7 papers
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…
An Adaptive Random Fourier Features approach Applied to Learning Stochastic Differential Equations
Owen Douglas, Aku Kammonen, Anamika Pandey +1
This work proposes a training algorithm based on adaptive random Fourier features (ARFF) with Metropolis sampling and resampling \cite{kammonen2024adaptiverandomfourierfeatures} fo…
Adaptive Random Fourier Features Training Stabilized By Resampling With Applications in Image Regression
Aku Kammonen, Anamika Pandey, Erik von Schwerin +1
This paper presents an enhanced adaptive random Fourier features (ARFF) training algorithm for shallow neural networks, building upon the work introduced in "Adaptive Random Fourie…
Comparing Spectral Bias and Robustness For Two-Layer Neural Networks: SGD vs Adaptive Random Fourier Features
Aku Kammonen, Lisi Liang, Anamika Pandey +1
We present experimental results highlighting two key differences resulting from the choice of training algorithm for two-layer neural networks. The spectral bias of neural networks…
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…
Canonical quantum observables for molecular systems approximated by ab initio molecular dynamics
Aku Kammonen, Petr Plechac, Mattias Sandberg +1
It is known that ab initio molecular dynamics based on the electron ground state eigenvalue can be used to approximate quantum observables in the canonical ensemble when the temper…