I've seen some recent papers describing complex valued neural networks like this one. What I'm wondering is, rather than invent a new complex network architecture that takes a complex value as a single channel, why not just separate the real and imaginary components into two separate channels fed into a regular neural network, and then let the network figure out the relations?
For example, for each training iteration, instead of a single complex input [a+bi], use two real inputs [a,b].
I assume there must be some disadvantage to doing it this way, or some relation between real and imaginary components that the network can't capture, so if that's the case would someone please provide me with a high-level explanation of why this two-channel standard network approach is inferior to the novel single-channel complex network?
(By the way, the application I have in mind for researching deep complex networks is RF signal classification.)