ways. First we discuss the use of nonlinearities in the
process of data augmentation to increase the robustness of the neural networks
recognition capacity. To this end, we randomly disturb the input data set by
applying exponents within a certain numerical range to individual data points
of the input space. Second we propose nonlinear convolutional neural networks
where we apply the exponential operation to each element of the receptive
field. To this end, we define an additional weight matrix of the same dimension
as the standard kernel weight matrix. The weights of this matrix then
constitute the exponents of the corresponding components of the receptive
field. In the basic setting, we keep the weight parameters fixed during
training by defining suitable parameters. Alternatively, we make the
exponential weight parameters end-to-end trainable using a suitable
parameterization. The network architecture is applied to time series analysis
data set showing a considerable increase in the classification performance
compared to baseline networks.
