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Jul, 2023
加权变差空间与浅层ReLU网络的逼近
Weighted variation spaces and approximation by shallow ReLU networks
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Ronald DeVore, Robert D. Nowak, Rahul Parhi, Jonathan W. Siegel
TL;DR
通过引入加权变分空间的概念,本文给出了在域中定义这些新模型类的更加恰当的定义。这些新模型类固有于域本身,并且与经典(与域无关)模型类相比更大,但仍然保持着相同的神经网络逼近速率。
Abstract
We investigate the
approximation
of functions $f$ on a bounded
domain
$\Omega\subset \mathbb{R}^d$ by the outputs of single-hidden-layer ReLU
neu
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