5 papers · 1 filter
Convergence for adaptive resampling of random Fourier features
Xin Huang, Aku Kammonen, Anamika Pandey +4
The machine learning random Fourier feature method for data in high dimension is computationally and theoretically attractive since the optimization is based on a convex standard l…
Convergence rates for random feature neural network approximation in molecular dynamics
Xin Huang, Petr Plechac, Mattias Sandberg +1
Random feature neural network approximations of the potential in Hamiltonian systems yield approximations of molecular dynamics correlation observables that have the expected error…
Path integral molecular dynamics approximations of quantum canonical observables
Xin Huang, Petr Plechac, Mattias Sandberg +1
Mean-field molecular dynamics based on path integrals is used to approximate canonical quantum observables for particle systems consisting of nuclei and electrons. A computational…
Smaller generalization error derived for a deep residual neural network compared to shallow networks
Aku Kammonen, Jonas Kiessling, Petr Plecháč +3
Estimates of the generalization error are proved for a residual neural network with random Fourier features layers $\bar z_{\ell+1}=\bar z_\ell + \mathrm{Re}\sum_{k=1}^K\bar b_…
Adaptive random Fourier features with Metropolis sampling
Aku Kammonen, Jonas Kiessling, Petr Plecháč +2
The supervised learning problem to determine a neural network approximation with one hidden layer is studied…