Conventional probability theory, as commonly applied, seems to have some major blind spots. Using deep learning, Yann LeCun's team was able to find uniquely different sets of points that had the same statistical properties. They are calling into question the approach of throwing probability theory at every and any problem. Nonlinear systems in particular often exhibit behavior that is not easy to grasp via probability theory.

But deep learning is terrible at learning nonlinear systems which are easy to model with things like stochastic differential equations... this is just another case of machine learning being pushed too far.

There is no silver bullet.

Things work until they don't.