Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Review

This work addresses the theoretical understanding of deep learning's superiority for researchers and practitioners, but it is incremental as it reviews and characterizes existing conditions rather than introducing new methods.

The paper identifies function classes where deep learning models achieve exponentially better performance than shallow ones, with deep convolutional networks serving as a key example, though weight sharing is not the primary factor for this advantage.