"Graph Convolutional Neural Networks Sensitivity Under Probabilistic Error Model" presented by Dr. Sergiy A. Vorobyov. Based on the IEEE Xplore® article under the same title. Published: IEEE Transactions on Signal and Information Processing over Networks, October 2024. Visit article article here.
This presentation examines the sensitivity and stability of Graph Convolutional Neural Networks (GCNNs) when subjected to topological uncertainties. The primary objective is to establish an analytical framework for evaluating how probabilistic graph perturbations, specifically edge errors modeled probabilistically, affect the Graph Shift Operator (GSO) and propagate through the network layers.
To analyze these effects, the methodology establishes tight expected GSO error bounds directly tied to the parameters of the underlying error model. The analysis demonstrates a linear relationship between GSO perturbations and output deviations at each layer, indicating that single-layer GCNNs remain stable under bounded GSO errors regardless of the perturbation scale. For deeper architectures, the error propagation is characterized as a recursion of linear operations, supported by empirical evaluations on specific models such as the Graph Isomorphism Network (GIN) and Simple Graph Convolution Network (SGCN).
The study concludes that GCNNs possess an inherent mathematical stability against probabilistic structural noise under bounded GSO conditions. This theoretical framework provides crucial guidelines for designing resilient graph neural networks, ensuring reliable performance in real-world signal processing and machine learning applications where graph topologies are inherently noisy or uncertain.
