Deep Belief Networks Are Compact Universal Approximators

@article{Roux2010DeepBN,
  title={Deep Belief Networks Are Compact Universal Approximators},
  author={Nicolas Le Roux and Yoshua Bengio},
  journal={Neural Computation},
  year={2010},
  volume={22},
  pages={2192-2207}
}
Deep belief networks (DBN) are generative models with many layers of hidden causal variables, recently introduced by Hinton, Osindero, and Teh (2006), along with a greedy layer-wise unsupervised learning algorithm. Building on Le Roux and Bengio (2008) and Sutskever and Hinton (2008), we show that deep but narrow generative networks do not require more parameters than shallow ones to achieve universal approximation. Exploiting the proof technique, we prove that deep but narrow feedforward… CONTINUE READING
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