We prove a theorem concerning the approximation of multivariate functions by deep ReLU networks, for which the curse of the dimensionality is lessened. Our theorem is based on a constructive proof of the Kolmogorov–Arnold superposition theorem, and on a subset of multivariate continuous functions whose outer superposition functions can be efficiently approximated by deep ReLU networks.

中文翻译：

---

使用Kolmogorov-Arnold叠加定理的深度ReLU网络的误差范围。

我们证明了一个关于通过深层ReLU网络逼近多元函数的定理，从而减少了维数的诅咒。我们的定理基于Kolmogorov–Arnold叠加定理的构造证明，以及多元连续函数的子集，其外部叠加函数可以通过深ReLU网络有效地近似。