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Automatic differentiation only works on functions which are locally complex analytic. It fails on things that fall outside that model, but are still differentia
by nthompson 7y ago
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.
- ChrisRackauckas 7y agoJulia'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 :).