On the Universal Representation Property of Spiking Neural Networks

2025-12-18

AI Summary

Existing theoretical analyses of spiking neural networks (SNNs) lack quantitative characterizations of their universal representational capacity as sequence-to-sequence processors over spike trains. Method: We propose a function approximation framework grounded in spike-train modeling, integrating constructive weight design with rigorous temporal complexity quantification. Contribution/Results: We establish the first constructively provable, near-optimal universal approximation theorem for naturally spikable function classes—i.e., functions admitting efficient spike-based realization. Theorematically, SNNs achieve near-optimal complexity in both neuron count and synaptic weight count. They exhibit significant representational advantages for sparse inputs, low-order temporal functions, and composite functions. Moreover, our analysis provides rigorous theoretical foundations for modular deep SNN architectures and downstream tasks such as spike-sequence classification.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Deep Neural Architectures and Foundation Models
• 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
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Inspired by biology, spiking neural networks (SNNs) process information via discrete spikes over time, offering an energy-efficient alternative to the classical computing paradigm and classical artificial neural networks (ANNs). In this work, we analyze the representational power of SNNs by viewing them as sequence-to-sequence processors of spikes, i.e., systems that transform a stream of input spikes into a stream of output spikes. We establish the universal representation property for a natural class of spike train functions. Our results are fully quantitative, constructive, and near-optimal in the number of required weights and neurons. The analysis reveals that SNNs are particularly well-suited to represent functions with few inputs, low temporal complexity, or compositions of such functions. The latter is of particular interest, as it indicates that deep SNNs can efficiently capture composite functions via a modular design. As an application of our results, we discuss spike train classification. Overall, these results contribute to a rigorous foundation for understanding the capabilities and limitations of spike-based neuromorphic systems.

Problem

• Establishes universal representation for spiking neural networks
• Quantifies neuron and weight efficiency for spike functions
• Shows suitability for low-complexity or composite temporal functions

Innovation

• SNNs process information via discrete spikes over time
• Establish universal representation property for spike train functions
• Deep SNNs efficiently capture composite functions via modular design