Deep learning is one of the most universal techniques in the modern big data era, achieving remarkable success across imaging, healthcare, natural language processing, and more.  As applications begin to rely more heavily on deep learning, it is crucial that we understand how these algorithms make predictions and how we can make them better (e.g., faster, more reliable, automated, etc.).

In this two-part tutorial, we will introduce the building blocks of deep neural networks (DNNs), the most common deep learning tool, and discuss modern mathematical advancements of DNNs.  The first part will provide a crash course on DNNs from a computational math perspective.  We will cover the architecture design, popular training algorithms, and good implementation practices, among other topics. In the second part, we will focus on brainstorming and exploring crucial research questions in deep learning, e.g., how do we design good DNN architectures? How can we incorporate prior knowledge? How much can we trust our network predictions? etc.  We will explore our questions by bringing mathematical perspectives to deep learning, such as clever choices of regularization and interpretations of DNNs as dynamical systems.

Both parts of the tutorial will be highly interactive, and we will leave with working DNN code,  classical illustrative examples, and new directions to continue deep learning explorations.