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- W2938185552 abstract "We discuss the expressive power of neural networks which use the non-smooth ReLU activation function $varrho(x) = max{0,x}$ by analyzing the approximation theoretic properties of such networks. The existing results mainly fall into two categories: approximation using ReLU networks with a fixed depth, or using ReLU networks whose depth increases with the approximation accuracy. After reviewing these findings, we show that the results concerning networks with fixed depth--- which up to now only consider approximation in $L^p(lambda)$ for the Lebesgue measure $lambda$--- can be generalized to approximation in $L^p(mu)$, for any finite Borel measure $mu$. In particular, the generalized results apply in the usual setting of statistical learning theory, where one is interested in approximation in $L^2(mathbb{P})$, with the probability measure $mathbb{P}$ describing the distribution of the data." @default.
- W2938185552 created "2019-04-25" @default.
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- W2938185552 date "2019-04-09" @default.
- W2938185552 modified "2023-09-27" @default.
- W2938185552 title "Approximation in $L^p(mu)$ with deep ReLU neural networks." @default.
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