Evolving Network Model That Almost Regenerates Epileptic Data

An Echo State Network Imparts a Curve Fitting

Recurrent neural networks (RNNs) are successfully employed in processing information from temporal data. Approaches to training such networks are varied and reservoir computing-based attainments, such as the echo state network (ESN), provide great ease in training. Akin to many machine learning algorithms rendering an interpolation function or fitting a curve, we observe that a driven system, such as an RNN, renders a continuous curve fitting if and only if it satisfies the echo state property. The domain of the learned curve is an abstract space of the left-infinite sequence of inputs and the codomain is the space of readout values. When the input originates from discrete-time dynamical systems, we find theoretical conditions under which a topological conjugacy between the input and reservoir dynamics can exist and present some numerical results relating the linearity in the reservoir to the forecasting abilities of the ESNs.

Stability and memory-loss go hand-in-hand: three results in dynamics and computation

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.