Douglas Hofstadter in his book "I am a Strange Loop" coined this idea: In the end, we are self-perceiving, self-inventing, locked-in mirages that are little miracles of self-reference. Loops are not typical in Deep Learning systems. This is not hyperbole, this is happening today where researchers are training'narrow' intelligence systems to create very capable specialist automation that surpass human capabilities. For more on this in this "strange loop" please consult:

My first recollection of an effective Deep Learning system that used feedback loops where in "Ladder Networks". In an architecture developed by Stanford called "Feedback Networks", the researchers explored a different kind of network that feeds back into itself and develops the internal representation incrementally: In an even more recently published research (March 2017) from UC Berkeley have created astonishingly capable image to image translations using GANs and a novel kind of regularization. The major difficulty of training Deep Learning systems has been the lack of labeled data. So the next time you see some mind boggling Deep Learning results, seek to find the strange loops that are embedded in the method.