Time to Spike? Understanding the Representational Power of Spiking Neural Networks in Discrete Time

Nguyen, Duc Anh; Araya, Ernesto; Fono, Adalbert und Kutyniok, Gitta (2025): Time to Spike? Understanding the Representational Power of Spiking Neural Networks in Discrete Time. ICML 2025: Forty-second International Conference on Machine Learning, Vancouver, Canada, 13-19 July 2025.

Abstract

Recent years have seen significant progress in developing spiking neural networks (SNNs) as a potential solution to the energy challenges posed by conventional artificial neural networks (ANNs). However, our theoretical understanding of SNNs remains relatively limited compared to the ever-growing body of literature on ANNs. In this paper, we study a discrete-time model of SNNs based on leaky integrate-and-fire (LIF) neurons, referred to as discrete-time LIF-SNNs, a widely used framework that still lacks solid theoretical foundations. We demonstrate that discrete-time LIF-SNNs with static inputs and outputs realize piecewise constant functions defined on polyhedral regions, and more importantly, we quantify the network size required to approximate continuous functions. Moreover, we investigate the impact of latency (number of time steps) and depth (number of layers) on the complexity of the input space partitioning induced by discrete-time LIF-SNNs. Our analysis highlights the importance of latency and contrasts these networks with ANNs employing piecewise linear activation functions. Finally, we present numerical experiments to support our theoretical findings.

• Dokumententyp: Konferenzbeitrag (Paper)
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Professur für Mathematische Grundlagen des Verständnisses der künstlichen Intelligenz
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• Sprache: Englisch