3 papers
cs.NE2025
Dynamics of Structured Complex-Valued Hopfield Neural Networks
Rama Murthy Garimella, Marcos Eduardo Valle, Guilherme Vieira +2
In this paper, we explore the dynamics of structured complex-valued Hopfield neural networks (CvHNNs), which arise when the synaptic weight matrix possesses specific structural pro…
cs.LG2024
Universal Approximation Theorem for Vector- and Hypercomplex-Valued Neural Networks
Marcos Eduardo Valle, Wington L. Vital, Guilherme Vieira
The universal approximation theorem states that a neural network with one hidden layer can approximate continuous functions on compact sets with any desired precision. This theorem…
cs.LG2024
Understanding Vector-Valued Neural Networks and Their Relationship with Real and Hypercomplex-Valued Neural Networks
Marcos Eduardo Valle
Despite the many successful applications of deep learning models for multidimensional signal and image processing, most traditional neural networks process data represented by (mul…