Poster
Computational Separation Between Convolutional and Fully-Connected Networks
Eran Malach · Shai Shalev-Shwartz
Keywords: [ Fully-Connected Networks ] [ convolutional networks ] [ gradient descent ] [ neural networks ] [ deep learning ]
Convolutional neural networks (CNN) exhibit unmatched performance in a multitude of computer vision tasks. However, the advantage of using convolutional networks over fully-connected networks is not understood from a theoretical perspective. In this work, we show how convolutional networks can leverage locality in the data, and thus achieve a computational advantage over fully-connected networks. Specifically, we show a class of problems that can be efficiently solved using convolutional networks trained with gradient-descent, but at the same time is hard to learn using a polynomial-size fully-connected network.