Backdoor attack is a powerful attack algorithm to deep learning model. Recently, GNN's vulnerability to backdoor attack has been proved especially on graph classification task. In this paper, we propose the first backdoor detection and defense method on GNN. Most backdoor attack depends on injecting small but influential trigger to the clean sample. For graph data, current backdoor attack focus on manipulating the graph structure to inject the trigger. We find that there are apparent differences between benign samples and malicious samples in some explanatory evaluation metrics, such as fidelity and infidelity. After identifying the malicious sample, the explainability of the GNN model can help us capture the most significant subgraph which is probably the trigger in a trojan graph. We use various dataset and different attack settings to prove the effectiveness of our defense method. The attack success rate all turns out to decrease considerably.
Graph Neural Networks (GNNs) have become the backbone for a myriad of tasks pertaining to graphs and similar topological data structures. While many works have been established in domains related to node and graph classification/regression tasks, they mostly deal with a single task. Continual learning on graphs is largely unexplored and existing graph continual learning approaches are limited to the task-incremental learning scenarios. This paper proposes a graph continual learning strategy that combines the architecture-based and memory-based approaches. The structural learning strategy is driven by reinforcement learning, where a controller network is trained in such a way to determine an optimal number of nodes to be added/pruned from the base network when new tasks are observed, thus assuring sufficient network capacities. The parameter learning strategy is underpinned by the concept of Dark Experience replay method to cope with the catastrophic forgetting problem. Our approach is numerically validated with several graph continual learning benchmark problems in both task-incremental learning and class-incremental learning settings. Compared to recently published works, our approach demonstrates improved performance in both the settings. The implementation code can be found at \url{https://github.com/codexhammer/gcl}.
Graph Neural Networks (GNNs) are widely used for graph representation learning. Despite its prevalence, GNN suffers from two drawbacks in the graph classification task, the neglect of graph-level relationships, and the generalization issue. Each graph is treated separately in GNN message passing/graph pooling, and existing methods to address overfitting operate on each individual graph. This makes the graph representations learnt less effective in the downstream classification. In this paper, we propose a Class-Aware Representation rEfinement (CARE) framework for the task of graph classification. CARE computes simple yet powerful class representations and injects them to steer the learning of graph representations towards better class separability. CARE is a plug-and-play framework that is highly flexible and able to incorporate arbitrary GNN backbones without significantly increasing the computational cost. We also theoretically prove that CARE has a better generalization upper bound than its GNN backbone through Vapnik-Chervonenkis (VC) dimension analysis. Our extensive experiments with 11 well-known GNN backbones on 9 benchmark datasets validate the superiority and effectiveness of CARE over its GNN counterparts.
This paper presents the Persistent Weisfeiler-Lehman Random walk scheme (abbreviated as PWLR) for graph representations, a novel mathematical framework which produces a collection of explainable low-dimensional representations of graphs with discrete and continuous node features. The proposed scheme effectively incorporates normalized Weisfeiler-Lehman procedure, random walks on graphs, and persistent homology. We thereby integrate three distinct properties of graphs, which are local topological features, node degrees, and global topological invariants, while preserving stability from graph perturbations. This generalizes many variants of Weisfeiler-Lehman procedures, which are primarily used to embed graphs with discrete node labels. Empirical results suggest that these representations can be efficiently utilized to produce comparable results to state-of-the-art techniques in classifying graphs with discrete node labels, and enhanced performances in classifying those with continuous node features.
We propose a new graph neural network (GNN) module, based on relaxations of recently proposed geometric scattering transforms, which consist of a cascade of graph wavelet filters. Our learnable geometric scattering (LEGS) module enables adaptive tuning of the wavelets to encourage band-pass features to emerge in learned representations. The incorporation of our LEGS-module in GNNs enables the learning of longer-range graph relations compared to many popular GNNs, which often rely on encoding graph structure via smoothness or similarity between neighbors. Further, its wavelet priors result in simplified architectures with significantly fewer learned parameters compared to competing GNNs. We demonstrate the predictive performance of LEGS-based networks on graph classification benchmarks, as well as the descriptive quality of their learned features in biochemical graph data exploration tasks. Our results show that LEGS-based networks match or outperforms popular GNNs, as well as the original geometric scattering construction, on many datasets, in particular in biochemical domains, while retaining certain mathematical properties of handcrafted (non-learned) geometric scattering.
