In this article we identify a general class of high-dimensional continuous functions that can be approximated by deep neural networks (DNNs) with the rectified linear unit (ReLU) activation without the curse of dimensionality. In other words, the number of DNN parameters grows at most polynomially in the input dimension and the approximation error. The functions in our class can be expressed as a potentially unbounded number of compositions of special functions which include products, maxima, and certain parallelized Lipschitz continuous functions.

翻译：本文识别了一类高维连续函数，该类函数可通过使用修正线性单元（ReLU）激活函数的深度神经网络（DNN）进行逼近，且无维数灾难。换言之，DNN参数数量在输入维度和逼近误差上最多呈多项式增长。我们所研究的函数类可表示为特殊函数（包括乘积、最大值及特定并行化Lipschitz连续函数）的潜在无界复合形式。