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Nowak will lead project to investigate the mathematical underpinnings of deep learning

Written By: Ascedia

Rob Nowak
Rob Nowak

Robert Nowak, the Keith and Jane Morgan Nosbusch Professor in Electrical and Computer Engineering at the University of Wisconsin—Madison, is the primary investigator on a $900,000 grant recently awarded by the National Science Foundation’s Stimulating Collaborative Advances Leveraging Expertise in the Mathematical and Scientific Foundations of Deep Learning (SCALE MoDL) program.

Deep learning is a subfield of machine learning that in some ways simulates the behavior of the human brain, using multiple layers to optimize and refine accuracy. However, most current deep learning systems and applications were developed primarily through experiments and engineering practice. The mathematical concepts underpinning deep learning systems have not been worked out, which has begun to negatively impact the field.

Nowak’s project aims to fix this by developing new mathematical foundations for deep learning, pulling together approximation, statistical and algorithmic theories. The goal of the project is to mathematically characterize the strengths and limitations of deep learning models and to understand the properties of deep learning models trained using examples of desired behavior (training data) as well as the tradeoffs between the performance of deep learning systems and the training dataset size.

Broader impacts of the project also include education and mentoring, including the training of graduate students in mathematical fields such as approximation theory, signal processing, statistics and machine learning. Most importantly, they will examine how these fields collectively inform the theory and practice of deep learning.

Co-PI’s on the project include Guergana Petrova, a mathematician at Texas A&M University and Aarti Singh, a computer scientist at Carnegie Mellon University.