I can't express the extent to which autodifferentiation was like a revelation to me. I don't work in ML, but in grad school around 2010 I was implementing densi

I can't express the extent to which autodifferentiation was like a revelation to me. I don't work in ML, but in grad school around 2010 I was implementing density functional theory computations in a code that was written in Fortran 77. My particular optimization needs required computing to second derivatives. I had Mathematica to actually calculate the derivatives, but even just the step of mechanically translating the computed derivatives into Fortran 77 code would be a week of tedious work. Worse was rewriting these derivative expressions for numerical stability. The worst was realizing you made a mistake in an expression high in the tree and having to rewrite everything below. The whole process took months for a single model, and that's with chain rule depth that probably could be counted on one hand. I can't imagine deep learning making the kind of progress it has without autodifferentiation - the only saving grace is that neural networks tend to be composed from large number of copies of identical functions, and you only need to go to first derivatives.