47 citations · 174 across the 18 of their papers we have counts for
25 papers
From Many Models, One: Macroeconomic Forecasting with Reservoir Ensembles
Giovanni Ballarin, Lyudmila Grigoryeva, Yui Ching Li
Model combination is a powerful approach for achieving superior performance compared to selecting a single model. We study both theoretically and empirically the effectiveness of e…
Memory Capacity of Nonlinear Recurrent Networks: Is it Informative?
Giovanni Ballarin, Lyudmila Grigoryeva, Juan-Pablo Ortega
The total memory capacity (MC) of linear recurrent neural networks (RNNs) has been proven to be equal to the rank of the corresponding Kalman controllability matrix, and it is almo…
Infinite-dimensional next-generation reservoir computing
Lyudmila Grigoryeva, Hannah Lim Jing Ting, Juan-Pablo Ortega
Next-generation reservoir computing (NG-RC) has attracted much attention due to its excellent performance in spatio-temporal forecasting of complex systems and its ease of implemen…
Forecasting causal dynamics with universal reservoirs
Lyudmila Grigoryeva, James Louw, Juan-Pablo Ortega
An iterated multistep forecasting scheme based on recurrent neural networks (RNN) is proposed for the time series generated by causal chains with infinite memory. This forecasting…
Data-driven cold starting of good reservoirs
Lyudmila Grigoryeva, Boumediene Hamzi, Felix P. Kemeth +4
Using short histories of observations from a dynamical system, a workflow for the post-training initialization of reservoir computing systems is described. This strategy is called…
Memory of recurrent networks: Do we compute it right?
Giovanni Ballarin, Lyudmila Grigoryeva, Juan-Pablo Ortega
Numerical evaluations of the memory capacity (MC) of recurrent neural networks reported in the literature often contradict well-established theoretical bounds. In this paper, we st…
Infinite-dimensional reservoir computing
Lukas Gonon, Lyudmila Grigoryeva, Juan-Pablo Ortega
Reservoir computing approximation and generalization bounds are proved for a new concept class of input/output systems that extends the so-called generalized Barron functionals to…
Reservoir kernels and Volterra series
Lukas Gonon, Lyudmila Grigoryeva, Juan-Pablo Ortega
A universal kernel is constructed whose sections approximate any causal and time-invariant filter in the fading memory category with inputs and outputs in a finite-dimensional Eucl…
Reservoir Computing for Macroeconomic Forecasting with Mixed Frequency Data
Giovanni Ballarin, Petros Dellaportas, Lyudmila Grigoryeva +3
Macroeconomic forecasting has recently started embracing techniques that can deal with large-scale datasets and series with unequal release periods. MIxed-DAta Sampling (MIDAS) and…
Learning strange attractors with reservoir systems
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 rep…
Chaos on compact manifolds: Differentiable synchronizations beyond the Takens theorem
Lyudmila Grigoryeva, Allen Hart, Juan-Pablo Ortega
This paper shows that a large class of fading memory state-space systems driven by discrete-time observations of dynamical systems defined on compact manifolds always yields contin…
Discrete-time signatures and randomness in reservoir computing
Christa Cuchiero, Lukas Gonon, Lyudmila Grigoryeva +2
A new explanation of geometric nature of the reservoir computing phenomenon is presented. Reservoir computing is understood in the literature as the possibility of approximating in…
Dimension reduction in recurrent networks by canonicalization
Lyudmila Grigoryeva, Juan-Pablo Ortega
Many recurrent neural network machine learning paradigms can be formulated using state-space representations. The classical notion of canonical state-space realization is adapted i…
Memory and forecasting capacities of nonlinear recurrent networks
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…
Approximation Bounds for Random Neural Networks and Reservoir Systems
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. These methods, in which only the la…
Risk bounds for reservoir computing
Lukas Gonon, Lyudmila Grigoryeva, Juan-Pablo Ortega
We analyze the practices of reservoir computing in the framework of statistical learning theory. In particular, we derive finite sample upper bounds for the generalization error co…
Differentiable reservoir computing
Lyudmila Grigoryeva, Juan-Pablo Ortega
Much effort has been devoted in the last two decades to characterize the situations in which a reservoir computing system exhibits the so-called echo state (ESP) and fading memory…
Echo state networks are universal
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…
Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systems
Lyudmila Grigoryeva, Juan-Pablo Ortega
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 res…
Singular ridge regression with homoscedastic residuals: generalization error with estimated parameters
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 generalizatio…
Nonlinear memory capacity of parallel time-delay reservoir computers in the processing of multidimensional signals
Lyudmila Grigoryeva, Julie Henriques, Laurent Larger +1
This paper addresses the reservoir design problem in the context of delay-based reservoir computers for multidimensional input signals, parallel architectures, and real-time multit…
Quantitative evaluation of the performance of discrete-time reservoir computers in the forecasting, filtering, and reconstruction of stochastic stationary signals
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). The presence of input autocorrelation…
Optimal nonlinear information processing capacity in delay-based reservoir computers
Lyudmila Grigoryeva, Julie Henriques, Laurent Larger +1
Reservoir computing is a recently introduced brain-inspired machine learning paradigm capable of excellent performances in the processing of empirical data. We focus in a particula…
Stability of Hamiltonian relative equilibria in symmetric magnetically confined rigid bodies
Lyudmila Grigoryeva, Juan-Pablo Ortega, Stanislav Zub
This work studies the symmetries, the associated momentum map, and relative equilibria of a mechanical system consisting of a small axisymmetric magnetic body-dipole in an also axi…