@dan-zheng Apparently here is more serious problem which is not addressed by #58644. Consider the following case:

• a.swift uses function A
• b.swift defines function A
• c.swift defines custom derivative vjpA for A

#58644 handles the case when A and vjpA are both defined in the same file. However, it does not handle the case as above. There is one important special case: when A is some runtime function or defined in some external module. Then we'd effectively won't be able to register a custom derivative for it. Consider e.g. the following:

a.swift:

import _Differentiation

@differentiable(reverse)
func clamp(_ value: Double, _ lowerBound: Double, _ upperBound: Double) -> Double {
    return max(min(value, upperBound), lowerBound)
}

b.swift:

import _Differentiation

@inlinable
@derivative(of: min)
func minVJP<T: Comparable & Differentiable>(
    _ x: T,
    _ y: T
) -> (value: T, pullback: (T.TangentVector) -> (T.TangentVector, T.TangentVector)) {
    func pullback(_ v: T.TangentVector) -> (T.TangentVector, T.TangentVector) {
        if x <= y {
            return (v, .zero)
        }
        else {
            return (.zero, v)
        }
    }
    return (value: min(x, y), pullback: pullback)
}

@inlinable
@derivative(of: max)
func maxVJP<T: Comparable & Differentiable>(
    _ x: T,
    _ y: T
) -> (value: T, pullback: (T.TangentVector) -> (T.TangentVector, T.TangentVector)) {
    func pullback(_ v: T.TangentVector) -> (T.TangentVector, T.TangentVector) {
        if x < y {
            return (.zero, v)
        }
        else {
            return (v, .zero)
        }
    }
    return (value: max(x, y), pullback: pullback)
}

Looks like we'd need a dedicated pass over all non-primary sources to pull these custom derivatives :( Or something similar...

#58644 handles the case when A and vjpA are both defined in the same file. However, it does not handle the case as above. There is one important special case: when A is some runtime function or defined in some external module. Then we'd effectively won't be able to register a custom derivative for it. Consider e.g. the following:

Are you sure this is not currently working as intended?

My understanding of the test case:

• a.swift defines clamp which uses max and min.
• b.swift defines custom derivatives for max and min.
• I believe derivative functions are already defined for max and min in the _Differentiation library.
  • If not, compilation of a.swift should fail as the body of clamp cannot be differentiated as there are no registered derivatives for external functions max and min.

Expected behavior:

• If max and min are not defined in a.swift, then compilation of a.swift should produce extern references to their derivative functions.
• Files that import a.swift but not b.swift will use the max and min derivatives defined in the _Differentiation library.
• Files that import both a.swift and b.swift will use the max and min derivatives defined in b.swift.
  • This is like a "multiple conformances" scenario. I'm not sure we have logic for deterministically resolving the right "registered derivative" when multiple options exist, or if multiple registrations are even allowed.

If you'd like to investigate this case, writing a multi-file test would be helpful!

Are you sure this is not currently working as intended?

Well, I'd not put comment here w/o checking the testcase first ;)

# ./swiftc a.swift b.swift
a.swift:5:12: error: expression is not differentiable
    return max(min(value, upperBound), lowerBound)
           ^
a.swift:5:12: note: cannot differentiate functions that have not been marked '@differentiable' and that are defined in other files
    return max(min(value, upperBound), lowerBound)
           ^
a.swift:5:16: error: expression is not differentiable
    return max(min(value, upperBound), lowerBound)
               ^
a.swift:5:16: note: cannot differentiate functions that have not been marked '@differentiable' and that are defined in other files
    return max(min(value, upperBound), lowerBound)

Compiling both files together makes this error disappear obviously.

I'm reopening this issue as a1e138b implemented only partial fix