Computational Separation Between Convolutional and Fully-Connected Networks

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.

Authors

• Eran Malach
• Shai Shalev-Shwartz

Keywords

• Neural Networks
• Deep Learning
• Convolutional Networks
• Fully-Connected Networks
• Gradient Descent