Building A Mathematical Model and an Algorithm for Training A Neural Network with Sparse Dipole Synaptic Connections for Image Recognition

Large enough structured neural networks are used for solving the tasks to recognize distorted images involving computer systems. One such neural network that can completely restore a distorted image is a fully connected pseudospin (dipole) neural network that possesses associative memory. When submitting some image to its input, it automatically selects and outputs the image that is closest to the input one. This image is stored in the neural network memory within the Hopfield paradigm. Within this paradigm, it is possible to memorize and reproduce arrays of information that have their own internal structure. In order to reduce learning time, the size of the neural network is minimized by simplifying its structure based on one of the approaches: underlying the first is «regularization» while the second is based on the removal of synaptic connections from the neural network. In this work, the simplification of the structure of a fully connected dipole neural network is based on the dipole-dipole interaction between the nearest adjacent neurons of the network. It is proposed to minimize the size of a neural network through dipole-dipole synaptic connections between the nearest neurons, which reduces the time of the computational resource in the recognition of distorted images. The ratio for weight coefficients of synaptic connections between neurons in dipole approximation has been derived. A training algorithm has been built for a dipole neural network with sparse synaptic connections, which is based on the dipole-dipole interaction between the nearest neurons. A computer experiment was conducted that showed that the neural network with sparse dipole connections recognizes distorted images 3 times Faster (numbers from 0 to 9, which are shown at 25 pixels), compared to a fully connected neural networ