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Deep neural networks are state-of-the-art in a wide variety of tasks,however, they exhibit important limitations which hinder their use anddeployment in real-world applications. When developing and training neuralnetworks, the accuracy should not be the only concern, neural networks mustalso be cost-effective and reliable. Although accurate, large neural networksoften lack these properties. This thesis focuses on the problem of trainingneural networks which are not only accurate but also compact, easy to train,reliable and robust to adversarial examples. To tackle these problems, weleverage the properties of structured matrices from the Toeplitz family tobuild compact and secure neural networks.

Building Compact and Robust Deep Neural Networks with Toeplitz Matrices