Provable approximation properties for deep neural networks

@article{Shaham2016ProvableAP,
  title={Provable approximation properties for deep neural networks},
  author={Uri Shaham and Alexander Cloninger and Ronald R. Coifman},
  journal={ArXiv},
  year={2016},
  volume={abs/1509.07385}
}
Abstract We discuss approximation of functions using deep neural nets. Given a function f on a d -dimensional manifold Γ ⊂ R m , we construct a sparsely-connected depth-4 neural network and bound its error in approximating f . The size of the network depends on dimension and curvature of the manifold Γ, the complexity of f , in terms of its wavelet description, and only weakly on the ambient dimension m . Essentially, our network computes wavelet functions, which are computed from Rectified… CONTINUE READING
BETA

Similar Papers

Figures and Topics from this paper.

Citations

Publications citing this paper.
SHOWING 1-10 OF 45 CITATIONS

References

Publications referenced by this paper.
SHOWING 1-10 OF 34 REFERENCES

Universal approximation bounds for superpositions of a sigmoidal function

  • IEEE Trans. Information Theory
  • 1993
VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL

Deep learning and the information bottleneck principle

  • 2015 IEEE Information Theory Workshop (ITW)
  • 2015
VIEW 1 EXCERPT

Deep nets and manifold learning

Charles K. Chui, H. N Mhaskar
  • Personal Communication,
  • 2015
VIEW 1 EXCERPT

Going deeper with convolutions

  • 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
  • 2014
VIEW 1 EXCERPT