
Stable Gabor phase retrieval in Gaussian shiftinvariant spaces via biorthogonality
We study the phase reconstruction of signals f belonging to complex Gaus...
read it

Solving the electronic Schrödinger equation for multiple nuclear geometries with weightsharing deep neural networks
Accurate numerical solutions for the Schrödinger equation are of utmost ...
read it

The Modern Mathematics of Deep Learning
We describe the new field of mathematical analysis of deep learning. Thi...
read it

Proof of the TheorytoPractice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces
We study the computational complexity of (deterministic or randomized) a...
read it

Deep neural network approximation for highdimensional parabolic HamiltonJacobiBellman equations
The approximation of solutions to second order Hamilton–Jacobi–Bellman (...
read it

Lower bounds for artificial neural network approximations: A proof that shallow neural networks fail to overcome the curse of dimensionality
Artificial neural networks (ANNs) have become a very powerful tool in th...
read it

Numerically Solving Parametric Families of HighDimensional Kolmogorov Partial Differential Equations via Deep Learning
We present a deep learning algorithm for the numerical solution of param...
read it

Phase Transitions in Rate Distortion Theory and Deep Learning
Rate distortion theory is concerned with optimally encoding a given sign...
read it

Deep neural network approximation for highdimensional elliptic PDEs with boundary conditions
In recent work it has been established that deep neural networks are cap...
read it

Uniform error estimates for artificial neural network approximations for heat equations
Recently, artificial neural networks (ANNs) in conjunction with stochast...
read it

Deep neural network approximations for Monte Carlo algorithms
Recently, it has been proposed in the literature to employ deep neural n...
read it

Spacetime error estimates for deep neural network approximations for differential equations
Over the last few years deep artificial neural networks (DNNs) have very...
read it

How degenerate is the parametrization of neural networks with the ReLU activation function?
Neural network training is usually accomplished by solving a nonconvex ...
read it

Towards a regularity theory for ReLU networks  chain rule and global error estimates
Although for neural networks with locally Lipschitz continuous activatio...
read it

The Oracle of DLphi
We present a novel technique based on deep learning and set theory which...
read it

Deep Neural Network Approximation Theory
Deep neural networks have become stateoftheart technology for a wide ...
read it

Analysis of the generalization error: Empirical risk minimization over deep artificial neural networks overcomes the curse of dimensionality in the numerical approximation of B
The development of new classification and regression algorithms based on...
read it

A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of BlackScholes partial differential equations
Artificial neural networks (ANNs) have very successfully been used in nu...
read it

The universal approximation power of finitewidth deep ReLU networks
We show that finitewidth deep ReLU neural networks yield ratedistortio...
read it

Solving stochastic differential equations and Kolmogorov equations by means of deep learning
Stochastic differential equations (SDEs) and the Kolmogorov partial diff...
read it

Topology Reduction in Deep Convolutional Feature Extraction Networks
Deep convolutional neural networks (CNNs) used in practice employ potent...
read it

Energy Propagation in Deep Convolutional Neural Networks
Many practical machine learning tasks employ very deep convolutional neu...
read it

Discrete Deep Feature Extraction: A Theory and New Architectures
First steps towards a mathematical theory of deep convolutional neural n...
read it

Deep Convolutional Neural Networks on Cartoon Functions
Wiatowski and Bölcskei, 2015, proved that deformation stability and vert...
read it
Philipp Grohs
is this you? claim profile