Graph Convolutional Neural Networks Sensitivity Under Probabilistic Error Model

About this Topic:

Graph Neural Networks (GNNs), particularly Graph Convolutional Neural Networks (GCNNs), have emerged as pivotal instruments in machine learning and signal processing for processing graph-structured data. 

This talk will present an analysis framework to investigate the sensitivity of GCNNs to probabilistic graph perturbations, directly impacting the graph shift operator (GSO). The presenters study establishes tight expected GSO error bounds, which are explicitly linked to the error model parameters, and reveals a linear relationship between GSO perturbations and the resulting output differences at each layer of GCNNs. This linearity demonstrates that a single-layer GCNN maintains stability under graph edge perturbations, provided that the GSO errors remain bounded, regardless of the perturbation scale. For multilayer GCNNs, the dependency of system’s output difference on GSO perturbations is shown to be a recursion of linearity. Finally, they exemplify the framework with the Graph Isomorphism Network (GIN) and Simple Graph Convolution Network (SGCN). Experiments validate our theoretical derivations and the effectiveness of our approach.

About the Presenters:

Xinjue Wang (M’26) received the B.Eng. degree in electronic and information engineering from Northwestern Polytechnical University, Xi’an, China, the M.Sc. degree in computer, communication and information sciences and the Ph.D. degree in signal processing and data science, both from Aalto University, Espoo, Finland, in 2020, 2022 & 2025 respectively.

His research interests include graph signal processing and machine learning.

Sergiy A. Vorobyov (F’18) received the M.Sc. and Ph.D. Degrees in systems and control from the National University of Radio Electronics, Kharkiv, Ukraine, in 1994 and 1997, respectively.

He is currently a Professor with the Department of Information and Communications Engineering, Aalto University, Finland. Since his graduation, he held various faculty and research positions with the University of Alberta, Canada; the Joint Research Institute between Heriot Watt University and Edinburgh University, U.K.; Darmstadt University of Technology and Duisburg Essen University, Germany; McMaster University, Canada; the Institute of Physical and Chemical Research, Japan; and the National University of Radio Electronics, Ukraine. His research interests include optimization and multi linear algebra methods in signal processing and data analysis; statistical, array, and graph signal processing; estimation, detection and learning theory and methods; computational imaging; multi-antenna, very large, cooperative, and cognitive systems, and integrated sensing and communications. 

Dr. Vorobyov is the recipient of the 2004 IEEE Signal Processing Society Best Paper Award, the 2007 Alberta Ingenuity New Faculty Award, the 2011 Carl Zeiss Award (Germany), the 2012 NSERC Discovery Accelerator Award, and IEEE ICASSP 2023 Top 3% paper recognition, and other awards. He was a Senior Area Editor for the IEEE Signal Processing Letters in 2016—2020, an Associate Editor for the IEEE Transactions on Signal Processing in 2006–2010 and the IEEE Signal Processing Letters in 2007–2009. He was a member of the Sensor Array and Multi-Channel Signal Processing and Signal Processing for Communications and Networking Technical Committees of the IEEE Signal Processing Society in 2007–2012 and 2010–2016, respectively. He was the Track Chair for Asilomar 2011, Pacific Grove, CA, USA; the Technical Co-Chair for IEEE CAMSAP 2011, Puerto Rico; the Tutorial Chair for ISWCS 2013, Ilmenau, Germany; the Technical Co-Chair for IEEE SAM 2018, Sheffield, U.K.; the Technical Co-Chair for IEEE CAMSAP 2023, Costa Rica; and the General Co-Chair for EUSIPCO 2023, Helsinki, Finland.