Equivalence of approximation by networks of single- and multi-spike neurons

2026-03-13

AI Summary

This study investigates whether single-spike spiking neural networks—where each neuron fires at most once—possess function approximation capabilities comparable to those of multi-spike networks. Through rigorous theoretical analysis that integrates the dynamical properties of widely used neuron models such as the leaky integrate-and-fire (LIF) model with complexity transformation techniques, the work establishes for the first time a formal equivalence between the two network classes in terms of universal function approximation. Specifically, it demonstrates that matching approximation bounds can be achieved by merely increasing the number of neurons linearly. This result challenges the conventional view that single-spike models are inherently limited in expressive power and further implies that numerous existing theoretical guarantees for single-spike networks can be directly extended to their multi-spike counterparts.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Learning Theory
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Web Mining and Content Analysis: Models for Web evolution

Abstract

In a spiking neural network, is it enough for each neuron to spike at most once? In recent work, approximation bounds for spiking neural networks have been derived, quantifying how well they can fit target functions. However, these results are only valid for neurons that spike at most once, which is commonly thought to be a strong limitation. Here, we show that the opposite is true for a large class of spiking neuron models, including the commonly used leaky integrate-and-fire model with subtractive reset: for every approximation bound that is valid for a set of multi-spike neural networks, there is an equivalent set of single-spike neural networks with only linearly more neurons (in the maximum number of spikes) for which the bound holds. The same is true for the reverse direction too, showing that regarding their approximation capabilities in general machine learning tasks, single-spike and multi-spike neural networks are equivalent. Consequently, many approximation results in the literature for single-spike neural networks also hold for the multi-spike case.

Problem

• spiking neural networks
• single-spike neurons
• multi-spike neurons
• approximation capability
• leaky integrate-and-fire

Innovation

• spiking neural networks
• single-spike neurons
• multi-spike neurons
• function approximation
• leaky integrate-and-fire