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