Universal Approximation Theorem for Tessarine-Valued Neural Networks - Carniello, Rafael A. F.; Vital, Wington L.; Valle, Marcos Eduardo (Anais do Encontro Nacional de Inteligência Artificial e Computacional (ENIAC); 2021: Anais do XVIII Encontro Nacional de Inteligência Artificial e ComputacionalDO - 10.5753/eniac.2021.18256, 2021)
The universal approximation theorem ensures that any continuous real-valued function defined on a compact subset can be approximated with arbitrary precision by a single hidden layer neural network. In this paper, we show that the universal approximation theorem also holds for tessarine-valued neural networks. Precisely, any continuous tessarine-valued function can be approximated with arbitrary precision by a single hidden layer tessarine-valued neural network with split activation functions in the hidden layer. A simple numerical example, confirming the theoretical result and revealing the superior performance of a tessarine-valued neural network over a real-valued model for interpolating a vector-valued function, is presented in the paper.