耦合图神经网络与分数阶连续动力学：一项鲁棒性研究
Coupling Graph Neural Networks with Fractional Order Continuous Dynamics: A Robustness Study
AI总结：
本文研究图神经分数阶微分方程模型在对抗扰动下的鲁棒性，通过理论界分析与实证评估证明其相较整数阶图神经 ODE 具有更强稳定性。
摘要：
在本工作中，我们严格考察了图神经分数阶微分方程（FDE）模型的鲁棒性。该框架通过实现时间分数阶 Caputo 导数，超越了传统的图神经（整数阶）常微分方程（ODE）模型。利用分数阶微积分使我们的模型能够在特征更新过程中考虑长期记忆，这不同于传统图神经 ODE 模型中所见的无记忆马尔可夫更新。在不存在攻击或扰动的环境中，图神经 FDE 模型相对于图神经 ODE 模型的优越性已经得到确立。尽管现有文献已经证实传统图神经 ODE 模型在对抗攻击存在时具有一定程度的稳定性和恢复力，但图神经 FDE 模型的鲁棒性，尤其是在对抗条件下的鲁棒性，仍基本未被探索。本文对图神经 FDE 模型的鲁棒性进行了详细评估。我们建立了一个理论基础，阐明图神经 FDE 模型的鲁棒性特征，并强调与整数阶对应模型相比，它们在面对输入和图拓扑扰动时保持更严格的输出扰动界。我们的实证评估进一步证实了图神经 FDE 模型增强的鲁棒性，突显了其在对抗鲁棒应用中的潜力。
英文摘要：
In this work, we rigorously investigate the robustness of graph neural fractional-order differential equation (FDE) models. This framework extends beyond traditional graph neural (integer-order) ordinary differential equation (ODE) models by implementing the time-fractional Caputo derivative. Utilizing fractional calculus allows our model to consider long-term memory during the feature updating process, diverging from the memoryless Markovian updates seen in traditional graph neural ODE models. The superiority of graph neural FDE models over graph neural ODE models has been established 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 characteristics of graph neural FDE models, highlighting that they maintain more stringent output perturbation bounds in the face of input and graph topology disturbances, compared to their integer-order counterparts. Our empirical evaluations further confirm the enhanced robustness of graph neural FDE models, highlighting their potential in adversarially robust applications.
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