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Depth-Width Tradeoffs in Approximating Natural Functions With Neural Networks
Itay Safran · Ohad Shamir

Mon Aug 07 01:30 AM -- 05:00 AM (PDT) @ Gallery #119
We provide several new depth-based separation results for feed-forward neural networks, proving that various types of simple and natural functions can be better approximated using deeper networks than shallower ones, even if the shallower networks are much larger. This includes indicators of balls and ellipses; non-linear functions which are radial with respect to the $L_1$ norm; and smooth non-linear functions. We also show that these gaps can be observed experimentally: Increasing the depth indeed allows better learning than increasing width, when training neural networks to learn an indicator of a unit ball.

Author Information

Itay Safran (Weizmann Institute of Science)
Ohad Shamir (Weizmann Institute of Science)

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