832 citations · 1.3k across the 79 of their papers we have counts for
7 papers · 1 filter
Deep Narrow Boltzmann Machines are Universal Approximators
Guido Montufar
We show that deep narrow Boltzmann machines are universal approximators of probability distributions on the activities of their visible units, provided they have sufficiently many…
Sequential Recurrence-Based Multidimensional Universal Source Coding of Lempel-Ziv Type
Tyll Krueger, Guido Montufar, Ruedi Seiler +1
We define an algorithm that parses multidimensional arrays sequentially into mainly unrepeated but nested multidimensional sub-arrays of increasing size, and show that the resultin…
A Theory of Cheap Control in Embodied Systems
Guido Montufar, Keyan Ghazi-Zahedi, Nihat Ay
We present a framework for designing cheap control architectures for embodied agents. Our derivation is guided by the classical problem of universal approximation, whereby we explo…
Expressive Power and Approximation Errors of Restricted Boltzmann Machines
Guido Montufar, Johannes Rauh, 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 a…
On the Fisher Metric of Conditional Probability Polytopes
Guido Montufar, Johannes Rauh, Nihat Ay
We consider three different approaches to define natural Riemannian metrics on polytopes of stochastic matrices. First, we define a natural class of stochastic maps between these p…
Geometry and Expressive Power of Conditional Restricted Boltzmann Machines
Guido Montufar, Nihat Ay, Keyan Ghazi-Zahedi
Conditional restricted Boltzmann machines are undirected stochastic neural networks with a layer of input and output units connected bipartitely to a layer of hidden units. These n…
On the Number of Linear Regions of Deep Neural Networks
Guido Montúfar, Razvan Pascanu, Kyunghyun Cho +1
We study the complexity of functions computable by deep feedforward neural networks with piecewise linear activations in terms of the symmetries and the number of linear regions th…