There seems to be a subtle misunderstanding. A focus on the mathematics, such as verification or high-dimensional convex studies, will show that there is some b

There seems to be a subtle misunderstanding. A focus on the mathematics, such as verification or high-dimensional convex studies, will show that there is some basis for WHY DNNs work. This would be equivalent to showing WHY Fourier Transforms work. It shows a sound basis for things like backprop and why iterated partial derivatives converge. It is interesting to know why kernels can flatten a higher space. That is a far cry from WHY a DNN-based program works. That is like asking WHY I used a Fourier Transform, not why a Fourier Transform works. We will soon reach a situation where a self-driving car decides to suddenly slam into a parked car. Probably because the heat waves rising from the road made the telephone pole look like it "moved" and was "alive" so the car decided to avoid it, choosing the "inanimate" parked car instead. Oh, the joys of debugging THAT program... the weight on the third layer node 1273134 should be .077651 not .077650 There is a government Broad Agency Announcement (BAA) (http://www.darpa.mil/attachments/DARPA-BAA-16-53.pdf http://www.darpa.mil/attachments/DARPA-BAA-16-53.pdf) that hopes to address this issue. It will be interesting to see if that research addresses the first idea or the second.