In recent years, deep learning has had a profound impact on machine learning and artificial intelligence. Here we investigate if quantum algorithms for deep learning lead to an advantage over existing classical deep learning algorithms. We develop two quantum machine learning algorithms that reduce the time required to train a deep Boltzmann machine and allow richer classes of models, namely mu...

1. Hinton, Geo rey E., Terrence J. Sejnowski and David H. Ackley, Boltzmann Machines: Constraint Satisfaction Networks that Learn, Technical Report CMU-CS-84-119, May 1984. 2. Simpson, Patrick K., Arti cial Neural Systems: Foundations, Paradigms, Applications, and Implementations, 1990. Chapter 5: ANS Paradigms and Their Applications and Implementations, pages 120-127. 3. Hinton, Geo rey, Lectu...

7 Acknowledgments We want to thank specially Stefan Mießbach for numerous contributions in proving the convergence properties of the net dynamic and for advice concerning the " cornered rat " example. We are very grateful to Ingrid Gabler for supplying the experimental data for this same example. 6.3 Convergence of the dynamic We show now the local convergence of the dynamic defined by the MF e...

Shape completion is an important task in the field of image processing. An alternative method is to capture the shape information and finish the completion by a generative model, such as Deep Boltzmann Machine. With its powerful ability to deal with the distribution of the shapes, it is quite easy to acquire the result by sampling from the model. In this paper, we make use of the hidden activat...

The Temporal Restricted Boltzmann Machine (TRBM) is a probabilistic model for sequences that is able to successfully model (i.e., generate nice-looking samples of) several very high dimensional sequences, such as motion capture data and the pixels of low resolution videos of balls bouncing in a box. The major disadvantage of the TRBM is that exact inference is extremely hard, since even computi...

Many biological and cognitive systems do not operate deep into one or other regime of activity. Instead, they exploit critical surfaces poised at transitions in their parameter space. The pervasiveness of criticality in natural systems suggests that there may be general principles inducing this behaviour. However, there is a lack of conceptual models explaining how embodied agents propel themse...

Greedy Restrictive Boltzmann Machines yield an fairly low 0.72% error rate on the famous MNIST database of handwritten digits. All that was required to achieve this result was a high number of hidden layers consisting of many neurons, and a graphics card to greatly speed up the rate of learning. Keywords—ANN (Artificial Neural Networks), RBM (Restrictive Boltzmann Machine), MNIST handwritten da...

We review a nonparametric version of Amari’s information geometry in which the set of positive probability densities on a given sample space is endowed with an atlas of charts to form a differentiable manifold modeled on Orlicz Banach spaces. This nonparametric setting is used to discuss the setting of typical problems in machine learning and statistical physics, such as black-box optimization,...