Graph neural networks (GNNs) have achieved tremendous success in the task of graph classification and its diverse downstream real-world applications. Despite the huge success in learning graph representations, current GNN models have demonstrated their vulnerability to potentially existent adversarial examples on graph-structured data. Existing approaches are either limited to structure attacks or restricted to local information, urging for the design of a more general attack framework on graph classification, which faces significant challenges due to the complexity of generating local-node-level adversarial examples using the global-graph-level information. To address this "global-to-local" attack challenge, we present a novel and general framework to generate adversarial examples via manipulating graph structure and node features. Specifically, we make use of Graph Class Activation Mapping and its variant to produce node-level importance corresponding to the graph classification task. Then through a heuristic design of algorithms, we can perform both feature and structure attacks under unnoticeable perturbation budgets with the help of both node-level and subgraph-level importance. Experiments towards attacking four state-of-the-art graph classification models on six real-world benchmarks verify the flexibility and effectiveness of our framework.
Graph similarity measurement, which computes the distance/similarity between two graphs, arises in various graph-related tasks. Recent learning-based methods lack interpretability, as they directly transform interaction information between two graphs into one hidden vector and then map it to similarity. To cope with this problem, this study proposes a more interpretable end-to-end paradigm for graph similarity learning, named Similarity Computation via Maximum Common Subgraph Inference (INFMCS). Our critical insight into INFMCS is the strong correlation between similarity score and Maximum Common Subgraph (MCS). We implicitly infer MCS to obtain the normalized MCS size, with the supervision information being only the similarity score during training. To capture more global information, we also stack some vanilla transformer encoder layers with graph convolution layers and propose a novel permutation-invariant node Positional Encoding. The entire model is quite simple yet effective. Comprehensive experiments demonstrate that INFMCS consistently outperforms state-of-the-art baselines for graph-graph classification and regression tasks. Ablation experiments verify the effectiveness of the proposed computation paradigm and other components. Also, visualization and statistics of results reveal the interpretability of INFMCS.
Downsampling produces coarsened, multi-resolution representations of data and it is used, for example, to produce lossy compression and visualization of large images, reduce computational costs, and boost deep neural representation learning. Unfortunately, due to their lack of a regular structure, there is still no consensus on how downsampling should apply to graphs and linked data. Indeed reductions in graph data are still needed for the goals described above, but reduction mechanisms do not have the same focus on preserving topological structures and properties, while allowing for resolution-tuning, as is the case in regular data downsampling. In this paper, we take a step in this direction, introducing a unifying interpretation of downsampling in regular and graph data. In particular, we define a graph coarsening mechanism which is a graph-structured counterpart of controllable equispaced coarsening mechanisms in regular data. We prove theoretical guarantees for distortion bounds on path lengths, as well as the ability to preserve key topological properties in the coarsened graphs. We leverage these concepts to define a graph pooling mechanism that we empirically assess in graph classification tasks, providing a greedy algorithm that allows efficient parallel implementation on GPUs, and showing that it compares favorably against pooling methods in literature.
Recently, graph neural networks (GNNs) have been widely used to develop successful recommender systems. Although powerful, it is very difficult for a GNN-based recommender system to attach tangible explanations of why a specific item ends up in the list of suggestions for a given user. Indeed, explaining GNN-based recommendations is unique, and existing GNN explanation methods are inappropriate for two reasons. First, traditional GNN explanation methods are designed for node, edge, or graph classification tasks rather than ranking, as in recommender systems. Second, standard machine learning explanations are usually intended to support skilled decision-makers. Instead, recommendations are designed for any end-user, and thus their explanations should be provided in user-understandable ways. In this work, we propose GREASE, a novel method for explaining the suggestions provided by any black-box GNN-based recommender system. Specifically, GREASE first trains a surrogate model on a target user-item pair and its $l$-hop neighborhood. Then, it generates both factual and counterfactual explanations by finding optimal adjacency matrix perturbations to capture the sufficient and necessary conditions for an item to be recommended, respectively. Experimental results conducted on real-world datasets demonstrate that GREASE can generate concise and effective explanations for popular GNN-based recommender models.
Convolutional neural networks (CNN) have enabled major advances in image classification through convolution and pooling. In particular, image pooling transforms a connected discrete grid into a reduced grid with the same connectivity and allows reduction functions to take into account all the pixels of an image. However, a pooling satisfying such properties does not exist for graphs. Indeed, some methods are based on a vertex selection step which induces an important loss of information. Other methods learn a fuzzy clustering of vertex sets which induces almost complete reduced graphs. We propose to overcome both problems using a new pooling method, named MIVSPool. This method is based on a selection of vertices called surviving vertices using a Maximal Independent Vertex Set (MIVS) and an assignment of the remaining vertices to the survivors. Consequently, our method does not discard any vertex information nor artificially increase the density of the graph. Experimental results show an increase in accuracy for graph classification on various standard datasets.
