Theory of Classification: a Survey of Some Recent Advances Page 1 ESAIM: PS ESAIM:
Probability and Statistics November 2005, Vol. 9, p. 323–375 DOI: 10.1051/ps:2005018 …

We study expressive power of shallow and deep neural networks with piece-wise linear
activation functions. We establish new rigorous upper and lower bounds for the network …

We prove new upper and lower bounds on the VC-dimension of deep neural networks with
the ReLU activation function. These bounds are tight for almost the entire range of …

We consider approximations of general continuous functions on finite-dimensional cubes by
general deep ReLU neural networks and study the approximation rates with respect to the …

While quantum state tomography is notoriously hard, most states hold little interest to
practically minded tomographers. Given that states and unitaries appearing in nature are of …

Deep learning is usually described as an experiment-driven field under continuous criticizes
of lacking theoretical foundations. This problem has been partially fixed by a large volume of …

The computational power of formal models for networks of spiking neurons is compared with
that of other neural network models based on McCulloch Pitts neurons (ie, threshold gates) …

We compare discriminative and generative learning as typified by logistic regression and
naive Bayes. We show, contrary to a widely (cid: 173) held belief that discriminative …

Pattern recognition presents one of the most significant challenges for scientists and
engineers, and many different approaches have been proposed. The aim of this book is to …

This important work describes recent theoretical advances in the study of artificial neural
networks. It explores probabilistic models of supervised learning problems, and addresses …