Benefits Of Depth In Neural Networks.pdf

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Preview of Benefits of depth in neural networks
🔗 Source: proceedings.mlr.press
📊 Size: 320 KB
📄 Pages: 23 pages
⬇️ Downloads: 89

Summary

Specifically, it shows that for any positive integer k, there exist neural networks with Θ(k3) layers, Θ(1) nodes per layer, and Θ(1) distinct parameters that cannot be approximated by networks with O(k) layers unless they are exponentially large. The result is proved for a class of nodes called semi-algebraic gates, which includes common choices such as ReLU, maximum, indicator, and piecewise polynomial functions. The paper also provides a bound on the number of special functions that cannot be approximated by shallow networks and shows that even on the task of fitting O(k9) points, the class of shallow networks is useless on most random labelings.

Description

Specifically, it shows that for any positive integer k, there exist neural networks with Θ(k3) layers, Θ(1) nodes per layer, and Θ(1) distinct parameters that...

Technical Information

  • File Format: PDF
  • File Size: 320 KB
  • Pages: 23
  • Language: EN
  • Total Downloads: 89
  • Last Updated: 1 week ago

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