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SMALLER GENERALIZAT...
SMALLER GENERALIZATION ERROR DERIVED FOR DEEP COMPARED TO SHALLOW RESIDUAL NEURAL NETWORKS
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- Kammonen, Aku, 1984- (författare)
- KTH,Numerisk analys, NA
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- Kiessling, Jonas (författare)
- KTH,Numerisk analys, NA
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Petr, Plecháč (författare)
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- Sandberg, Mattias (författare)
- KTH,Numerisk analys, NA
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- Szepessy, Anders, 1960- (författare)
- KTH,Numerisk analys, NA
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Tempone, Raúl (författare)
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(creator_code:org_t)
- Engelska.
- Relaterad länk:
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http://arxiv-export-...
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https://urn.kb.se/re...
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Abstract
Ämnesord
Stäng
- Estimates of the generalization error are proved for a residual neural network with $L$ random Fourier features layers $\bar z_{\ell+1}=\bar z_\ell + \mathrm{Re}\sum_{k=1}^K\bar b_{\ell k}e^{\mathrm{i}\omega_{\ell k}\bar z_\ell}+\mathrm{Re}\sum_{k=1}^K\bar c_{\ell k}e^{\mathrm{i}\omega'_{\ell k}\cdot x}$. An optimal distribution for the frequencies $(\omega_{\ell k},\omega'_{\ell k})$ of the random Fourier features $e^{\mathrm{i}\omega_{\ell k}\bar z_\ell}$ and $e^{\mathrm{i}\omega'_{\ell k}\cdot x}$ is derived. This derivation is based on the corresponding generalization error for the approximation of the 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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Nyckelord
- residual network
- deep random feature
- supervised learning
- error estimates
- layer by layer algorithm
- Numerical Analysis
- Numerisk analys
Publikations- och innehållstyp
- vet (ämneskategori)
- ovr (ämneskategori)