Deep Learning is the big thing in Machine Learning right now, it just netted a win in theGalaxy Zoo Kaggle contest and it is the thing being talked about by major media outlets. The technique rightfully deserves serious attention as it has proven effective in a large number of tasks, but I see one key problem with it that is similar to but actually worse than its cousin Neural Networks; it is a black box that cannot explain "why" at even the highest level.
Now some Data Scientists will tell you that the why doesn't matter, they'll quote the Wired article and Peter Norvig about the "Unreasonable Effectiveness of Data", but in my experience doing Data Science, the why's do matter. When one does a study and finds that they can lift sales by following a predictive algorithm then next thing they will hear from the product manager is "why" or "how". In the real world the humans who make decisions care about "why" the algorithms we run are able to make things better, and it is our job as Data Scientists to tell the story of "why" to a level that they can understand.
Deep Learning (at least with convolutional neural nets) is a black box in this fashion. Unlike Random Forests (and they are very different, so this is a simplistic comparison) which hand back a list of feature importances, Deep Learning with multiple layers are creating features at multiple levels in the system, and those features are not well understood. They can't even offer the simplistic explanation that Random Forests can of "why? well b/c feature X is important".
Even the aforementioned Galaxy Zoo Kaggle competition which was won by Deep Learning is somewhat problematic, in my opinion. Sure, the winning algorithm can classify galaxy morphologies well, but because all the features are not understood it doesn't really help scientists know why the galaxies where classified in a given way. That understanding (something akin to the standard deviation of the incoming light is great < 10 pixels from the center of the galaxy) would help in doing actual science.
I started thinking about this a few days ago, and next thing you know a blog post popped up on my Twitter timeline about someone trying to interpret what Deep Learning Convolutional Neural Networks are really doing and grasp at some of the "why" of their application. I think this is the next frontier with these techniques, getting some grasp of the "why" and "how" they work so that we can use them do real science and tell real stories about data.