Synthesis of parameterized families of correctly functioning sigma-pi neurons

The ΣΠ-neuron is a biologically inspired formal model for logical information processing. The ΣΠ-neuron model adequately reflects information processing processes in the cerebral cortex and in the dendritic trees of neurons. The advantage of the ΣΠ-neuron model is the ability to accurately represent any Boolean function and the possibility of constructive learning (direct construction) in a single pass of the training sample. Another possibility is the direct construction of an ensemble of ΣΠ-neurons that function correctly on the training sample. This article discusses a new algorithm for constructing such ensemble of ΣΠ-neurons in parameterized form. This form can also be easily represented as a single ΣΠ-neuron with a hidden layer of linear and threshold linear units. In some cases, this makes it easier to retrain on new inputs by setting the appropriate control parameter values.