I often see neural networks extended to complex-values. Those networks allow complex input, complex parameters, and complex output. My understanding is that the inner products and point nonlinearities are simply extended. I can see it's advantage for signals that are naturally complex (e.g., phase/amplitude decomposition, oscillations, frequency domain processing, ...). However, computationally speaking, is it any different from converting complex signals to real values?What is the computational advantage of using the complex field compared to the real field?What is the computational advantage of complex vs real vector space?References:Akira Hirose. Complex-Valued Neural Networks. Springer Science & Business Media. 2006, 2012Danilo P. Mandic, Vanessa Su Lee Goh.Complex Valued Nonlinear Adaptive Filters: Noncircularity, Widely Linear and Neural Models. 2009
Power of complex-valued neural network
complex;neural network