From automatic differentiation to message passing [video]

This is a perspective I’ve been taking recently as I’ve been investigating next-gen DL frameworks like Julia’s Zygote and Swift for Twnsorflow. So it’s very nice to see this articulated so well here by someone who has been thinking deeply about it for so long.

I’ll add some things that relate to this perspective: there is a follow up paper to the DL via Hessian-free optimization paper by James Martens that develops a variant of AD which calculates a special curvature quantity which is useful for efficient second order optimization. This emphasizes that AD is just one of a family of program transformations, most of which are probably waiting to be discovered. For example, would it be useful to have an AD-like pass that calculated trusted regions for gradient updates? And: why do we not do more iteration during DL in which we interleave forward and backward for a single layer only? (rhetorical question, there are many reasons but asking this question forces you to think deeply about a lot of things)

Also, if you generalize VAEs to be arbitrary differentiable programs you immediately run into versions of message passing. For example, vector quantized VAEs are a precisely a soft version of the EM step in k-means. So how would we develop more advanced variational programs in which this process is better managed? There may be very different forms for the inference and generation phases that are not related by a program transformation, or ARE related but only in a high-level way best captured by functional programming primitives.

Any other people nerding out about this stuff please say hi!

> Automatic differentiation is an elegant technique for converting a computable function expressed as a program into a derivative-computing program with similar time complexity. It does not execute the original program as a black-box, nor does it expand the program into a mathematical formula, both of which would be counter-productive. By generalizing this technique, you can produce efficient algorithms for constraint satisfaction, optimization, and Bayesian inference on models specified as programs. This approach can be broadly described as compiling into a message-passing program.

https://www.microsoft.com/en-us/research/video/from-automati...

At the end of the presentation the presented mentions that this is structurally identical to loopy belief propagation... Isn't that a big issue, since they inherit many of its tractability issues with regards to training and inference? Modern DL models are far too interconnected for inference to be tractable in general, so the best we can hope for is that we can make simplifying assumptions that make loopy belief propagation feasible.

As a side note, when modern compilers optimize abstract syntax trees, I'm pretty sure they do operations that are similar to the message-passing algorithm described. And they work great, albeit for specialized purposes.

It seems to me that the message-passing aspect is kind of an implementation detail.

In any case, compare and contrast with "Compiling to categories" http://conal.net/papers/compiling-to-categories/

Another approach to AD is: https://github.com/keithalewis/epsilon.