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!