Partial Structural Equivalence Between Integral Neurons and a Subclass of RHONN Neurons

Abstract

This paper presents a comparative theoretical and experimental study of two contemporary neuron models: the integral neuron and the Recurrent High-Order Neural Networks (RHONN) neuron. The integral neuron forms its internal signal through an integral aggregation of the input stimuli modulated by a continuous weight function, whose form can be adapted to the requirements of a given problem. In contrast, the RHONN neuron employs high-order products of the input variables, enabling the modeling of complex and nonlinear interactions among inputs. The analysis examines structural properties, computational complexity, robustness to noise, and behavior under varying data volumes and input dimensionality. A partial structural equivalence is established between an integral neuron with a polynomial weight function and a specific subclass of RHONN neurons with symmetric interactions of the corresponding order. Furthermore, the integral neuron is shown to exhibit significantly lower computational complexity during training, as well as increased robustness in scenarios involving limited data and noisy inputs. The results indicate that, while the two neuron models possess distinct expressive capabilities, the integral neuron provides a compact and robust alternative to RHONN neurons for a broad class of approximation and learning tasks, particularly in high-dimensional or noise-contaminated settings.