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"Deep learning" is the new big trend in Machine Learning. It promises general, powerful, and fast machine learning, moving us one step closer to AI.
An algorithm is deep if the input is passed through several non-linearities before being output. Most modern learning algorithms (including decision trees and SVMs and naive bayes) are "shallow".
For intuition, imagine if I told you that your main routine can call subroutines, and your subroutines could call subsubroutines, but you couldn't have any more abstraction than that. You can't have subsubsubroutines in your "shallow" program. You could compute whatever you wanted in a "shallow" program, but your code would involve a lot of duplicated code and would not be as compact as it should be. Similarly, a shallow machine learning architecture would involve a lot of duplication of effort to express things that a deep architecture could more compactly. The point being, a deep architecture can more gracefully reuse previous computations.
Deep learning is motivated by intuition, theoretical arguments from circuit theory, empirical results, and current knowledge of neuroscience.
(Text courtesy of www.quora.com/What-is-deep-learning)