"Here's what you should remember: the only real success of deep learning so far has been the ability to map space X to space Y using a continuous geometric transform, given large amounts of human-annotated data."

This statement has a few problems - there is no real reason to interpret the transforms as geometric (they are fundamentally just processing a bunch of numbers into other numbers, in what sense is this geometric), and the focus on human-annotated data is not quite right (Deep RL and other things such as representation learning have also achieved impressive results in Deep Learning). More importantly, saying " a deep learning model is "just" a chain of simple, continuous geometric transformations " is pretty misleading; things like the Neural Turing Machine have shown that enough composed simple functions can do pretty surprisingly complex stuff. It's good to point out that most of deep learning is just fancy input->output mappings, but I feel like this post somewhat overstates the limitations.