Common interface for rule definition

[gdalle]

It would be nice to have a universal translator between:

• ChainRulesCore.jl
• ForwardDiffChainRules.jl
• Enzyme.jl rules
• Mooncakes.jl rules

At the moment, DI.DifferentiateWith is a partial answer, but

• it only works for one argument, number or array
• it only defines rules for ForwardDiff and ChainRules (but that's not a limitation just a question of time)
• it requires users to replace every f with DifferentiateWith(f, other_backend)

[gdalle]

@antoine-levitt feel free to add comments here

@willtebbutt I'd love to hear your thoughts

[willtebbutt]

I think we ought to be able to do a reasonable job of translating between Mooncake tangents / fdata / rdata and Enzyme's Duplicated / Active system, because they're both quite precisely specified. There are some differences, for example, if the primal value is a Vector{Int}, then the Mooncake tangent type is Vector{Mooncake.NoTangent} while the Enzyme type would (I believe) be another Vector{Int}, or might require that you make it a Const.

Re ChainRules, we'd have to make some choices, because the conversion is fundamentally ambiguous (ChainRules permits you to represent the tangent of anything with anything). That being said, I have to attempt to do this for ChainRules integration in Mooncake -- see here -- it's currently rather unsatisfying and incomplete.

This is all to say that I doubt a truly universal translator is possible, but we ought to be able to identify a set of types for which the conversion is possible, and provide reasonably informative error messages if someone attempts to do something we don't know how to handle.

[yebai]

ReverseDiff and ForwardDiff are likely the most used autograd backends for Turing.jl, so we would like to keep supporting them even after Mooncake / Enzyme becomes more stable. Meanwhile, we likely will depreciate Zygote / Tracker in favour of Mooncake.

Unfortunately, supporting ReverseDiff and ForwardDiff means we must maintain and add many extra rules (see, e.g. DistributionsAD.jl, Bijectors.jl, and DynamicPPL.jl). I'd like to see an option to use Mooncake / Enzyme to define rules for ReverseDiff / ForwardDiff straightforwardly in the near future.

EDIT: I just noticed it is already possible to define ForwardDiff rules via Enzyme / Mooncake using DI.DifferentiateWith. Can similar functionality be added for ReverseDiff?

EDIT 2: it is often okay to manually replace f with DifferentiateWith(f, backend), so we don't necessarily need a new (universal) rule system. But please hook DifferentiateWith(f, backend) in more autograd libraries similar to ForwardDiff / Zygote.

[antoine-levitt]

Yeah, from a user point of view it doesn't really matter what rule system we use, but we'd like to use just one. That unfortunately looks quite tricky.

In my application I want to differentiate wrt things that are hidden in structs, eg struct A{T} a::T end; f(x::A) = x.a^2. The appropriate ForwardDiff overload is f(x::A{<:Dual)), but really there's no way for a rule system to know this automatically, so I guess some amount of manual adaptation is needed, see eg ForwardDiffChainRules which requires you to say something like @ForwardDiff_frule f(x::A{Dual}). Is there something else that would prevent a UniversalChainRules package (the naming is bad I know) where I would say @universal_rrule f(x)... and that would do @rrule and also tell Enzyme/whatever to import it?

[wsmoses]

You can just do Enzyme.@import_rrule / @import_frule and it'll import whatever chainrule is defined for that.

So your "universal_rrule" macro for the moment would be something like

macro universal_rrule
  @rrule. args...
  Enzyme.@import_rrule args...
end

That said I really don't think this should go here, probably in Chainrules or something

[gdalle]

I have added this page to the docs in order to explain rule definition in more detail: https://juliadiff.org/DifferentiationInterface.jl/DifferentiationInterface/stable/faq/differentiability/