Deep, narrow sigmoid belief networks are universal approximators.
In this note, we show that exponentially deep belief networks can approximate any distribution over binary vectors to arbitrary accuracy, even when the width of each layer is limited to the dimensionality of the data. We further show that such networks can be greedily learned in an easy yet impractical way.
Sutskever
Ilya
I
Department of Computer Science, University of Toronto, Toronto, Ontario M55 3G4, Canada. ilya@cs.utoronto.ca
Hinton
Geoffrey E
GE
D000465:Algorithms; D006801:Humans; D007858:Learning; D016571:Neural Networks, Computer; D017711:Nonlinear Dynamics