Graph Convolutional Neural Networks Sensitivity under Probabilistic Error Model
This work addresses stability issues in GNNs for graph-structured data, which is incremental as it builds on existing methods to analyze sensitivity.
The paper tackles the sensitivity of Graph Convolutional Neural Networks (GCNNs) to probabilistic graph perturbations by establishing tight error bounds and showing a linear relationship between perturbations and output differences, with experiments validating the theory on networks like GIN and SGCN.
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 paper proposes an analysis framework to investigate the sensitivity of GCNNs to probabilistic graph perturbations, directly impacting the graph shift operator (GSO). Our 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, we 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.