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A new class of non-homogeneous state-affine systems is introduced for use inreservoir 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 asubset of this class is universal in the category of fading memory filters withstochastic almost surely uniformly bounded inputs. This means that anydiscrete-time filter that satisfies the fading memory property with randominputs of that type can be uniformly approximated by elements in thenon-homogeneous state-affine family.

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