From https://stackoverflow.com/questions/36370129/does-tensorflow-use-automatic-or-symbolic-gradients, I understood TensorFlow requires all the operations in the Graph to be explicit formulas (instead of black-boxes, such as raw python functions) to do Automatic Differentiation. Then it will do some kind of Gradient Descent based on that to minimization.
I'm wondering, since it already know all the explicit formulas, can it directly find out the minimum by examining the equation itself? Like computing the points where gradient is zero or do not exist, then do some kind of processing to find out the minimum.
I found it is simple to do this "symbolic minimization" above with few variables such as minimizing
Σ(a_i - v)^2 where
v is the trainable variable an
a_i are all the training samples. I'm not sure is there a general way though.