论文标题
深层神经网络对近似的局限
Limitations on approximation by deep and shallow neural networks
论文作者
论文摘要
我们证明了卡尔的类型不等式，即通过深层和浅的神经网络近似紧凑型集的误差。反过来，这给出了我们在要求从此类网络输出的近似值来近似k中的功能的下限。我们的结果是作为最近引入Lipschitz宽度的研究的副产品获得的。
We prove Carl's type inequalities for the error of approximation of compact sets K by deep and shallow neural networks. This in turn gives lower bounds on how well we can approximate the functions in K when requiring the approximants to come from outputs of such networks. Our results are obtained as a byproduct of the study of the recently introduced Lipschitz widths.
