Automatic differentiation only works on functions which are locally complex analytic. It fails on things that fall outside that model, but are still differentiable. Daubechies wavelets are a good example of this.
Julia's systems can make use of ChainRules.jl which doesn't assume locally complex analytic, and instead uses its Wirtinger derivatives (df/dz and df/dzbar), and if complex analytic just uses the well-known simplification df/dzbar=0. This allows for non-analytic functions to be used, and you just need to supply all primitives in Wirtinger form. Julia has enough non-ML people using this stuff that complex numbers actually get used here :).