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?
- Akira Hirose. Complex-Valued Neural Networks. Springer Science & Business Media. 2006, 2012
- Danilo P. Mandic, Vanessa Su Lee Goh.Complex Valued Nonlinear Adaptive Filters: Noncircularity, Widely Linear and Neural Models. 2009
- Tygert, M., Bruna, J., Chintala, S., LeCun, Y., Piantino, S., & Szlam, A. (2016). A Mathematical Motivation for Complex-Valued Convolutional Networks. Neural Computation, 28(5), 815–825.