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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...
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04/02/2023
Infinite-dimensional reservoir computing
Reservoir computing approximation and generalization bounds are proved f...
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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...
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12/30/2022
Reservoir kernels and Volterra series
A universal kernel is constructed whose sections approximate any causal ...
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10/19/2022
Deep neural network expressivity for optimal stopping problems
This article studies deep neural network expression rates for optimal st...
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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 ...
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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 ...
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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...
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10/22/2020
Fading memory echo state networks are universal
Echo state networks (ESNs) have been recently proved to be universal app...
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09/17/2020
Discrete-time signatures and randomness in reservoir computing
A new explanation of geometric nature of the reservoir computing phenome...
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07/03/2020
Weak error analysis for stochastic gradient descent optimization algorithms
Stochastic gradient descent (SGD) type optimization schemes are fundamen...
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04/22/2020
Memory and forecasting capacities of nonlinear recurrent networks
The notion of memory capacity, originally introduced for echo state and ...
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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...
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02/14/2020
Approximation Bounds for Random Neural Networks and Reservoir Systems
This work studies approximation based on single-hidden-layer feedforward...
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11/20/2019
Uniform error estimates for artificial neural network approximations for heat equations
Recently, artificial neural networks (ANNs) in conjunction with stochast...
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10/30/2019
Risk bounds for reservoir computing
We analyze the practices of reservoir computing in the framework of stat...
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07/07/2018