Variability of the Wide Learning Neural Network Learning Algorithm

There are a large number of datasets on the publicly available kaggle resource, from which five datasets and their corresponding structures of artificial neural networks were selected. After training neural networks, the work of the neurons of the first hidden layers was reproduced in spreadsheets. A significant number of useless neurons were found (20—60 %). A neuron is called useless if the scalar products of all instances of the training sample are less than zero. The relu activation function converts negative values to zero, therefore, such a neuron does not contribute to the work of the neural network. Thus, it is necessary to learn how to find and remove useless neurons in trained networks. The following describes the principle of functioning of a reproducible neural network learning algorithm. To do this, the instance belonging to a certain class is replaced by belonging to one of the categories of ternary logic (true, zero, false) and a linearly separable subsample is formed. The properties of the Wide Learning algorithm are considered, the code of the first version of the software implementation is posted in the Github repository under the Apache 2.0 license https://github.com/brinkinvision/wideLearning. The scalar product of the input vector by the weights of the neuron projects the n-dimensional input space onto a one-dimensional digital line. The ternary activation threshold function on this line marks with true (false) categories a part of instances belonging to a certain class. The hypothesis of the normality of the distribution of scalar products of labeled instances was tested. In most cases, the hypothesis was justified, and sometimes it was possible to prove normality after additional manipulations. Once a two-modal distribution was discovered, the emulation of two-modality demonstrates the adequacy of the described methodology.