Dual leakage

[MikeInnes]

I can make the dual type leak out into a global variable:

julia> function f(x)
         global y = sin(x)
       end
f (generic function with 1 method)

julia> ForwardDiff2.D(f)(1)*1
0.5403023058681398

julia> y
(0.8414709848078965 + 0.5403023058681398ϵ₁)

Presumably this can happen any time a differentiated value escapes the program, e.g. when you have a global cache or similar.

[ChrisRackauckas]

I am assume that's going to be useful for defining mutable buffers.

[MikeInnes]

FWIW, this is not just academic since it can lead to bad gradients (effectively a form of perturbation confusion). For example:

julia> function f(x)
         global y = sin(x)
       end
f (generic function with 1 method)

julia> g(x) = x+y
g (generic function with 1 method)

julia> ForwardDiff2.D(f)(2)*1
-0.4161468365471424

julia> ForwardDiff2.D(g)(2)*1
0.5838531634528576

Compare Zygote:

julia> gradient(f, 2)[1]
-0.4161468365471424

julia> gradient(g, 2)[1]
1.0

This is a little contrived, but a function that updates and uses a global cache in some way could follow the same pattern and get silent incorrect gradients.