In this work, we propose the first backdoor attack to graph neural networks (GNN). Specifically, we propose a \emph{subgraph based backdoor attack} to GNN for graph classification. In our backdoor attack, a GNN classifier predicts an attacker-chosen target label for a testing graph once a predefined subgraph is injected to the testing graph. Our empirical results on three real-world graph datasets show that our backdoor attacks are effective with a small impact on a GNN's prediction accuracy for clean testing graphs. Moreover, we generalize a randomized smoothing based certified defense to defend against our backdoor attacks. Our empirical results show that the defense is effective in some cases but ineffective in other cases, highlighting the needs of new defenses for our backdoor attacks.
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Graph neural networks, a popular class of models effective in a wide range of graph-based learning tasks, have been shown to be vulnerable to adversarial attacks. While the majority of the literature focuses on such vulnerability in node-level classification tasks, little effort has been dedicated to analysing adversarial attacks on graph-level classification, an important problem with numerous real-life applications such as biochemistry and social network analysis. The few existing methods often require unrealistic setups, such as access to internal information of the victim models, or an impractically-large number of queries. We present a novel Bayesian optimisation-based attack method for graph classification models. Our method is black-box, query-efficient and parsimonious with respect to the perturbation applied. We empirically validate the effectiveness and flexibility of the proposed method on a wide range of graph classification tasks involving varying graph properties, constraints and modes of attack. Finally, we analyse common interpretable patterns behind the adversarial samples produced, which may shed further light on the adversarial robustness of graph classification models.
While many existing graph neural networks (GNNs) have been proven to perform $\ell_2$-based graph smoothing that enforces smoothness globally, in this work we aim to further enhance the local smoothness adaptivity of GNNs via $\ell_1$-based graph smoothing. As a result, we introduce a family of GNNs (Elastic GNNs) based on $\ell_1$ and $\ell_2$-based graph smoothing. In particular, we propose a novel and general message passing scheme into GNNs. This message passing algorithm is not only friendly to back-propagation training but also achieves the desired smoothing properties with a theoretical convergence guarantee. Experiments on semi-supervised learning tasks demonstrate that the proposed Elastic GNNs obtain better adaptivity on benchmark datasets and are significantly robust to graph adversarial attacks. The implementation of Elastic GNNs is available at \url{//github.com/lxiaorui/ElasticGNN}.
Deep neural networks (DNNs) are known vulnerable to backdoor attacks, a training time attack that injects a trigger pattern into a small proportion of training data so as to control the model's prediction at the test time. Backdoor attacks are notably dangerous since they do not affect the model's performance on clean examples, yet can fool the model to make incorrect prediction whenever the trigger pattern appears during testing. In this paper, we propose a novel defense framework Neural Attention Distillation (NAD) to erase backdoor triggers from backdoored DNNs. NAD utilizes a teacher network to guide the finetuning of the backdoored student network on a small clean subset of data such that the intermediate-layer attention of the student network aligns with that of the teacher network. The teacher network can be obtained by an independent finetuning process on the same clean subset. We empirically show, against 6 state-of-the-art backdoor attacks, NAD can effectively erase the backdoor triggers using only 5\% clean training data without causing obvious performance degradation on clean examples. Code is available in //github.com/bboylyg/NAD.
In order to overcome the expressive limitations of graph neural networks (GNNs), we propose the first method that exploits vector flows over graphs to develop globally consistent directional and asymmetric aggregation functions. We show that our directional graph networks (DGNs) generalize convolutional neural networks (CNNs) when applied on a grid. Whereas recent theoretical works focus on understanding local neighbourhoods, local structures and local isomorphism with no global information flow, our novel theoretical framework allows directional convolutional kernels in any graph. First, by defining a vector field in the graph, we develop a method of applying directional derivatives and smoothing by projecting node-specific messages into the field. Then we propose the use of the Laplacian eigenvectors as such vector field, and we show that the method generalizes CNNs on an n-dimensional grid, and is provably more discriminative than standard GNNs regarding the Weisfeiler-Lehman 1-WL test. Finally, we bring the power of CNN data augmentation to graphs by providing a means of doing reflection, rotation and distortion on the underlying directional field. We evaluate our method on different standard benchmarks and see a relative error reduction of 8\% on the CIFAR10 graph dataset and 11% to 32% on the molecular ZINC dataset. An important outcome of this work is that it enables to translate any physical or biological problems with intrinsic directional axes into a graph network formalism with an embedded directional field.
There has been an ongoing cycle where stronger defenses against adversarial attacks are subsequently broken by a more advanced defense-aware attack. We present a new approach towards ending this cycle where we "deflect'' adversarial attacks by causing the attacker to produce an input that semantically resembles the attack's target class. To this end, we first propose a stronger defense based on Capsule Networks that combines three detection mechanisms to achieve state-of-the-art detection performance on both standard and defense-aware attacks. We then show that undetected attacks against our defense often perceptually resemble the adversarial target class by performing a human study where participants are asked to label images produced by the attack. These attack images can no longer be called "adversarial'' because our network classifies them the same way as humans do.
