Building better neural networks

A group of professors and researchers at the Technical University of Berlin, the University of Vienna, and ETH Zurich have recently been working on understanding deep neural networks (computer systems that are modelled after the human brain) in "a mathematically sound way", as Dr. Phillip Petersen refers to it. Although the official paper for this research, "Optimal Approximation with Sparse Deep Neural Networks," will not be published until next week, Professor Gitta Kutyniok graciously presented a preview of their work for the Center's Math & Data Seminar group this past Thursday. Neural networks, or artificial brains, represent functions in mathematics. For these researchers, the main goal is to uncover how well a deep neural network with sparse connectivity can approximate a function. Dr. Petersen likens the network to a tree -- deep neural networks are composed of multiple layers and are connected by edges. Those layers are made of nodes, or neurons where computation occurs, and are sparsely connected if they have few non-zero weights or edges.