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no code implementations • 11 Aug 2021 • Lyudmila Grigoryeva, Allen Hart, Juan-Pablo Ortega

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.

no code implementations • 22 Oct 2020 • Lukas Gonon, Juan-Pablo Ortega

Echo state networks (ESNs) have been recently proved to be universal approximants for input/output systems with respect to various $L ^p$-type criteria.

no code implementations • 17 Sep 2020 • Christa Cuchiero, Lukas Gonon, Lyudmila Grigoryeva, Juan-Pablo Ortega, Josef Teichmann

A new explanation of geometric nature of the reservoir computing phenomenon is presented.

no code implementations • 23 Jul 2020 • Lyudmila Grigoryeva, Juan-Pablo Ortega

Many recurrent neural network machine learning paradigms can be formulated using state-space representations.

no code implementations • 22 Apr 2020 • Lukas Gonon, Lyudmila Grigoryeva, Juan-Pablo Ortega

The notion of memory capacity, originally introduced for echo state and linear networks with independent inputs, is generalized to nonlinear recurrent networks with stationary but dependent inputs.

no code implementations • 14 Feb 2020 • Lukas Gonon, Lyudmila Grigoryeva, Juan-Pablo Ortega

This work studies approximation based on single-hidden-layer feedforward and recurrent neural networks with randomly generated internal weights.

no code implementations • 30 Oct 2019 • Lukas Gonon, Lyudmila Grigoryeva, Juan-Pablo Ortega

We analyze the practices of reservoir computing in the framework of statistical learning theory.

no code implementations • 16 Feb 2019 • Lyudmila Grigoryeva, Juan-Pablo Ortega

That research is complemented in this paper with the characterization of the differentiability of reservoir filters for very general classes of discrete-time deterministic inputs.

no code implementations • 7 Jul 2018 • Lukas Gonon, Juan-Pablo Ortega

The universal approximation properties with respect to $L ^p $-type criteria of three important families of reservoir computers with stochastic discrete-time semi-infinite inputs is shown.

no code implementations • 3 Jun 2018 • Lyudmila Grigoryeva, Juan-Pablo Ortega

This paper shows that echo state networks are universal uniform approximants in the context of discrete-time fading memory filters with uniformly bounded inputs defined on negative infinite times.

1 code implementation • 3 Dec 2017 • Lyudmila Grigoryeva, Juan-Pablo Ortega

A new class of non-homogeneous state-affine systems is introduced for use in reservoir computing.

no code implementations • 29 May 2016 • Lyudmila Grigoryeva, Juan-Pablo Ortega

This paper characterizes the conditional distribution properties of the finite sample ridge regression estimator and uses that result to evaluate total regression and generalization errors that incorporate the inaccuracies committed at the time of parameter estimation.

no code implementations • 13 Oct 2015 • Lyudmila Grigoryeva, Julie Henriques, Laurent Larger, Juan-Pablo Ortega

This paper addresses the reservoir design problem in the context of delay-based reservoir computers for multidimensional input signals, parallel architectures, and real-time multitasking.

no code implementations • 1 Aug 2015 • Lyudmila Grigoryeva, Julie Henriques, Juan-Pablo Ortega

This paper extends the notion of information processing capacity for non-independent input signals in the context of reservoir computing (RC).

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