Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systems

Lyudmila Grigoryeva; Juan-Pablo Ortega

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arXiv · 1712.00754

Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systems

Lyudmila Grigoryeva·Juan-Pablo Ortega

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Abstract

A new class of non-homogeneous state-affine systems is introduced for use in reservoir computing. Sufficient conditions are identified that guarantee first, that the associated reservoir computers with linear readouts are causal, time-invariant, and satisfy the fading memory property and second, that a subset of this class is universal in the category of fading memory filters with stochastic almost surely uniformly bounded inputs. This means that any discrete-time filter that satisfies the fading memory property with random inputs of that type can be uniformly approximated by elements in the non-homogeneous state-affine family.

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Lyudmila Grigoryeva, Juan-Pablo Ortega. 2017-12-03. Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systems. https://arxiv.org/abs/1712.00754

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