About this Event
135 N Skinker Blvd, St. Louis, MO 63112, USA
##WashUESESeminarTitle: Manifold Filters and Neural Networks: Geometric Graph Signal Processing in the Limit
Abstract: Graph Neural Networks (GNNs) are the tool of choice for scalable and stable learning in graph-structured data applications involving geometric information. My research addresses the fundamental questions of how GNNs can generalize across different graph scales and how they can remain stable on large-scale graphs. I do so by considering manifolds as graph limit models. In this talk, we will explain how to build manifold convolutional filters and manifold neural networks (MNNs) as the limit objects of graph convolutional filters and GNNs when the graphs are sampled from manifolds. Using the Laplace-Beltrami operator exponentials to define manifold convolutions, we demonstrate their algebraic equivalence to both graph convolutions and standard time convolutions in nodal and spectral domains. This equivalence provides a unifying framework to analyze key theoretical properties of GNNs: i) Convergence of GNNs to MNNs allows the scalability of GNNs on graphs across scales. ii) The stability of MNNs to deformations indicates the stability of large-scale GNNs. These findings offer practical guidelines for designing GNN architectures, particularly by imposing constraints on the spectral properties of filter functions. Theoretical results are verified in real-world scenarios, including point cloud analysis, wireless resource allocation, and wind field studies on vector fields.
Bio: Zhiyang Wang is a Ph.D. candidate at the University of Pennsylvania in the Electrical and Systems Engineering Department. Previously, she received her B.E. and M.E. degrees in 2016 and 2019, respectively, from the Department of Electronic Engineering and Information Science, University of Science and Technology of China. Her research interests include graph signal processing, graph neural networks, geometric deep learning, and wireless communications. She received the best student paper award at the 29th European Signal Processing Conference and the Bruce Ford Memorial Fellowship at the University of Pennsylvania. She was chosen as a Rising Star in Signal Processing and an EECS Rising Star in 2023, as well as a Rising Star in Data Science in 2024.