47 citations · 174 across the 18 of their papers we have counts for
6 papers · 1 filter
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…
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…
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…