Saturday, July 23, 2016

Saturday Morning Video: The Power of Depth for Feedforward Neural Networks by Ohad Shamir @ COLT2016

The attendant paper is here:

The Power of Depth for Feedforward Neural Networks by Ronen Eldan, Ohad Shamir

We show that there is a simple (approximately radial) function on $\reals^d$, expressible by a small 3-layer feedforward neural networks, which cannot be approximated by any 2-layer network, to more than a certain constant accuracy, unless its width is exponential in the dimension. The result holds for virtually all known activation functions, including rectified linear units, sigmoids and thresholds, and formally demonstrates that depth -- even if increased by 1 -- can be exponentially more valuable than width for standard feedforward neural networks. Moreover, compared to related results in the context of Boolean functions, our result requires fewer assumptions, and the proof techniques and construction are very different.

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