Coupling Graph Neural Networks with Non-Integer Order Dynamics: A Robustness Study

In this work, we rigorously investigate the robustness of graph neural fractional-order differential equation (FDE) models. This framework extends beyond traditional graph neural ordinary differential equation (ODE) models by implementing the time-fractional Caputo derivative. Utilizing fractional calculus allows our model to consider long-term dependencies during the feature updating process, diverging from the Markovian updates seen in traditional graph neural ODE models. The efficacy of FDE models in surpassing ODE models has been confirmed in a different submitted work, particularly in environments free from attacks or perturbations.While traditional graph neural ODE models have been verified to possess a degree of stability and resilience in the presence of adversarial attacks in existing literature, the robustness of graph neural FDE models, especially under adversarial conditions, remains largely unexplored. This paper undertakes a detailed assessment of the robustness of graph neural FDE models. We establish a theoretical foundation outlining the robustness features of graph neural FDE models, highlighting that they maintain more stringent output perturbation bounds in the face of input and functional disturbances, relative to their integer-order counterparts. Through rigorous experimental assessments, which include graph alteration scenarios and adversarial attack contexts, we empirically validate the improved robustness of graph neural FDE models against their conventional graph neural ODE counterparts.