Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systems
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A new class of non-homogeneous state-affine systems is introduced. 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 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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