In this work, we consider the approximation of a large class of bounded functions, with minimal regularity assumptions, by ReLU neural networks. We show that the approximation error can be bounded from above by a quantity proportional to the uniform norm of the target function and inversely proportional to the product of network width and depth. We inherit this approximation error bound from Fourier features residual networks, a type of neural network that uses complex exponential activation functions. Our proof is constructive and proceeds by conducting a careful complexity analysis associated with the approximation of a Fourier features residual network by a ReLU network.

翻译：本文考虑利用ReLU神经网络逼近一类具有最小正则性假设的大范围有界函数。我们证明逼近误差可由目标函数的一致范数与网络宽度和深度乘积成反比的量从上方界定。该逼近误差界源自傅里叶特征残差网络——一种使用复指数激活函数的神经网络。我们的证明是构造性的，通过细致分析ReLU网络逼近傅里叶特征残差网络的复杂度来实现。