37 research outputs found
Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systems
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.Comment: 41 page
Learning strange attractors with reservoir systems
This paper shows that the celebrated Embedding Theorem of Takens is a
particular case of a much more general statement according to which, randomly
generated linear state-space representations of generic observations of an
invertible dynamical system carry in their wake an embedding of the phase space
dynamics into the chosen Euclidean state space. This embedding coincides with a
natural generalized synchronization that arises in this setup and that yields a
topological conjugacy between the state-space dynamics driven by the generic
observations of the dynamical system and the dynamical system itself. This
result provides additional tools for the representation, learning, and analysis
of chaotic attractors and sheds additional light on the reservoir computing
phenomenon that appears in the context of recurrent neural networks.Comment: 36 pages, 11 figure