Graph neural networks (GNNs) have shown great success in learning from graph-based data. The key mechanism of current GNNs is message passing, where a node's feature is updated based on the information passing from its local neighbourhood. A limitation of this mechanism is that node features become increasingly dominated by the information aggregated from the neighbourhood as we use more rounds of message passing. Consequently, as the GNN layers become deeper, adjacent node features tends to be similar, making it more difficult for GNNs to distinguish adjacent nodes, thereby, limiting the performance of GNNs. In this paper, we propose conditional local feature encoding (CLFE) to help prevent the problem of node features being dominated by the information from local neighbourhood. The idea of our method is to extract the node hidden state embedding from message passing process and concatenate it with the nodes feature from previous stage, then we utilise linear transformation to form a CLFE based on the concatenated vector. The CLFE will form the layer output to better preserve node-specific information, thus help to improve the performance of GNN models. To verify the feasibility of our method, we conducted extensive experiments on seven benchmark datasets for four graph domain tasks: super-pixel graph classification, node classification, link prediction, and graph regression. The experimental results consistently demonstrate that our method improves model performance across a variety of baseline GNN models for all four tasks.
In this paper, we study semi-supervised graph classification, which aims at accurately predicting the categories of graphs in scenarios with limited labeled graphs and abundant unlabeled graphs. Despite the promising capability of graph neural networks (GNNs), they typically require a large number of costly labeled graphs, while a wealth of unlabeled graphs fail to be effectively utilized. Moreover, GNNs are inherently limited to encoding local neighborhood information using message-passing mechanisms, thus lacking the ability to model higher-order dependencies among nodes. To tackle these challenges, we propose a Hypergraph-Enhanced DuAL framework named HEAL for semi-supervised graph classification, which captures graph semantics from the perspective of the hypergraph and the line graph, respectively. Specifically, to better explore the higher-order relationships among nodes, we design a hypergraph structure learning to adaptively learn complex node dependencies beyond pairwise relations. Meanwhile, based on the learned hypergraph, we introduce a line graph to capture the interaction between hyperedges, thereby better mining the underlying semantic structures. Finally, we develop a relational consistency learning to facilitate knowledge transfer between the two branches and provide better mutual guidance. Extensive experiments on real-world graph datasets verify the effectiveness of the proposed method against existing state-of-the-art methods.
Graph neural networks have emerged as a specialized branch of deep learning, designed to address problems where pairwise relations between objects are crucial. Recent advancements utilize graph convolutional neural networks to extract features within graph structures. Despite promising results, these methods face challenges in real-world applications due to sparse features, resulting in inefficient resource utilization. Recent studies draw inspiration from the mammalian brain and employ spiking neural networks to model and learn graph structures. However, these approaches are limited to traditional Von Neumann-based computing systems, which still face hardware inefficiencies. In this study, we present a fully neuromorphic implementation of spiking graph neural networks designed for Loihi 2. We optimize network parameters using Lava Bayesian Optimization, a novel hyperparameter optimization system compatible with neuromorphic computing architectures. We showcase the performance benefits of combining neuromorphic Bayesian optimization with our approach for citation graph classification using fixed-precision spiking neurons. Our results demonstrate the capability of integer-precision, Loihi 2 compatible spiking neural networks in performing citation graph classification with comparable accuracy to existing floating point implementations.
Knowledge Graph Completion (KGC) has garnered massive research interest recently, and most existing methods are designed following a transductive setting where all entities are observed during training. Despite the great progress on the transductive KGC, these methods struggle to conduct reasoning on emerging KGs involving unseen entities. Thus, inductive KGC, which aims to deduce missing links among unseen entities, has become a new trend. Many existing studies transform inductive KGC as a graph classification problem by extracting enclosing subgraphs surrounding each candidate triple. Unfortunately, they still face certain challenges, such as the expensive time consumption caused by the repeat extraction of enclosing subgraphs, and the deficiency of entity-independent feature learning. To address these issues, we propose a global-local anchor representation (GLAR) learning method for inductive KGC. Unlike previous methods that utilize enclosing subgraphs, we extract a shared opening subgraph for all candidates and perform reasoning on it, enabling the model to perform reasoning more efficiently. Moreover, we design some transferable global and local anchors to learn rich entity-independent features for emerging entities. Finally, a global-local graph reasoning model is applied on the opening subgraph to rank all candidates. Extensive experiments show that our GLAR outperforms most existing state-of-the-art methods.
