Abstract
We show that there is a simple (approximately radial) function on Rd, 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.
Original language | English |
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Article number | 1909.00860 |
Number of pages | 22 |
Journal | arXiv |
State | Published - 12 Dec 2015 |
Event | 29th Conference on Learning Theory, COLT 2016 - New York, United States Duration: 23 Jun 2016 → 26 Jun 2016 |
All Science Journal Classification (ASJC) codes
- Software
- Control and Systems Engineering
- Statistics and Probability
- Artificial Intelligence