Enhancing Robustness of Graph Neural Networks through p-Laplacian
Anuj Kumar Sirohi, Subhanu Halder, Kabir Kumar, Sandeep Kumar
TL;DR
This work tackles the vulnerability of Graph Neural Networks to adversarial graph perturbations by introducing pLapGNN, a robustness framework that denoises the graph using a $p$-Laplacian prior before learning. The method formulates a joint (or two-stage) optimization to recover a clean Laplacian $\Phi^*$ parameterized as $\mathcal{L}w$ and to train GNN parameters $\theta$ concurrently, leveraging the nonlinear and robust properties of the $p$-Laplacian for both outlier resistance and sparsity control. Empirical results on Cora and Citeseer under Nettack and Metattack show competitive robustness and notably faster convergence than state-of-the-art baselines, with a favorable runtime profile due to lower computational complexity. The approach offers a practical, scalable defense for real-world GNN deployments facing adversarial manipulation, particularly in settings with heterogeneous or noisy graph structures.
Abstract
With the increase of data in day-to-day life, businesses and different stakeholders need to analyze the data for better predictions. Traditionally, relational data has been a source of various insights, but with the increase in computational power and the need to understand deeper relationships between entities, the need to design new techniques has arisen. For this graph data analysis has become an extraordinary tool for understanding the data, which reveals more realistic and flexible modelling of complex relationships. Recently, Graph Neural Networks (GNNs) have shown great promise in various applications, such as social network analysis, recommendation systems, drug discovery, and more. However, many adversarial attacks can happen over the data, whether during training (poisoning attack) or during testing (evasion attack), which can adversely manipulate the desired outcome from the GNN model. Therefore, it is crucial to make the GNNs robust to such attacks. The existing robustness methods are computationally demanding and perform poorly when the intensity of attack increases. This paper presents a computationally efficient framework, namely, pLapGNN, based on weighted p-Laplacian for making GNNs robust. Empirical evaluation on real datasets establishes the efficacy and efficiency of the proposed method.