Quantization in Spiking Neural Networks

TL;DR

This paper analyzes the quantization process in spiking neural networks using the LIF neuron model, introduces a quantization error formula, and proposes a new reset method called 'reset-to-mod' based on this understanding.

Contribution

It provides a novel quantization perspective on LIF neurons, derives an error formula, and introduces a new reset mechanism for improved neural network modeling.

Findings

Quantization in SNNs can be modeled and analyzed mathematically.

A formula for quantization error using the Alexiewicz norm is derived.

The 'reset-to-mod' reset variant improves LIF neuron re-initialization.

Abstract

In spiking neural networks (SNN), at each node, an incoming sequence of weighted Dirac pulses is converted into an output sequence of weighted Dirac pulses by a leaky-integrate-and-fire (LIF) neuron model based on spike aggregation and thresholding. We show that this mapping can be understood as a quantization operator and state a corresponding formula for the quantization error by means of the Alexiewicz norm. This analysis has implications for rethinking re-initialization in the LIF model, leading to the proposal of 'reset-to-mod' as a modulo-based reset variant.