31 citations · 152 across the 38 of their papers we have counts for
4 papers · 1 filter
Approximation Rates for Deep Calibration of (Rough) Stochastic Volatility Models
Francesca Biagini, Lukas Gonon, Niklas Walter
We derive quantitative error bounds for deep neural networks (DNNs) approximating option prices on a -dimensional risky asset as functions of the underlying model parameters, pa…
Universal Approximation Theorem and error bounds for quantum neural networks and quantum reservoirs
Lukas Gonon, Antoine Jacquier
Universal approximation theorems are the foundations of classical neural networks, providing theoretical guarantees that the latter are able to approximate maps of interest. Recent…
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…
The necessity of depth for artificial neural networks to approximate certain classes of smooth and bounded functions without the curse of dimensionality
Lukas Gonon, Robin Graeber, Arnulf Jentzen
In this article we study high-dimensional approximation capacities of shallow and deep artificial neural networks (ANNs) with the rectified linear unit (ReLU) activation. In partic…