Linear Leaky-Integrate-and-Fire Neuron Model Based Spiking Neural Networks and Its Mapping Relationship to Deep Neural Networks

TL;DR

This paper establishes a mathematical mapping between Linear Leaky-Integrate-and-Fire spiking neural networks and deep neural networks, providing a theoretical foundation for their relationship and potential integration.

Contribution

It introduces a precise analytical mapping between LIF/SNN parameters and ReLU-DNN parameters, supported by proofs and experiments, advancing theoretical understanding.

Findings

Mapping relationship is analytically proven under certain conditions.

Simulation and real data experiments validate the mapping.

Provides a theoretical basis for combining SNNs and DNNs.

Abstract

Spiking neural networks (SNNs) are brain-inspired machine learning algorithms with merits such as biological plausibility and unsupervised learning capability. Previous works have shown that converting Artificial Neural Networks (ANNs) into SNNs is a practical and efficient approach for implementing an SNN. However, the basic principle and theoretical groundwork are lacking for training a non-accuracy-loss SNN. This paper establishes a precise mathematical mapping between the biological parameters of the Linear Leaky-Integrate-and-Fire model (LIF)/SNNs and the parameters of ReLU-AN/Deep Neural Networks (DNNs). Such mapping relationship is analytically proven under certain conditions and demonstrated by simulation and real data experiments. It can serve as the theoretical basis for the potential combination of the respective merits of the two categories of neural networks.