Zhiyang Wang

Research Abstract:

Convolutional neural networks (CNNs) have achieved impressive success in a wide range of applications. When processing non-Euclidean data, graphs are commonly used as a discrete model to capture the underlying geometric structure. Convolutions can be readily extended to graph convolutions, which allows defining convolutional graph neural networks (GNNs). In graphs of moderate size, GNNs are well backed by their expressive power and stability. However, in the large-scale regime which is the setting of most problems of practical interest, their behavior is not as well understood. My research focuses on building manifold convolutional filters and manifold neural networks (MNNs) as a limit model for convolutional filters and neural networks on large geometric graphs. With manifold convolutions defined in terms of Laplace-Beltrami operator exponentials, graph convolutions can be recovered through discretization of the manifold and standard time convolutions can also be recovered by considering the manifold as a real line. Manifold convolutions admit a spectral representation which is also a generalization of both the frequency responses of graph convolutions and standard time convolutions. I further propose a two-way connection between filters and neural networks on graphs and on manifolds by showing GNNs running on graphs sampled from a manifold converge to the MNN running on the underlying manifold with non-asymptotic convergence results. The convergence allows the transferability of GNNs among different graphs sampled from the same underlying manifold which enables us to design GNNs on small graphs and transfer them to larger graphs. MNNs as a formal limit of GNNs provide a theoretical tool for understanding large-scale GNNs. I proceed to analyze the stability of manifold filters and MNNs to smooth deformations of the manifold. This sheds light on the behavior of large-scale graph filters and GNNs which are prone to undergo perturbations and changes in real-world scenarios. The theoretical results are verified under wireless resource allocation, point cloud analysis and navigation control problem settings.

Bio:

Zhiyang Wang is a 5th year Ph.D. candidate at the University of Pennsylvania in the Electrical and Systems Engineering Department, advised by Prof. Alejandro Ribeiro. Previously, she received 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. She has been working on analyzing the limits of graph signal processing via proposing manifold filters and manifold neural networks. She also seeks the application of large graph neural networks in wireless communication networks, point-cloud analysis and navigation control. 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 selected to participate in Rising Stars in Signal Processing program held by 2023 IEEE International Conference on Acoustics, Speech, and Signal Processing.