In federated learning, multiple client devices jointly learn a machine learning model: each client device maintains a local model for its local training dataset, while a master device maintains a global model via aggregating the local models from the client devices. The machine learning community recently proposed several federated learning methods that were claimed to be robust against Byzantine failures (e.g., system failures, adversarial manipulations) of certain client devices. In this work, we perform the first systematic study on local model poisoning attacks to federated learning. We assume an attacker has compromised some client devices, and the attacker manipulates the local model parameters on the compromised client devices during the learning process such that the global model has a large testing error rate. We formulate our attacks as optimization problems and apply our attacks to four recent Byzantine-robust federated learning methods. Our empirical results on four real-world datasets show that our attacks can substantially increase the error rates of the models learnt by the federated learning methods that were claimed to be robust against Byzantine failures of some client devices. We generalize two defenses for data poisoning attacks to defend against our local model poisoning attacks. Our evaluation results show that one defense can effectively defend against our attacks in some cases, but the defenses are not effective enough in other cases, highlighting the need for new defenses against our local model poisoning attacks to federated learning.
Graph neural networks (GNNs) are widely used in many applications. However, their robustness against adversarial attacks is criticized. Prior studies show that using unnoticeable modifications on graph topology or nodal features can significantly reduce the performances of GNNs. It is very challenging to design robust graph neural networks against poisoning attack and several efforts have been taken. Existing work aims at reducing the negative impact from adversarial edges only with the poisoned graph, which is sub-optimal since they fail to discriminate adversarial edges from normal ones. On the other hand, clean graphs from similar domains as the target poisoned graph are usually available in the real world. By perturbing these clean graphs, we create supervised knowledge to train the ability to detect adversarial edges so that the robustness of GNNs is elevated. However, such potential for clean graphs is neglected by existing work. To this end, we investigate a novel problem of improving the robustness of GNNs against poisoning attacks by exploring clean graphs. Specifically, we propose PA-GNN, which relies on a penalized aggregation mechanism that directly restrict the negative impact of adversarial edges by assigning them lower attention coefficients. To optimize PA-GNN for a poisoned graph, we design a meta-optimization algorithm that trains PA-GNN to penalize perturbations using clean graphs and their adversarial counterparts, and transfers such ability to improve the robustness of PA-GNN on the poisoned graph. Experimental results on four real-world datasets demonstrate the robustness of PA-GNN against poisoning attacks on graphs.
Learning node embeddings that capture a node's position within the broader graph structure is crucial for many prediction tasks on graphs. However, existing Graph Neural Network (GNN) architectures have limited power in capturing the position/location of a given node with respect to all other nodes of the graph. Here we propose Position-aware Graph Neural Networks (P-GNNs), a new class of GNNs for computing position-aware node embeddings. P-GNN first samples sets of anchor nodes, computes the distance of a given target node to each anchor-set,and then learns a non-linear distance-weighted aggregation scheme over the anchor-sets. This way P-GNNs can capture positions/locations of nodes with respect to the anchor nodes. P-GNNs have several advantages: they are inductive, scalable,and can incorporate node feature information. We apply P-GNNs to multiple prediction tasks including link prediction and community detection. We show that P-GNNs consistently outperform state of the art GNNs, with up to 66% improvement in terms of the ROC AUC score.
Capsule Networks preserve the hierarchical spatial relationships between objects, and thereby bears a potential to surpass the performance of traditional Convolutional Neural Networks (CNNs) in performing tasks like image classification. A large body of work has explored adversarial examples for CNNs, but their effectiveness on Capsule Networks has not yet been well studied. In our work, we perform an analysis to study the vulnerabilities in Capsule Networks to adversarial attacks. These perturbations, added to the test inputs, are small and imperceptible to humans, but can fool the network to mispredict. We propose a greedy algorithm to automatically generate targeted imperceptible adversarial examples in a black-box attack scenario. We show that this kind of attacks, when applied to the German Traffic Sign Recognition Benchmark (GTSRB), mislead Capsule Networks. Moreover, we apply the same kind of adversarial attacks to a 5-layer CNN and a 9-layer CNN, and analyze the outcome, compared to the Capsule Networks to study differences in their behavior.
There is a rising interest in studying the robustness of deep neural network classifiers against adversaries, with both advanced attack and defence techniques being actively developed. However, most recent work focuses on discriminative classifiers, which only model the conditional distribution of the labels given the inputs. In this paper we propose the deep Bayes classifier, which improves classical naive Bayes with conditional deep generative models. We further develop detection methods for adversarial examples, which reject inputs that have negative log-likelihood under the generative model exceeding a threshold pre-specified using training data. Experimental results suggest that deep Bayes classifiers are more robust than deep discriminative classifiers, and the proposed detection methods achieve high detection rates against many recently proposed attacks.
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