5 papers
Radon Measure Representations for Infinite-Width Neural Networks with Singular Activations
Mathias Dus
The theoretical foundation of infinite-width shallow neural networks relies heavily on continuous integral representations and Barron spaces. Recently, harmonic analysis-specifical…
Wasserstein Formulation of Reinforcement Learning. An Optimal Transport Perspective on Policy Optimization
Mathias Dus
We present a geometric framework for Reinforcement Learning (RL) that views policies as maps into the Wasserstein space of action probabilities. First, we define a Riemannian struc…
Grassmannian Geometry and Global Convergence of Variable Projection for Neural Networks
Mathias Dus
Training deep neural networks and Physics-Informed Neural Networks (PINNs) often leads to ill-conditioned and stiff optimization problems. A key structural feature of these models…
Comparison between tensor methods and neural networks in electronic structure calculations
Mathias Dus, Geneviève Dusson, Virginie Ehrlacher +2
This article compares the tensor method density matrix renormalization group (DMRG) with two neural network based methods -namely FermiNet and PauliNet) for determining the ground…
Two-layers neural networks for Schr{ö}dinger eigenvalue problems
Mathias Dus, Virginie Ehrlacher, Ehrlacher Virginie
The aim of this article is to analyze numerical schemes using two-layer neural networks with infinite width for the resolution of high-dimensional Schr{ö}dinger eigenvalue problems…