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07/15/2023
Variational Monte Carlo on a Budget – Fine-tuning pre-trained Neural Wavefunctions
Obtaining accurate solutions to the Schrödinger equation is the key chal...
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04/04/2023
FakET: Simulating Cryo-Electron Tomograms with Neural Style Transfer
Particle localization and -classification constitute two of the most fun...
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03/17/2023
Towards a Foundation Model for Neural Network Wavefunctions
Deep neural networks have become a highly accurate and powerful wavefunc...
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05/26/2022
Training ReLU networks to high uniform accuracy is intractable
Statistical learning theory provides bounds on the necessary number of t...
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05/19/2022
Gold-standard solutions to the Schrödinger equation using deep learning: How much physics do we need?
Finding accurate solutions to the Schrödinger equation is the key unsolv...
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12/20/2021
Integral representations of shallow neural network with Rectified Power Unit activation function
In this effort, we derive a formula for the integral representation of a...
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10/28/2021
Sobolev-type embeddings for neural network approximation spaces
We consider neural network approximation spaces that classify functions ...
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09/06/2021
Stable Gabor phase retrieval in Gaussian shift-invariant spaces via biorthogonality
We study the phase reconstruction of signals f belonging to complex Gaus...
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05/18/2021
Solving the electronic Schrödinger equation for multiple nuclear geometries with weight-sharing deep neural networks
Accurate numerical solutions for the Schrödinger equation are of utmost ...
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05/09/2021
The Modern Mathematics of Deep Learning
We describe the new field of mathematical analysis of deep learning. Thi...
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04/06/2021
Proof of the Theory-to-Practice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces
We study the computational complexity of (deterministic or randomized) a...
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03/09/2021
Deep neural network approximation for high-dimensional parabolic Hamilton-Jacobi-Bellman equations
The approximation of solutions to second order Hamilton–Jacobi–Bellman (...
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03/07/2021
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...
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11/09/2020
Numerically Solving Parametric Families of High-Dimensional Kolmogorov Partial Differential Equations via Deep Learning
We present a deep learning algorithm for the numerical solution of param...
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08/03/2020
Phase Transitions in Rate Distortion Theory and Deep Learning
Rate distortion theory is concerned with optimally encoding a given sign...
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07/10/2020
Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions
In recent work it has been established that deep neural networks are cap...
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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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08/28/2019
Deep neural network approximations for Monte Carlo algorithms
Recently, it has been proposed in the literature to employ deep neural n...
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08/11/2019
Space-time error estimates for deep neural network approximations for differential equations
Over the last few years deep artificial neural networks (DNNs) have very...
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05/23/2019
How degenerate is the parametrization of neural networks with the ReLU activation function?
Neural network training is usually accomplished by solving a non-convex ...
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05/13/2019
Towards a regularity theory for ReLU networks -- chain rule and global error estimates
Although for neural networks with locally Lipschitz continuous activatio...
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01/17/2019
The Oracle of DLphi
We present a novel technique based on deep learning and set theory which...
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01/08/2019
Deep Neural Network Approximation Theory
Deep neural networks have become state-of-the-art technology for a wide ...
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09/09/2018
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...
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09/07/2018
A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations
Artificial neural networks (ANNs) have very successfully been used in nu...
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06/05/2018
The universal approximation power of finite-width deep ReLU networks
We show that finite-width deep ReLU neural networks yield rate-distortio...
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06/01/2018
Solving stochastic differential equations and Kolmogorov equations by means of deep learning
Stochastic differential equations (SDEs) and the Kolmogorov partial diff...
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07/10/2017
Topology Reduction in Deep Convolutional Feature Extraction Networks
Deep convolutional neural networks (CNNs) used in practice employ potent...
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04/12/2017
Energy Propagation in Deep Convolutional Neural Networks
Many practical machine learning tasks employ very deep convolutional neu...
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05/26/2016
Discrete Deep Feature Extraction: A Theory and New Architectures
First steps towards a mathematical theory of deep convolutional neural n...
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04/29/2016