Lukas Gonon | DeepAI

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∙ 07/24/2023

Universal Approximation Theorem and error bounds for quantum neural networks and quantum reservoirs

Universal approximation theorems are the foundations of classical neural...

0 Lukas Gonon, et al. ∙

∙ 04/02/2023

Infinite-dimensional reservoir computing

Reservoir computing approximation and generalization bounds are proved f...

0 Lukas Gonon, et al. ∙

∙ 01/19/2023

The necessity of depth for artificial neural networks to approximate certain classes of smooth and bounded functions without the curse of dimensionality

In this article we study high-dimensional approximation capacities of sh...

0 Lukas Gonon, et al. ∙

∙ 12/30/2022

Reservoir kernels and Volterra series

A universal kernel is constructed whose sections approximate any causal ...

0 Lukas Gonon, et al. ∙

∙ 10/19/2022

Deep neural network expressivity for optimal stopping problems

This article studies deep neural network expression rates for optimal st...

0 Lukas Gonon, et al. ∙

∙ 06/14/2021

Random feature neural networks learn Black-Scholes type PDEs without curse of dimensionality

This article investigates the use of random feature neural networks for ...

0 Lukas Gonon, et al. ∙

∙ 02/23/2021

Deep ReLU Neural Network Approximation for Stochastic Differential Equations with Jumps

Deep neural networks (DNNs) with ReLU activation function are proved to ...

0 Lukas Gonon, et al. ∙

∙ 01/28/2021

Deep ReLU Network Expression Rates for Option Prices in high-dimensional, exponential Lévy models

We study the expression rates of deep neural networks (DNNs for short) f...

0 Lukas Gonon, et al. ∙

∙ 10/22/2020

Fading memory echo state networks are universal

Echo state networks (ESNs) have been recently proved to be universal app...

0 Lukas Gonon, et al. ∙

∙ 09/17/2020

Discrete-time signatures and randomness in reservoir computing

A new explanation of geometric nature of the reservoir computing phenome...

0 Christa Cuchiero, et al. ∙

∙ 07/03/2020

Weak error analysis for stochastic gradient descent optimization algorithms

Stochastic gradient descent (SGD) type optimization schemes are fundamen...

0 Aritz Bercher, et al. ∙

∙ 04/22/2020

Memory and forecasting capacities of nonlinear recurrent networks

The notion of memory capacity, originally introduced for echo state and ...

0 Lukas Gonon, et al. ∙

∙ 03/01/2020

Overcoming the curse of dimensionality in the numerical approximation of high-dimensional semilinear elliptic partial differential equations

Recently, so-called full-history recursive multilevel Picard (MLP) appro...

0 Christian Beck, et al. ∙

∙ 02/14/2020

Approximation Bounds for Random Neural Networks and Reservoir Systems

This work studies approximation based on single-hidden-layer feedforward...

0 Lukas Gonon, et al. ∙

∙ 11/20/2019

Uniform error estimates for artificial neural network approximations for heat equations

Recently, artificial neural networks (ANNs) in conjunction with stochast...

0 Lukas Gonon, et al. ∙

∙ 10/30/2019

Risk bounds for reservoir computing

We analyze the practices of reservoir computing in the framework of stat...

0 Lukas Gonon, et al. ∙

∙ 07/07/2018

Reservoir Computing Universality With Stochastic Inputs

The universal approximation properties with respect to L ^p -type criter...

0 Lukas Gonon, et al. ∙

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