  The paper proposes an approach to training a convolutional neural network
using information on the level of distortion of input data. The learning
process is modified with an additional layer, which is subsequently deleted, so
the architecture of the original network does not change. As an example, the
LeNet5 architecture network with training data based on the MNIST symbols and a
distortion model as Gaussian blur with a variable level of distortion is
considered. This approach does not have quality loss of the network and has a
significant error-free zone in responses on the test data which is absent in
the traditional approach to training. The responses are statistically dependent
on the level of input image's distortions and there is a presence of a strong
relationship between them.
