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Currying differentiable functions in Swift. Full version with transpose here: https://gist.github.com/rxwei/1cfb98027f656adb1ebfa8af56826c97.
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// Function-as-a-differentiable-type rule: | |
// Tangent space: ((T...) -> U...)' = Any | |
// Cotangent space: ((T...) -> U...)'* = Any | |
// Why? Because when a function value is varying, what's varying is it's context. | |
// In general cases, we need this to be a constrained existential with an | |
// `AdditiveArithmetic` conformance for its `.zero` and `+`, and `Differentiable` | |
// for being able to transpose between differential and a pullback. | |
// New associated function type calculation rules: | |
// original: (T...) -> (U...) | |
// jvp: (T...) -> (value: U, differential: (Any, T...') -> (U...')) | |
// jvp: (T...) -> (value: U, pullback: (U...'*) -> (Any, T...'*)) | |
func curry<T: Differentiable, U: Differentiable, V: Differentiable>( | |
_ 𝑓: @escaping @differentiable (T, U) -> V | |
) -> @differentiable (T) -> @differentiable (U) -> V { | |
// Outer function. | |
let f: @differentiable (T) -> @differentiable (U) -> (V) = makeDifferentiable { x in | |
// Inner function. | |
let g: @differentiable (U) -> V = makeDifferentiable { y in | |
let (z, φ٭ᶻ) = valueWithPullback(at: x, y, in: 𝑓) | |
let φ٭ᵍ: (V.CotangentVector) -> (Any, U.CotangentVector) = { z̅ in | |
let (x̅, y̅) = φ٭ᶻ(z̅) | |
return (x̅ as Any, y̅) | |
} | |
return (value: z, pullback: φ٭ᵍ) | |
} | |
let φ٭ᶠ: (Any) -> (Any, T.CotangentVector) = { g̅ in | |
return ((), g̅ as! T.CotangentVector) | |
} | |
return (value: g, pullback: φ٭ᶠ) | |
} | |
return f | |
} | |
// Turns the VJP for a thick function into a `@differentiable` function. | |
func makeDifferentiable<T: Differentiable, U: Differentiable>( | |
from vjp: (T) -> (value: U, pullback: (U.CotangentVector) -> (Any, T.CotangentVector)) | |
) -> @differentiable (T) -> U { | |
fatalError() | |
} | |
// Turns the VJP for a thick function whose result is a `@differentiable` function into a `@differentiable` function. | |
func makeDifferentiable<T: Differentiable, U: Differentiable, V: Differentiable>( | |
from vjp: (T) -> (value: @differentiable (U) -> V, pullback: (Any) -> (Any, T.CotangentVector)) | |
) -> @differentiable (T) -> @differentiable (U) -> V { | |
fatalError() | |
} |
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