Projecting a Tangent{Complex} to Numbers

[mzgubic]

At present:

julia> tc = Tangent{ComplexF64}(; re=1, im=NoTangent());

julia> ProjectTo(1.0)(tc)
Tangent{ComplexF64}(re = 1, im = NoTangent())

whereas I think we want

julia> ProjectTo(1.0)(tc)
1.0

The solution would be to change the current

(project::ProjectTo{<:Complex})(dx::Tangent{<:Complex}) = project(Complex(dx.re, dx.im))

to

(project::ProjectTo{<:Number})(dx::Tangent{<:Complex}) = project(Complex(dx.re, dx.im))

which would also fix e.g. ProjectTo(π)(tc).

[oxinabox]

Sounds right

[mcabbott]

Does this occur in the wild?

To get from real to complex, you must go through some function, and its gradient shouldn't really let a Tangent of the wrong type for the arguments propagate backwards.

[mzgubic]

I haven't ran into it, but how about this example?

julia> y, pb = rrule(+, 1.0, 1.0im); pb(Tangent{Complex}(;re=1.0))
(NoTangent(), Tangent{Complex}(re = 1.0,), 1.0 + 0.0im)

I guess if you take the stance that the Tangent{Complex}(;re=1.0) is always a wrong thing to return, and it should just be the natural differential, then the example is invalid and I can't think of a reasonable example.

[mcabbott]

Ok. I'm a little uneasy, but I agree that is a good example, and we do have a bit of a "if someone missed at first, catch it later" policy.