We constructively prove that every deep ReLU network can be rewritten as a
functionally identical three-layer network with weights valued in the extended
reals. Based on this proof, we provide an algorithm that, given a deep ReLU
network, finds the explicit weights of the corresponding shallow network. The
resulting shallow network is transparent and used to generate explanations of
the model s behaviour.

本文证明了每个深度 ReLU 网络可以被重写为具有扩展实值权重的功能相同的三层网络，并提供了一个算法，可以在给定深度 ReLU 网络的情况下找到相应浅层网络的显式权重，以透明地生成模型行为的解释。

任何深度的 ReLU 网络都是浅层的

Any Deep ReLU Network is Shallow

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.

通过 Kolmogorov - Arnold 叠加定理的建设性证明以及外部叠加函数可以通过深度 ReLU 网络有效逼近的一些多元连续函数的子集，我们证明了关于深度 ReLU 网络逼近多元函数的定理，其中降低了维度诅咒。