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arXiv · 1509.08101

Representation Benefits of Deep Feedforward Networks

Matus Telgarsky
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Abstract

This note provides a family of classification problems, indexed by a positive integer $k$, where all shallow networks with fewer than exponentially (in $k$) many nodes exhibit error at least $1/6$, whereas a deep network with 2 nodes in each of $2k$ layers achieves zero error, as does a recurrent network with 3 distinct nodes iterated $k$ times. The proof is elementary, and the networks are standard feedforward networks with ReLU (Rectified Linear Unit) nonlinearities.

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Matus Telgarsky. 2015-09-27. Representation Benefits of Deep Feedforward Networks. https://arxiv.org/abs/1509.08101

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