Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Review
Tomaso Poggio, H. N. Mhaskar, Lorenzo Rosasco, Brando Miranda, Qianli Liao · arXiv (Cornell University) · 2016
The paper characterizes classes of functions for which deep learning can be exponentially better than shallow learning. Deep convolutional networks are a special case of these conditions, though weight sharing is not the main reason for their exponential advantage.