Coupling Graph Neural Networks with Fractional Order Continuous Dynamics: A Robustness Study
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arXiv
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| Hauptverfasser: | , , , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917603442688000 |
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| author | Kang, Qiyu Zhao, Kai Song, Yang Xie, Yihang Zhao, Yanan Wang, Sijie She, Rui Tay, Wee Peng |
| author_facet | Kang, Qiyu Zhao, Kai Song, Yang Xie, Yihang Zhao, Yanan Wang, Sijie She, Rui Tay, Wee Peng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04331 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Coupling Graph Neural Networks with Fractional Order Continuous Dynamics: A Robustness Study Kang, Qiyu Zhao, Kai Song, Yang Xie, Yihang Zhao, Yanan Wang, Sijie She, Rui Tay, Wee Peng Machine Learning Artificial Intelligence 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. |
| title | Coupling Graph Neural Networks with Fractional Order Continuous Dynamics: A Robustness Study |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2401.04331 |