Graph Neural Networks (GNNs), inspired by Convolutional Neural Networks (CNNs), aggregate the message of nodes' neighbors and structure information to acquire expressive representations of nodes for node classification, graph classification, and link prediction. Previous studies have indicated that GNNs are vulnerable to Membership Inference Attacks (MIAs), which infer whether a node is in the training data of GNNs and leak the node's private information, like the patient's disease history. The implementation of previous MIAs takes advantage of the models' probability output, which is infeasible if GNNs only provide the prediction label (label-only) for the input. In this paper, we propose a label-only MIA against GNNs for node classification with the help of GNNs' flexible prediction mechanism, e.g., obtaining the prediction label of one node even when neighbors' information is unavailable. Our attacking method achieves around 60\% accuracy, precision, and Area Under the Curve (AUC) for most datasets and GNN models, some of which are competitive or even better than state-of-the-art probability-based MIAs implemented under our environment and settings. Additionally, we analyze the influence of the sampling method, model selection approach, and overfitting level on the attack performance of our label-only MIA. Both of those factors have an impact on the attack performance. Then, we consider scenarios where assumptions about the adversary's additional dataset (shadow dataset) and extra information about the target model are relaxed. Even in those scenarios, our label-only MIA achieves a better attack performance in most cases. Finally, we explore the effectiveness of possible defenses, including Dropout, Regularization, Normalization, and Jumping knowledge. None of those four defenses prevent our attack completely.
In the past few years, graph neural networks (GNNs) have become the de facto model of choice for graph classification. While, from the theoretical viewpoint, most GNNs can operate on graphs of any size, it is empirically observed that their classification performance degrades when they are applied on graphs with sizes that differ from those in the training data. Previous works have tried to tackle this issue in graph classification by providing the model with inductive biases derived from assumptions on the generative process of the graphs, or by requiring access to graphs from the test domain. The first strategy is tied to the quality of the assumptions made for the generative process, and requires the use of specific models designed after the explicit definition of the generative process of the data, leaving open the question of how to improve the performance of generic GNN models in general settings. On the other hand, the second strategy can be applied to any GNN, but requires access to information that is not always easy to obtain. In this work we consider the scenario in which we only have access to the training data, and we propose a regularization strategy that can be applied to any GNN to improve its generalization capabilities from smaller to larger graphs without requiring access to the test data. Our regularization is based on the idea of simulating a shift in the size of the training graphs using coarsening techniques, and enforcing the model to be robust to such a shift. Experimental results on standard datasets show that popular GNN models, trained on the 50% smallest graphs in the dataset and tested on the 10% largest graphs, obtain performance improvements of up to 30% when trained with our regularization strategy.
Aiming at two molecular graph datasets and one protein association subgraph dataset in OGB graph classification task, we design a graph neural network framework for graph classification task by introducing PAS(Pooling Architecture Search). At the same time, we improve it based on the GNN topology design method F2GNN to further design the feature selection and fusion strategies, so as to further improve the performance of the model in the graph property prediction task while overcoming the over smoothing problem of deep GNN training. Finally, a performance breakthrough is achieved on these three datasets, which is significantly better than other methods with fixed aggregate function. It is proved that the NAS method has high generalization ability for multiple tasks and the advantage of our method in processing graph property prediction tasks.
The Weisfeiler-Lehman (WL) test is a widely used algorithm in graph machine learning, including graph kernels, graph metrics, and graph neural networks. However, it focuses only on the consistency of the graph, which means that it is unable to detect slight structural differences. Consequently, this limits its ability to capture structural information, which also limits the performance of existing models that rely on the WL test. This limitation is particularly severe for traditional metrics defined by the WL test, which cannot precisely capture slight structural differences. In this paper, we propose a novel graph metric called the Wasserstein WL Subtree (WWLS) distance to address this problem. Our approach leverages the WL subtree as structural information for node neighborhoods and defines node metrics using the $L_1$-approximated tree edit distance ($L_1$-TED) between WL subtrees of nodes. Subsequently, we combine the Wasserstein distance and the $L_1$-TED to define the WWLS distance, which can capture slight structural differences that may be difficult to detect using conventional metrics. We demonstrate that the proposed WWLS distance outperforms baselines in both metric validation and graph classification experiments.
