Computational Separation Between Convolutional and Fully-Connected Networks

Eran Malach · Shai Shalev-Shwartz

Keywords: [ deep learning ] [ neural networks ] [ gradient descent ] [ convolutional networks ] [ 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.

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