How are neural networks related to Fourier transforms

本篇是转载的文章，来源链接如下：

https://www.quora.com/How-are-neural-networks-related-to-Fourier-transforms

核心是解答一个常见的、但是又不容易搞清楚的问题：CNN为基础的深度学习跟常规的数学运算，例如FFT是什么关系？

下文的回答主要包含两个部分，即深度学习与FFT的相同和不同之处。

Taylor series and Fourier Series are  function approximation techniques.

The neural network is itself is a function approximation( Universal Function approximation).

Image Source:   Neural Networks by Raul Rojas.

This image shows how to use Taylor series and Fourier series as Neural Network.

But the difference between the (Taylor series or Fourier series )and Artificial Neural networks is ..

Artificial Neural Networks are used to approximate an unknown function and only function value at some points are given. Task is to learn the function ( or approximate) by using these given points and generalize as best as we can by a learning technique. Parameters are learned using an iterative technique like gradient descent.

The parameters in Taylor series a1,a2,a3,... are found by finding the nth order derivatives of the function at particular points. In the same way Fourier parameters can also be found by evaluating the given function. Parameters are directly computed using formula applied to actual function.