On the Sampling Sparsity of Neuromorphic Analog-to-Spike Conversion based on Leaky Integrate-and-Fire

TL;DR

This paper rigorously analyzes how neuromorphic analog-to-spike conversion using LIF and SOD models achieves maximum sparsity while maintaining accurate stimulus representation, emphasizing bio-inspired event-based sensing.

Contribution

It provides a mathematical framework linking threshold-based encoding with optimal sparsity in neuromorphic analog-to-spike conversion.

Findings

Threshold-based encoding guarantees maximum sparsity.

The approach ensures accurate stimulus approximation.

Mathematical proof of the sparsity-accuracy relationship.

Abstract

In contrast to the traditional principle of periodic sensing neuromorphic engineering pursues a paradigm shift towards bio-inspired event-based sensing, where events are primarily triggered by a change in the perceived stimulus. We show in a rigorous mathematical way that information encoding by means of Threshold-Based Representation based on either Leaky Integrate-and-Fire (LIF) or Send-on-Delta (SOD) is linked to an analog-to-spike conversion that guarantees maximum sparsity while satisfying an approximation condition based on the Alexiewicz norm.