miguelhdo / complexad

Rules for gradients of complex loss functions

Examples of automatic differentiation mentioned in the paper arXiv:~. The fold src contains utility functions which are used to derive the numerical gradient by finite difference method.

• In the file "common_funcs.jl", we show the definition of the adjoint function for the non-holomorphic function "dot", and checked the gradient.

• In the file "arjovsky16.jl", we parameterize the W matrix using a mixture of real and complex numbers, which is used for unitary recurrent neural network in the paper Unitary Evolution Recurrent Neural Networks

• In the file "wisdom.jl", we use complex numbers to parameterize the W matrix propose in the paper Full-Capacity Unitary Recurrent Neural Networks. Compared to the original work which split the W matrix into two matrices which contain the real and imaginary parts separately, we use a single complex matrix to represent it, and the gradient of any complex function built with W can be computed as straightforward as the real case.