Graph Transformers (GTs) have demonstrated their advantages across a wide range of tasks. However, the self-attention mechanism in GTs overlooks the graph's inductive biases, particularly biases related to structure, which are crucial for the graph tasks. Although some methods utilize positional encoding and attention bias to model inductive biases, their effectiveness is still suboptimal analytically. Therefore, this paper presents Gradformer, a method innovatively integrating GT with the intrinsic inductive bias by applying an exponential decay mask to the attention matrix. Specifically, the values in the decay mask matrix diminish exponentially, correlating with the decreasing node proximities within the graph structure. This design enables Gradformer to retain its ability to capture information from distant nodes while focusing on the graph's local details. Furthermore, Gradformer introduces a learnable constraint into the decay mask, allowing different attention heads to learn distinct decay masks. Such an design diversifies the attention heads, enabling a more effective assimilation of diverse structural information within the graph. Extensive experiments on various benchmarks demonstrate that Gradformer consistently outperforms the Graph Neural Network and GT baseline models in various graph classification and regression tasks. Additionally, Gradformer has proven to be an effective method for training deep GT models, maintaining or even enhancing accuracy compared to shallow models as the network deepens, in contrast to the significant accuracy drop observed in other GT models.Codes are available at \url{https://github.com/LiuChuang0059/Gradformer}.
Graph neural networks (GNNs) have revolutionized the field of machine learning on non-Euclidean data such as graphs and networks. GNNs effectively implement node representation learning through neighborhood aggregation and achieve impressive results in many graph-related tasks. However, most neighborhood aggregation approaches are summation-based, which can be problematic as they may not be sufficiently expressive to encode informative graph structures. Furthermore, though the graph pooling module is also of vital importance for graph learning, especially for the task of graph classification, research on graph down-sampling mechanisms is rather limited. To address the above challenges, we propose a concatenation-based graph convolution mechanism that injectively updates node representations to maximize the discriminative power in distinguishing non-isomorphic subgraphs. In addition, we design a novel graph pooling module, called WL-SortPool, to learn important subgraph patterns in a deep-learning manner. WL-SortPool layer-wise sorts node representations (i.e. continuous WL colors) to separately learn the relative importance of subtrees with different depths for the purpose of classification, thus better characterizing the complex graph topology and rich information encoded in the graph. We propose a novel Subgraph Pattern GNN (SPGNN) architecture that incorporates these enhancements. We test the proposed SPGNN architecture on many graph classification benchmarks. Experimental results show that our method can achieve highly competitive results with state-of-the-art graph kernels and other GNN approaches.
The existing definitions of graph convolution, either from spatial or spectral perspectives, are inflexible and not unified. Defining a general convolution operator in the graph domain is challenging due to the lack of canonical coordinates, the presence of irregular structures, and the properties of graph symmetries. In this work, we propose a novel and general graph convolution framework by parameterizing the kernels as continuous functions of pseudo-coordinates derived via graph positional encoding. We name this Continuous Kernel Graph Convolution (CKGConv). Theoretically, we demonstrate that CKGConv is flexible and expressive. CKGConv encompasses many existing graph convolutions, and exhibits a stronger expressiveness, as powerful as graph transformers in terms of distinguishing non-isomorphic graphs. Empirically, we show that CKGConv-based Networks outperform existing graph convolutional networks and perform comparably to the best graph transformers across a variety of graph datasets. The code and models are publicly available at https://github.com/networkslab/CKGConv.
Graph Convolutional Networks (GCNs) have shown excellent performance in dealing with various graph structures such as node classification, graph classification and other tasks. However,recent studies have shown that GCNs are vulnerable to a novel threat known as backdoor attacks. However, all existing backdoor attacks in the graph domain require modifying the training samples to accomplish the backdoor injection, which may not be practical in many realistic scenarios where adversaries have no access to modify the training samples and may leads to the backdoor attack being detected easily. In order to explore the backdoor vulnerability of GCNs and create a more practical and stealthy backdoor attack method, this paper proposes a clean-graph backdoor attack against GCNs (CBAG) in the node classification task,which only poisons the training labels without any modification to the training samples, revealing that GCNs have this security vulnerability. Specifically, CBAG designs a new trigger exploration method to find important feature dimensions as the trigger patterns to improve the attack performance. By poisoning the training labels, a hidden backdoor is injected into the GCNs model. Experimental results show that our clean graph backdoor can achieve 99% attack success rate while maintaining the functionality of the GCNs model on benign samples.
Graph Transformers (GTs) have made remarkable achievements in graph-level tasks. However, most existing works regard graph structures as a form of guidance or bias for enhancing node representations, which focuses on node-central perspectives and lacks explicit representations of edges and structures. One natural question arises as to whether we can leverage a hypernode to represent some structures. Through experimental analysis, we explore the feasibility of this assumption. Based on our findings, we propose an efficient Loop and Clique Coarsening algorithm with linear complexity for Graph Classification (LCC4GC) on GT architecture. Specifically, we build three unique views, original, coarsening, and conversion, to learn a thorough structural representation. We compress loops and cliques via hierarchical heuristic graph coarsening and restrict them with well-designed constraints, which builds the coarsening view to learn high-level interactions between structures. We also introduce line graphs for edge embeddings and switch to edge-central perspective to alleviate the impact of coarsening reduction. Experiments on eight real-world datasets demonstrate the improvements of LCC4GC over 31 baselines from various architectures.
