Stability and Memory-loss go Hand-in-Hand: Three Results in Dynamics & Computation

TL;DR

This paper explores how memory-loss in driven dynamical systems influences stability and computation, providing new insights into stability conditions, parameter effects, and the edge-of-criticality, with implications for biologically inspired computing.

Contribution

It introduces a novel perspective linking memory-loss to stability in driven systems, addressing longstanding questions in dynamics and computation.

Findings

Memory-loss helps systems provide unambiguous responses.

Changing parameters affects system stability.

Defined the mathematical concept of the edge-of-criticality.

Abstract

The search for universal laws that help establish a relationship between dynamics and computation is driven by recent expansionist initiatives in biologically inspired computing. A general setting to understand both such dynamics and computation is a driven dynamical system that responds to a temporal input. Surprisingly, we find memory-loss a feature of driven systems to forget their internal states helps provide unambiguous answers to the following fundamental stability questions that have been unanswered for decades: what is necessary and sufficient so that slightly different inputs still lead to mostly similar responses? How does changing the driven system's parameters affect stability? What is the mathematical definition of the edge-of-criticality? We anticipate our results to be timely in understanding and designing biologically inspired computers that are entering an era of dedicated hardware implementations for neuromorphic computing and state-of-the-art reservoir computing applications.