3 papers
math.NA2020
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_…
math.NA2020
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…
math-ph2019
Classical Langevin dynamics derived from quantum mechanics
Håkon Hoel, Anders Szepessy
The classical work by Zwanzig [J. Stat. Phys. 9 (1973) 215-220] derived Langevin dynamics from a Hamiltonian system of a heavy particle coupled to a heat bath. This work extends Zw…