Neural Comput - Echo state property linked to an input: exploring a fundamental characteristic of recurrent neural networks.

Tópicos

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Resumo

The echo state property is a key for the design and training of recurrent neural networks within the paradigm of reservoir computing. In intuitive terms, this is a passivity condition: a network having this property, when driven by an input signal, will become entrained by the input and develop an internal response signal. This excited internal dynamics can be seen as a high-dimensional, nonlinear, unique transform of the input with a rich memory content. This view has implications for understanding neural dynamics beyond the field of reservoir computing. Available definitions and theorems concerning the echo state property, however, are of little practical use because they do not relate the network response to temporal or statistical properties of the driving input. Here we present a new definition of the echo state property that directly connects it to such properties. We derive a fundamental 0-1 law: if the input comes from an ergodic source, the network response has the echo state property with probability one or zero, independent of the given network. Furthermore, we give a sufficient condition for the echo state property that connects statistical characteristics of the input to algebraic properties of the network connection matrix. The mathematical methods that we employ are freshly imported from the young field of nonautonomous dynamical systems theory. Since these methods are not yet well known in neural computation research, we introduce them in some detail. As a side story, we hope to demonstrate the eminent usefulness of these methods.

Resumo Limpo

echo state properti key design train recurr neural network within paradigm reservoir comput intuit term passiv condit network properti driven input signal will becom entrain input develop intern respons signal excit intern dynam can seen highdimension nonlinear uniqu transform input rich memori content view implic understand neural dynam beyond field reservoir comput avail definit theorem concern echo state properti howev littl practic use relat network respons tempor statist properti drive input present new definit echo state properti direct connect properti deriv fundament law input come ergod sourc network respons echo state properti probabl one zero independ given network furthermor give suffici condit echo state properti connect statist characterist input algebra properti network connect matrix mathemat method employ fresh import young field nonautonom dynam system theori sinc method yet well known neural comput research introduc detail side stori hope demonstr emin use method

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