When dealing with tabular data, models based on decision trees are a popular choice due to their high accuracy on these data types, their ease of application, and explainability properties. However, when it comes to graph-structured data, it is not clear how to apply them effectively, in a way that incorporates the topological information with the tabular data available on the vertices of the graph. To address this challenge, we introduce TREE-G. TREE-G modifies standard decision trees, by introducing a novel split function that is specialized for graph data. Not only does this split function incorporate the node features and the topological information, but it also uses a novel pointer mechanism that allows split nodes to use information computed in previous splits. Therefore, the split function adapts to the predictive task and the graph at hand. We analyze the theoretical properties of TREE-G and demonstrate its benefits empirically on multiple graph and vertex prediction benchmarks. In these experiments, TREE-G consistently outperforms other tree-based models and often outperforms other graph-learning algorithms such as Graph Neural Networks (GNNs) and Graph Kernels, sometimes by large margins. Moreover, TREE-Gs models and their predictions can be explained and visualized
We show that standard Transformers without graph-specific modifications can lead to promising results in graph learning both in theory and practice. Given a graph, we simply treat all nodes and edges as independent tokens, augment them with token embeddings, and feed them to a Transformer. With an appropriate choice of token embeddings, we prove that this approach is theoretically at least as expressive as an invariant graph network (2-IGN) composed of equivariant linear layers, which is already more expressive than all message-passing Graph Neural Networks (GNN). When trained on a large-scale graph dataset (PCQM4Mv2), our method coined Tokenized Graph Transformer (TokenGT) achieves significantly better results compared to GNN baselines and competitive results compared to Transformer variants with sophisticated graph-specific inductive bias. Our implementation is available at https://github.com/jw9730/tokengt.
Popular graph neural networks are shallow models, despite the success of very deep architectures in other application domains of deep learning. This reduces the modeling capacity and leaves models unable to capture long-range relationships. The primary reason for the shallow design results from over-smoothing, which leads node states to become more similar with increased depth. We build on the close connection between GNNs and PageRank, for which personalized PageRank introduces the consideration of a personalization vector. Adopting this idea, we propose the Personalized PageRank Graph Neural Network (PPRGNN), which extends the graph convolutional network to an infinite-depth model that has a chance to reset the neighbor aggregation back to the initial state in each iteration. We introduce a nicely interpretable tweak to the chance of resetting and prove the convergence of our approach to a unique solution without placing any constraints, even when taking infinitely many neighbor aggregations. As in personalized PageRank, our result does not suffer from over-smoothing. While doing so, time complexity remains linear while we keep memory complexity constant, independently of the depth of the network, making it scale well to large graphs. We empirically show the effectiveness of our approach for various node and graph classification tasks. PPRGNN outperforms comparable methods in almost all cases.
The problem of interpreting the decisions of machine learning is a well-researched and important. We are interested in a specific type of machine learning model that deals with graph data called graph neural networks. Evaluating interpretability approaches for graph neural networks (GNN) specifically are known to be challenging due to the lack of a commonly accepted benchmark. Given a GNN model, several interpretability approaches exist to explain GNN models with diverse (sometimes conflicting) evaluation methodologies. In this paper, we propose a benchmark for evaluating the explainability approaches for GNNs called Bagel. In Bagel, we firstly propose four diverse GNN explanation evaluation regimes -- 1) faithfulness, 2) sparsity, 3) correctness. and 4) plausibility. We reconcile multiple evaluation metrics in the existing literature and cover diverse notions for a holistic evaluation. Our graph datasets range from citation networks, document graphs, to graphs from molecules and proteins. We conduct an extensive empirical study on four GNN models and nine post-hoc explanation approaches for node and graph classification tasks. We open both the benchmarks and reference implementations and make them available at https://github.com/Mandeep-Rathee/Bagel-benchmark.
Following the success of convolution on non-Euclidean space, the corresponding pooling approaches have also been validated on various tasks regarding graphs. However, because of the fixed compression quota and stepwise pooling design, these hierarchical pooling methods still suffer from local structure damage and suboptimal problem. In this work, inspired by structural entropy, we propose a hierarchical pooling approach, SEP, to tackle the two issues. Specifically, without assigning the layer-specific compression quota, a global optimization algorithm is designed to generate the cluster assignment matrices for pooling at once. Then, we present an illustration of the local structure damage from previous methods in the reconstruction of ring and grid synthetic graphs. In addition to SEP, we further design two classification models, SEP-G and SEP-N for graph classification and node classification, respectively. The results show that SEP outperforms state-of-the-art graph pooling methods on graph classification benchmarks and obtains superior performance on node classifications.
Graph instance contrastive learning has been proved as an effective task for Graph Neural Network (GNN) pre-training. However, one key issue may seriously impede the representative power in existing works: Positive instances created by current methods often miss crucial information of graphs or even yield illegal instances (such as non-chemically-aware graphs in molecular generation). To remedy this issue, we propose to select positive graph instances directly from existing graphs in the training set, which ultimately maintains the legality and similarity to the target graphs. Our selection is based on certain domain-specific pair-wise similarity measurements as well as sampling from a hierarchical graph encoding similarity relations among graphs. Besides, we develop an adaptive node-level pre-training method to dynamically mask nodes to distribute them evenly in the graph. We conduct extensive experiments on $13$ graph classification and node classification benchmark datasets from various domains. The results demonstrate that the GNN models pre-trained by our strategies can outperform those trained-from-scratch models as well as the variants obtained by existing methods.