Mathematical Foundations of Spiking Neural Networks: Strengths, challenges, and computational paradigm potential [Special Issue on the Mathematics of deep Learning]

Abstract

Deep learning’s success comes with growing energy demands, raising concerns about the long-term sustainability of the field. Spiking neural networks (SNNs), inspired by biological neurons, offer a promising alternative with potential computational and energy efficiency gains. This article examines the computational properties of spiking networks through the lens of learning theory, focusing on expressivity, training, and generalization, as well as energy-efficient implementations, while comparing them with artificial neural networks (ANNs). By categorizing spiking models based on time representation and information encoding, we highlight their strengths, challenges, and potential as an alternative computational paradigm.