We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
We improve recently published results about resources of Restricted Boltzmann Machines (RBM) and Deep Belief Networks (DBN) required to make them Universal Approximators. We show that any distribution
We construct a DBN with