Yes, it's the same idea. But Julia's differentiable programming capabilities are far more advanced and mature than Swift's. As far as I'm aware, Swift still doesn't support differentiating code with control flow (branches or loops), which, needless to say, eliminates pretty much all non-trivial programs.

Compare that to the situation in Julia: ∂P works today on arbitrary programs—like the ray tracer and other examples in this paper—programs which are highly non-trivial and use iteration, recursion, mutation and global state. All of which Julia's ∂P can take derivatives through.

When you additionally consider Swift's essentially non-existent computational and data science ecosystem, it's a bit hard (for me at least) to rationalize the Swift ∂P effort. (Are we going to differentiate iPhone apps?) They're attempting to bootstrap their computational/data ecosystem by allowing calling Python code, but as soon as you call into Python, you lose all ability to take derivatives which only works for pure Swift code. So any program which relies on Python to do some of the computation you want to take a derivative of won't be differentiable, which kind of defeats the point of having ∂P in the first place. We'll see how it pans out but the Swift effort has considerable technical and social challenges to overcome.

Does Swift have an equivalent to Python‘s numpy?

It seems to lack a nice way of doing vector and matrix operations.

Thanks for linking this. I have been curious how auto diff gets implemented.