31 citations · 152 across the 38 of their papers we have counts for
6 papers · 1 filter
Fading memory echo state networks are universal
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 -type criteria. When , onl…
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…
Weak error analysis for stochastic gradient descent optimization algorithms
Aritz Bercher, Lukas Gonon, Arnulf Jentzen +1
Stochastic gradient descent (SGD) type optimization schemes are fundamental ingredients in a large number of machine learning based algorithms. In particular, SGD type optimization…
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…
Overcoming the curse of dimensionality in the numerical approximation of high-dimensional semilinear elliptic partial differential equations
Christian Beck, Lukas Gonon, Arnulf Jentzen
Recently, so-called full-history recursive multilevel Picard (MLP) approximation schemes have been introduced and shown to overcome the curse of dimensionality in the numerical app…
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…