Based on a scatterogram of projections onto a plane of states of the output and hidden layers of a sigmoid neural network, its behavior in solving the problem of image recognition of letters is studied. In particular, it was found that the method of conjugate gradients for the entire training process affects both the weights of a hidden layer and the output layer, while the steepest descent method determines the weights of a hidden layer on the first iteration, and in the course of further education has practically no effect on them. An estimate for the number of neurons in the hidden layer that is sufficient for a quality solution of the problem of recognition is obtained. Visualization of the states of neurons is a powerful visual tool for developing and studying the behavior of different classes of neural networks.

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