MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

MiS Preprint

Expressive Power and Approximation Errors of Restricted Boltzmann Machines

Guido Montúfar, Johannes Rauh and Nihat Ay


We present explicit classes of probability distributions that can be learned by Restricted Boltzmann Machines (RBMs) depending on the number of units that they contain, and which are representative for the expressive power of the model. We use this to show that the maximal Kullback-Leibler divergence to the RBM model with $n$ visible and $m$ hidden units is bounded from above by $(n-1)-\log(m+1)$.

In this way we can specify the number of hidden units that guarantees a sufficiently rich model containing different classes of distributions and respecting a given error tolerance.

Jun 1, 2011
Jun 1, 2011
MSC Codes:
68Q32, 68T01, 62-04
Machine Learning, neural networks, Unsupervised Learning, Representational Power, Universal approximator

Related publications

2011 Repository Open Access
Guido Montúfar, Johannes Rauh and Nihat Ay

Expressive power and approximation errors of restricted Boltzmann machines

In: Advances in neural information processing systems 24 : NIPS 2011 ; 25th annual conference on neural information processing systems 2011, Granada, Spain December 12th - 15th / John Shawe-Taylor (ed.)
La Jolla, CA : Neural Information Processing Systems, 2011. - pp. 415-423