Status update on the Differentiable Swift language feature

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Status update on the Differentiable Swift language feature

It's been a while since our last update regarding Differentiable Swift! A lot has happened since then, and I'd like to give a quick overview of what we've been up to. Since our last update by Brad Larson, almost 70 pull requests related to Differentiation have been merged into swiftlang/swift, with another 9 PR's currently awaiting review!
The contents of these include performance improvements, bug fixes, standard library additions, as well as new function signatures we can now register/generate derivatives for!

For an approximation of the full list of PRs, take a look here

Notable improvements since last update

To summarize that list of bug fixes and performance improvements, here are some of notable changes we've made over the last year:

Release toolchain stability

Previously, we relied on nightly snapshots to use the latest Differentiation features in the compiler. @clackary has done some great work in tracking quality and performance of Swift Differentiation across both main and release branches. Over the last few release cycles, we have been able to identify and resolve issues on release branches, making using open source releases viable, and the most stable option for using Differentiation. We have adopted the latest open source releases for development and production.

Differentiable functions with multiple results

Thanks to this PR, we added a large collection of function signatures we can now define derivatives for. This enables using:

  • functions with an inout parameter which also returned a result
  • functions with multiple inout parameters
  • mutating functions which returned a result
  • functions that return a tuple of results

Work towards differentiable coroutines

A series of PRs that work towards adding Differentiation support to coroutines with the ultimate goal of supporting _modify accessors. This will improve the call site when reading and writing into types like Array.
Currently we have reached the point where the compiler can differentiate _modify accessors, but there is no way to register custom derivatives for them (meaning that code like Array.subscript._modify can not be made differentiable, yet! Since supporting this relies on the presence of custom derivatives in the Differentiation module).
A final proof-of-concept PR that completes the last pieces of the puzzle is currently under review and discussion here.

Improved performance when differentiating through Array types

The compiler is now able to optimize differentiation with Array types a lot more thanks to this PR. There are still more improvements to be discovered on this front however!

Improved usability of Optional<T>

A lot of work has gone towards improving differentiation of optionals. Optional support is much more complete now.

Ongoing performance work

A lot of improvements have been made in terms of performance over the last year. This is an ongoing effort, as we have another set of optimizations tailored to differentiable code, that we are currently working on.

Upcoming features (currently open PRs)

Along with bugfixes and other improvements, here are two PRs that we are working on that we are very excited about:

Support for _modify accessors.

There's a proof-of-concept PR by Anton Korobeynikov to add support for first-class coroutines in user code. The PR enables registration of custom derivatives for _modify accessors (as the derivative itself must be a coroutine). This will improve the user experience when using Differentiation with Array types, where we currently have to use a workaround.

@differentiable(reverse)
func setValue(array: inout [Double], value: Double) {
    array[2] = 6.0 // not differentiable yet, will be with the above mentioned patch!
}

// instead we have to use
@differentiable(reverse)
func setValue(array: inout [Double], value: Double) {
    array.updated(at: 2, with: 6.0) // is differentiable (defined in our swift-differentiation package)
}

This is both less performant and not as readable/familiar.

Custom derivatives for functions marked with @_alwaysEmitIntoClient

In this PR by Daniil Kovalev support for adding custom derivatives to functions marked with @_alwaysEmitIntoClient is introduced. This for example enables differentiation of more methods on SIMD types from the standard library.

Open source packages

We've started to collect and open source some useful extensions to the Differentiable Swift API currently available in Swift 6.1 under the differentiable-swift organization. The goal here is for these packages to be a slightly more flexible way to battle-test certain implementations before upstreaming them to the standard library or their respective repository.

We currently have three packages that each extend a preexisting library in their focused direction:

swift-differentiation (extends the standard library)

A collection of useful extensions to Swift Differentiation. The contents of this repository extend the current implementation of Differentiation to give the user access to more differentiable methods than currently provided in the Swift standard library. It also contains some workarounds for some methods that are not currently differentiable due to missing support in the language itself.

swift-numerics-differentiable (extends swift-numerics)

This package exports the swift-numerics products while also adding derivatives to many of the methods provided by the original package. This mainly extends Float, Double, and some of the SIMD types with derivatives for the functions provided by the ElementaryFunctions protocol and RealFunctions protocol.

swift-collections-differentiable (extends swift-collections)

This package exports the swift-collections products while also making room to add Differentiable support to some of the types the original provides. Currently, this mainly provides Differentiable support for OrderedDictionary.

Focus going forward

Differentiable Swift remains an incredibly important feature for our team at PassiveLogic.
Going forward, we will continue to maintain the feature, resolving issues as they arise. We will also direct more effort towards solidifying the architectural foundations of the language feature.

It is an ultimate goal of ours to advance this language feature through the Swift Evolution
process, and to that end we've identified some core architectural improvements to be made for us to move in that direction:

Protocol default derivatives

Currently, we cannot provide default implementations for derivatives of protocol methods that live in a different module. This limits the amount of generic code we can make differentiable as well as adding derivatives to preexisting libraries and the standard library itself that leverage protocols. Enabling this would allow us to define derivatives for many more APIs.

Improved Closure memory allocations

The performance of computing the pullback/derivative of a function is memory bound. Every intermediate value eventually needed to compute the pullback has to be allocated on the heap during the forward pass. We're currently exploring smarter allocation strategies to try and minimize the amount of malloc calls and get more data locality.

Concluding

In the long term, moving the feature past experimental status will require wider adoption and support from more than just us at PassiveLogic. We'd love to be a resource for anyone wanting to explore the potential applications of Differentiable Swift.
Most software frameworks around machine learning are built for the current needs of the most popular deep learning techniques, but there is a world of applications for gradient descent optimization and differentiability outside of that spotlight. It's our hope that the flexibility of a language feature like this could enable underserved areas of machine learning and general optimization techniques.
If you have feedback or questions or just want to show off some interesting uses of Differentiable Swift, please reach out! Either here on the swift forums to me (@JaapWijnen), @tmcdonell, @clackary or @_ck512, or on our recently opened discord channel.

Thanks

A lot of thanks goes out to @asl for the continuing large effort put into the above improvements.

I'd like to thank the following people for their current and previous work on the Differentiation language feature:

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I think it would be really great if Differentiable Swift Tutorials had more tutorials. Maybe something like the Iris Flower Classification using Swift Differentiable to beginners and other more advanced real world tutorial.

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