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- W3091336834 abstract "Estimates of the generalization error are proved for a residual neural network with $L$ random Fourier features layers $bar z_{ell+1}=bar z_ell + text{Re}sum_{k=1}^Kbar b_{ell k}e^{{rm i}omega_{ell k}bar z_ell}+ text{Re}sum_{k=1}^Kbar c_{ell k}e^{{rm i}omega'_{ell k}cdot x}$. An optimal distribution for the frequencies $(omega_{ell k},omega'_{ell k})$ of the random Fourier features $e^{{rm i}omega_{ell k}bar z_ell}$ and $e^{{rm i}omega'_{ell k}cdot x}$ is derived. The derivation is based on the corresponding generalization error to approximate function values $f(x)$. The generalization error turns out to be smaller than the estimate ${|hat f|^2_{L^1(mathbb{R}^d)}}/{(LK)}$ of the generalization error for random Fourier features with one hidden layer and the same total number of nodes $LK$, in the case the $L^infty$-norm of $f$ is much less than the $L^1$-norm of its Fourier transform $hat f$. This understanding of an optimal distribution for random features is used to construct a new training method for a deep residual network that shows promising results." @default.
- W3091336834 created "2020-10-08" @default.
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- W3091336834 date "2020-10-05" @default.
- W3091336834 modified "2023-10-16" @default.
- W3091336834 title "Smaller generalization error derived for deep compared to shallow residual neural networks" @default.
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