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Register a new userUnderstanding Structural Vulnerability in Graph Convolutional Networks
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Added by
Jintang Li
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Recent studies have shown that Graph Convolutional Networks (GCNs) are vulnerable to adversarial attacks on the graph structure. Although multiple works have been proposed to improve their robustness against such structural adversarial attacks, the reasons for the success of the attacks remain unclear. In this work, we theoretically and empirically demonstrate that structural adversarial examples can be attributed to the non-robust aggregation scheme (i.e., the weighted mean) of GCNs. Specifically, our analysis takes advantage of the breakdown point which can quantitatively measure the robustness of aggregation schemes. The key insight is that weighted mean, as the basic design of GCNs, has a low breakdown point and its output can be dramatically changed by injecting a single edge. We show that adopting the aggregation scheme with a high breakdown point (e.g., median or trimmed mean) could significantly enhance the robustness of GCNs against structural attacks. Extensive experiments on four real-world datasets demonstrate that such a simple but effective method achieves the best robustness performance compared to state-of-the-art models.
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In this paper, we study the robustness of graph convolutional networks (GCNs). Despite the good performance of GCNs on graph semi-supervised learning tasks, previous works have shown that the original GCNs are very unstable to adversarial perturbations. In particular, we can observe a severe performance degradation by slightly changing the graph adjacency matrix or the features of a few nodes, making it unsuitable for security-critical applications. Inspired by the previous works on adversarial defense for deep neural networks, and especially adversarial training algorithm, we propose a method called GraphDefense to defend against the adversarial perturbations. In addition, for our defense method, we could still maintain semi-supervised learning settings, without a large label rate. We also show that adversarial training in features is equivalent to adversarial training for edges with a small perturbation. Our experiments show that the proposed defense methods successfully increase the robustness of Graph Convolutional Networks. Furthermore, we show that with careful design, our proposed algorithm can scale to large graphs, such as Reddit dataset.
A Graph Convolutional Network (GCN) stacks several layers and in each layer performs a PROPagation operation (PROP) and a TRANsformation operation (TRAN) for learning node representations over graph-structured data. Though powerful, GCNs tend to suffer performance drop when the model gets deep. Previous works focus on PROPs to study and mitigate this issue, but the role of TRANs is barely investigated. In this work, we study performance degradation of GCNs by experimentally examining how stacking only TRANs or PROPs works. We find that TRANs contribute significantly, or even more than PROPs, to declining performance, and moreover that they tend to amplify node-wise feature variance in GCNs, causing variance inflammation that we identify as a key factor for causing performance drop. Motivated by such observations, we propose a variance-controlling technique termed Node Normalization (NodeNorm), which scales each nodes features using its own standard deviation. Experimental results validate the effectiveness of NodeNorm on addressing performance degradation of GCNs. Specifically, it enables deep GCNs to outperform shallow ones in cases where deep models are needed, and to achieve comparable results with shallow ones on 6 benchmark datasets. NodeNorm is a generic plug-in and can well generalize to other GNN architectures. Code is publicly available at https://github.com/miafei/NodeNorm.
In this paper, we study the robustness of graph convolutional networks (GCNs). Previous work have shown that GCNs are vulnerable to adversarial perturbation on adjacency or feature matrices of existing nodes; however, such attacks are usually unrealistic in real applications. For instance, in social network applications, the attacker will need to hack into either the client or server to change existing links or features. In this paper, we propose a new type of fake node attacks to attack GCNs by adding malicious fake nodes. This is much more realistic than previous attacks; in social network applications, the attacker only needs to register a set of fake accounts and link to existing ones. To conduct fake node attacks, a greedy algorithm is proposed to generate edges of malicious nodes and their corresponding features aiming to minimize the classification accuracy on the target nodes. In addition, we introduce a discriminator to classify malicious nodes from real nodes, and propose a Greedy-GAN attack to simultaneously update the discriminator and the attacker, to make malicious nodes indistinguishable from the real ones. Our non-targeted attack decreases the accuracy of GCN down to 0.03, and our targeted attack reaches a success rate of 78% on a group of 100 nodes, and 90% on average for attacking a single target node.
Graph convolutional networks (GCNs) have received considerable research attention recently. Most GCNs learn the node representations in Euclidean geometry, but that could have a high distortion in the case of embedding graphs with scale-free or hierarchical structure. Recently, some GCNs are proposed to deal with this problem in non-Euclidean geometry, e.g., hyperbolic geometry. Although hyperbolic GCNs achieve promising performance, existing hyperbolic graph operations actually cannot rigorously follow the hyperbolic geometry, which may limit the ability of hyperbolic geometry and thus hurt the performance of hyperbolic GCNs. In this paper, we propose a novel hyperbolic GCN named Lorentzian graph convolutional network (LGCN), which rigorously guarantees the learned node features follow the hyperbolic geometry. Specifically, we rebuild the graph operations of hyperbolic GCNs with Lorentzian version, e.g., the feature transformation and non-linear activation. Also, an elegant neighborhood aggregation method is designed based on the centroid of Lorentzian distance. Moreover, we prove some proposed graph operations are equivalent in different types of hyperbolic geometry, which fundamentally indicates their correctness. Experiments on six datasets show that LGCN performs better than the state-of-the-art methods. LGCN has lower distortion to learn the representation of tree-likeness graphs compared with existing hyperbolic GCNs. We also find that the performance of some hyperbolic GCNs can be improved by simply replacing the graph operations with those we defined in this paper.
Graphs have been widely adopted to denote structural connections between entities. The relations are in many cases heterogeneous, but entangled together and denoted merely as a single edge between a pair of nodes. For example, in a social network graph, users in different latent relationships like friends and colleagues, are usually connected via a bare edge that conceals such intrinsic connections. In this paper, we introduce a novel graph convolutional network (GCN), termed as factorizable graph convolutional network(FactorGCN), that explicitly disentangles such intertwined relations encoded in a graph. FactorGCN takes a simple graph as input, and disentangles it into several factorized graphs, each of which represents a latent and disentangled relation among nodes. The features of the nodes are then aggregated separately in each factorized latent space to produce disentangled features, which further leads to better performances for downstream tasks. We evaluate the proposed FactorGCN both qualitatively and quantitatively on the synthetic and real-world datasets, and demonstrate that it yields truly encouraging results in terms of both disentangling and feature aggregation. Code is publicly available at https://github.com/ihollywhy/FactorGCN.PyTorch.
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