The concept is to have a (randomly initialized) single layer network doing a dimensional reduction (DR) to a much smaller evolved controller network. The controller network decides when and what the DR net learns. Also the controller net will be connected to an information reservoir (a random projection feeding back into itself) to act as short term memory and to allow timing/sequencing.
I can evolve deep networks on my laptop if the number of dimensions isn't too big, less than 2^12 (=4096). The other things I also have.