APPROXIMATION OF INDICATOR FUNCTIONS IN THE CONTEXT OF PROBABILISTICDISCRETE PERCEPTRON - YAKOVYN, SERHIY; MELNYCHUK, STEPAN (Herald of Khmelnytskyi National University. Technical sciences, 2025)
One of the promising applications of perceptron structures, as independent digital components implemented based on correlation and convolution functions, is signal and stream data processing. Specifically, this includes tasks such as pattern recognition, detection of harmonic and periodic components, etc. The main aspects of the properties of the discrete perceptron can be utilized for solving problems related to recognizing various types of signals by their form, identifying frequency components of a signal (an element of spectral analysis), dynamically adjusting filtering parameters, and so on. In general, a perceptron can be viewed as a standalone self-sufficient component, whose functionality may vary depending on the task at hand, although its structural, schematic, algorithmic, and software solutions remain unchanged. Essentially, this is a digital component that can be trained on datasets containing necessary informational features and possible distortion variations and applied for signal or data processing as a specialized component of a computer system.The article's materials examine the specific features of implementing perceptrons based on the use of probabilistic estimates of discrete synaptic signals, which have undergone prior bias. Key aspects of aggregating discrete input signals, realized through addition and probabilistic estimation operations, are shown. Additionally, methods for approximating activation functions that ensure smoothness and differentiability required for efficient neural network training have been proposed. Research has established that using statistical estimates can significantly reduce computational costs, enhance signal processing efficiency, and accelerate the training process. The obtained results have the potential to be utilized in computer systems and components that solve various applied tasks, including signal and stream data processing.
Keywords: artificial neural networks; perceptron; discrete signals; probabilistic estimates; activation functions; signal processing