I am reading about conjugated gradient methods to understand how they exactly work. I understand that a pair of vector $u$ and $v$ are conjugated with respect to $A$ if $u^TAv=0$. I also read that $A$ is symmetric, positive definite matrix.
I am trying to find out how is that related to training of neural network by minimalising mean-square error function using CG method. What will be $A$ matrix in that case? How $A$ matrix is connected to weights of neural network. And is it still symmetric and positive definite? I read What is conjugate gradient descent? this thread and resources linked there, but I still can't figure it out.
I'm sure I'm missing something simple, but could you give me a bit of explanation?