[FooBarBizBazz]

Reverse mode autodiff is best implemented with a non-local transformation of the program: First you run the original operations forward; then you run corresponding operations in reverse order.

You can do this with a library by implementing "number" types that, as a side effect of arithmetic operations, record those operations onto a "tape", so that corresponding (different) operations can be played back later in reverse order.

Unfortunately, those side effects have a cost during the forward pass. And during the backwards pass you are essentially running a little interpreter to execute your instructions.

Putting this stuff into the compiler lets the forward pass just be normal, native code on doubles/floats, and the same for the reverse-pass code. Moreover, all of this can now be worked on by the optimizing compiler.

This is especially important for embedded applications where you can't afford all this interpretation.

I guess the original TensorFlow "computation graph" approach is a little different to the "tape" I described because the graph is built explicitly rather than through side effects, but that just makes even more clear that you're really assembling an AST for some /other/ language and (when not using XLA) running an interpreter.

In principle some suitably powerful macro language with full access to the AST might be able to do good compile-time reverse-mode AD, but I am not aware of any language with powerful enough macros. Again, this is because the transformation is not just a local pattern replacement; it involves flipping the code upside down.

What's funny is that physicists have been able to do this kind of program transformation in a slightly clunky(?) way -- FORTRAN in, FORTRAN out -- since the 70s, supposedly.

It all makes me think that our ideas about what a "language" is, what a "compiler" is, what a "library" is, are all stuck in convention and prematurely ossified. The first compilers, which we celebrate, looked to their users like codegen (which we detest, I think)! I would love for the boundary between "language" and "compiler" to be broken down more so that AD could be more easily done "within the language"; maybe one day that will happen in Julia, or Nim, or Jai, or Terra.

But for now I think I agree with the designers that the best hope for good results, and really the most straightforward way, is to just do it in the compiler.

[ddragon]

Just complementing the other reply, there is a small article about how you can implement a source to source AD in Julia [1]. Basically Julia has a special type of macro called generated function [2] which instead of executing during the AST lowering phase (when the compiler still didn't evaluate the symbols) it executes during the final step of compilation (when type inference already ran and you have all the exact types), and in that function you can return either the AST or Julia's SSA IR directly (which is good for AD since it closely resembles the execution graph since it avoids mutability). And you can also inspect the IR of any function call and manipulate it within the language [3], so you can recursively create the tape entirely at compile time.

[1] http://blog.rogerluo.me/2019/07/27/yassad/

[2] https://docs.julialang.org/en/v1/manual/metaprogramming/inde...

[3] https://mikeinnes.github.io/IRTools.jl/latest/#Evaluating-IR...

[byt143]

It's already bring done in Julia. See zygote.jl.

Works with typed IR equivalent to a core compiler pass but from a third party package with regular Julia staged programming.