jkam

What was the gift from Google?

What kind of work are you referring to when you say higher-order SGD may _now_ be feasible for deep learning? I only find results that try to approximate second order information.

Are you referring to the Ricci notation when you are saying it uses a different representation of the tensors? Do you also plan to add non-differentiable functions like relu?

I think XLA is trying to reduce the overhead introduced by backprop, meaning when you optimize the computational graph you might end up with an efficient calculation of the gradient (closer to the calculation you get with MC). Regarding non-scalar valued functions: Don't you reduce a constrained problem to a series of unconstrained problems (via a penalty (or even augmented Lagrangian) or barrier method)? Then you only need the gradient of a scalar valued function to solve constrained problems. I imagine you can use the gradients of the constraints for solving the KKT conditions directly but this seems only useful if the system is not too big. But for sure it opens new possibilities.

I'm good. Looking at things from the data angle now. But unfortunately no public page. You can link to the old one, if you want to. Have you compared against TensorFlow XLA?

I wonder why they don't do it. In the tool I had running, we handled this by removing any transpose of a symmetric matrix (after propagating it before the leaves). Together with the simplification rule x + x -> 2*x for any x, you get the expected result. I could only guess why they didn't include it in the online matrix calculus tool. It was published after I left the group.