20 citations · 20 across the 2 of their papers we have counts for
7 papers
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…
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…
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…
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…