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

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.

arXiv commentTo appear in the Proceedings of the Royal Society of London, Series A

References in corpus (2)

• Embedding and Approximation Theorems for Echo State Networks
• Embedding Information onto a Dynamical System

Cited by in corpus (5)

• Chaos on compact manifolds: Differentiable synchronizations beyond the Takens theorem
• Learning strange attractors with reservoir systems
• Embedding Information onto a Dynamical System
• State-space systems as dynamic generative models
• Universal set of Observables for Forecasting Physical Systems through Causal Embedding