My understanding is that category theory can be considered as abstract function theory. If we can prove that a function (e.g. Haskell compiler) is equivalent to automatic differentiation with some transformation, according to category theory, we can write Haskell code to train neural network, instead of writing extra graph building code in, say, Tensorflow. This paper basically shows this. http://conal.net/papers/essence-of-ad/essence-of-ad-icfp.pdf.