LIMITATIONS ON THE SET OF POSSIBLE SOLUTIONSFOR A DISCRETE PERCEPTRON WITH SHIFTED SYNAPTIC SIGNALS IN EMULATION OF BINARY LOGIC FUNCTIONS

Abstract

Traditionally, perceptrons have been a core component of many modern neural network models. It is well known that the basic discrete perceptron is only suitable for linearly separable tasks; in fact, most theoretical research focuses on studying multilayer perceptrons (MLPs) as well as deep neural networks capable of solving nonlinear problems. The primary direction here is the improvement of the machine learning process, particularly in terms of finding acceptable solutions with limited data. Theoretical analysis makes it possible to understand how many training samples are required for effective learning and how well the model will perform on new datasets. The perceptron is generally regarded as a relatively simple model, which serves as an approximate informational analogy to a biological neuron. In essence, the digital model of the perceptron is based on a correlation approach to processing input signals, followed by the use of an activation function. In other words, the aggregation of input signals in a perceptron is implemented as the sum of the products of these signals and their respective weight coefficients.

In this context, autocorrelation functions play a key role, enabling the establishment of dependencies between the input signals of synapses and the target values that the system seeks to identify and classify. Specifically, the correlation approach allows for identifying which synapse input signals exert the greatest influence on the processing outcome, thereby enhancing the model's training process. However, correlation relies on the use of multiplication operations, which significantly complicates the hardware implementation of perceptron structures.

It is worth noting that the development aimed at enhancing and expanding the functionality of the perceptron structure, especially with regard to transitioning to a discrete basis, is often overlooked. Studying the limitations of perceptron structures and possible ways to overcome them, including the application of new approaches to structural organization, the adoption of various activation functions as well as the use of multilayer structures, may provide the opportunity to create more effective tools for solving classification and forecasting tasks.