The purpose of training neural networks is to minimize a loss function, in this process we usually use gradient descent method.
But in Calculus, if we want to find the global minimum of a multivariable function, we usually first calculate the partial derivatives of this function with respect to its variables, and then set these partial derivatives to zeros, and then find the solutions of these equations. Usually we get a bunch of points. We can use the second derivative method(involving Hesse Matrix) to determine whether these points give local minimum values, or we can directly evaluate the values of the function at these points and compare them to find the minimum.
So, I'm curious why don't we use this classical method in Calculus to find the global minimum value of the loss function and instead using gradient descent? Is it hard to for computer to find zeros of multivariable equations?