How are neural networks related to Fourier transforms

本篇是轉載的文章，來源鏈接如下：

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

核心是解答一個常見的、但是又不容易搞清楚的問題：CNN爲基礎的深度學習跟常規的數學運算，例如FFT是什麼關係？

下文的回答主要包含兩個部分，即深度學習與FFT的相同和不同之處。

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.