Understanding Convolutional Neural Networks Through Signal Processing
Convolutional neural networks (CNNs) are the go-to tool for signal processing tasks in machine learning. But how and why do they work so well? Using the basic guiding principles of CNNs, namely their convolutional structure, invariance properties, and multi-scale nature, we will discuss how the CNN architecture arises as a natural bi-product of these principles using the language of nonlinear signal processing. In doing so we will extract some core ideas that allow us to apply these types of algorithms in various contexts, including the multi-reference alignment inverse problem, generative models for textures, and supervised machine learning for quantum many particle systems. Time permitting, we will also discuss how these core ideas can be used to generalize CNNs to manifolds and graphs, while still being able to provide mathematical guarantees on the nature of the representation provided by these tools.
Matthew Hirn is an Associate Professor in the Department of Computational Mathematics, Science & Engineering and the Department of Mathematics at Michigan State University. At Michigan State he is the scientific leader of the ComplEx Data Analysis Research (CEDAR) team, which develops new tools in computational harmonic analysis, machine learning, and data science for the analysis of complex, high dimensional data. Hirn received his B.A. in Mathematics from Cornell University and his Ph.D. in Mathematics from the University of Maryland, College Park. Before arriving at MSU, he held postdoctoral appointments in the Applied Math Program at Yale University and in the Department of Computer Science at Ecole Normale Superieure, Paris. He is the recipient of the Alfred P. Sloan Fellowship (2016), the DARPA Young Faculty Award (2016), the DARPA Director’s Fellowship (2018), and the NSF CAREER award (2019), and was designated a Kavli Fellow by the National Academy of Sciences (2017).