We identify hidden layers inside a DNN with group actions on the data space, and formulate the DNN as a dual voice transform with respect to Koopman operator, a linear representation of the group action. Based on the group theoretic arguments, particularly by using Schur's lemma, we show a simple proof of the universality of those DNNs.

翻译：我们将深度神经网络中的隐藏层识别为数据空间上的群作用，并将深度神经网络形式化为关于Koopman算子（群作用的线性表示）的对偶Voice变换。基于群论论证，特别是利用Schur引理，我们给出了此类深度神经网络普适性的简洁证明。