On the foundation of artificial intelligence: spectral formulation and bioinspired models

Artificial intelligence (AI) has revolutionized numerous sectors, yet its theoretical foundations remain under scrutiny. This Thesis explores the intersection of AI, network theory and neuroscience to deepen our understanding of Artificial Neural Networks (ANNs). Leveraging insights from physics and complex systems, novel approaches are proposed for parameterization and node pruning of ANNs. Additionally, a new models, Recurrent Spectral Network (RSN) and Complex Recurrent Spectral Network (C-RSN), are introduced, aiming to bridge the gap between artificial and biological neural networks. Through these endeavors, this research contributes to advancing the interpretability and performance of AI models while shedding light on fundamental aspects of neural networks.