论文标题
Kolmogorov宽度衰减和机器学习中的近似差：浅神经网络，随机特征模型和神经切线内核
Kolmogorov Width Decay and Poor Approximators in Machine Learning: Shallow Neural Networks, Random Feature Models and Neural Tangent Kernels
论文作者
论文摘要
我们在给定BANACH空间的子空间之间建立了Kolmogorov宽度类型的比例分离，因为在其中一个子空间上，线性地图序列会收敛得更快。然后，将一般技术应用于表明，复制元素希尔伯特空间的$ l^2 $ - approximators用于高维度的两层神经网络的类别，并且具有小路径标准的多层网络是某些Lipschitz功能的较差的近似近似值，也是$ l^2 $ - 多功能学。
We establish a scale separation of Kolmogorov width type between subspaces of a given Banach space under the condition that a sequence of linear maps converges much faster on one of the subspaces. The general technique is then applied to show that reproducing kernel Hilbert spaces are poor $L^2$-approximators for the class of two-layer neural networks in high dimension, and that multi-layer networks with small path norm are poor approximators for certain Lipschitz functions, also in the $L^2$-topology.