Graph Neural Networks (GNNs) have achieved state-of-the-art performance in solving graph classification tasks. However, most GNN architectures aggregate information from all nodes and edges in a graph, regardless of their relevance to the task at hand, thus hindering the interpretability of their predictions. In contrast to prior work, in this paper we propose a GNN \emph{training} approach that jointly i) finds the most predictive subgraph by removing edges and/or nodes -- -\emph{without making assumptions about the subgraph structure} -- while ii) optimizing the performance of the graph classification task. To that end, we rely on reinforcement learning to solve the resulting bi-level optimization with a reward function based on conformal predictions to account for the current in-training uncertainty of the classifier. Our empirical results on nine different graph classification datasets show that our method competes in performance with baselines while relying on significantly sparser subgraphs, leading to more interpretable GNN-based predictions.
Graphs are ubiquitous in various fields, and deep learning methods have been successful applied in graph classification tasks. However, building large and diverse graph datasets for training can be expensive. While augmentation techniques exist for structured data like images or numerical data, the augmentation of graph data remains challenging. This is primarily due to the complex and non-Euclidean nature of graph data. In this paper, it has been proposed a novel augmentation strategy for graphs that operates in a non-Euclidean space. This approach leverages graphon estimation, which models the generative mechanism of networks sequences. Computational results demonstrate the effectiveness of the proposed augmentation framework in improving the performance of graph classification models. Additionally, using a non-Euclidean distance, specifically the Gromow-Wasserstein distance, results in better approximations of the graphon. This framework also provides a means to validate different graphon estimation approaches, particularly in real-world scenarios where the true graphon is unknown.
Handling graph data is one of the most difficult tasks. Traditional techniques, such as those based on geometry and matrix factorization, rely on assumptions about the data relations that become inadequate when handling large and complex graph data. On the other hand, deep learning approaches demonstrate promising results in handling large graph data, but they often fall short of providing interpretable explanations. To equip the graph processing with both high accuracy and explainability, we introduce a novel approach that harnesses the power of a large language model (LLM), enhanced by an uncertainty-aware module to provide a confidence score on the generated answer. We experiment with our approach on two graph processing tasks: few-shot knowledge graph completion and graph classification. Our results demonstrate that through parameter efficient fine-tuning, the LLM surpasses state-of-the-art algorithms by a substantial margin across ten diverse benchmark datasets. Moreover, to address the challenge of explainability, we propose an uncertainty estimation based on perturbation, along with a calibration scheme to quantify the confidence scores of the generated answers. Our confidence measure achieves an AUC of 0.8 or higher on seven out of the ten datasets in predicting the correctness of the answer generated by LLM.
We propose a novel model-selection method for dynamic networks. Our approach involves training a classifier on a large body of synthetic network data. The data is generated by simulating nine state-of-the-art random graph models for dynamic networks, with parameter range chosen to ensure exponential growth of the network size in time. We design a conceptually novel type of dynamic features that count new links received by a group of vertices in a particular time interval. The proposed features are easy to compute, analytically tractable, and interpretable. Our approach achieves a near-perfect classification of synthetic networks, exceeding the state-of-the-art by a large margin. Applying our classification method to real-world citation networks gives credibility to the claims in the literature that models with preferential attachment, fitness and aging fit real-world citation networks best, although sometimes, the predicted model does not involve vertex fitness.
In this paper, we develop a novel local graph pooling method, namely the Separated Subgraph-based Hierarchical Pooling (SSHPool), for graph classification. We commence by assigning the nodes of a sample graph into different clusters, resulting in a family of separated subgraphs. We individually employ the local graph convolution units as the local structure to further compress each subgraph into a coarsened node, transforming the original graph into a coarsened graph. Since these subgraphs are separated by different clusters and the structural information cannot be propagated between them, the local convolution operation can significantly avoid the over-smoothing problem caused by message passing through edges in most existing Graph Neural Networks (GNNs). By hierarchically performing the proposed procedures on the resulting coarsened graph, the proposed SSHPool can effectively extract the hierarchical global features of the original graph structure, encapsulating rich intrinsic structural characteristics. Furthermore, we develop an end-to-end GNN framework associated with the SSHPool module for graph classification. Experimental results demonstrate the superior performance of the proposed model on real-world datasets.
In this paper, we propose a new model to learn Adaptive Kernel-based Representations (AKBR) for graph classification. Unlike state-of-the-art R-convolution graph kernels that are defined by merely counting any pair of isomorphic substructures between graphs and cannot provide an end-to-end learning mechanism for the classifier, the proposed AKBR approach aims to define an end-to-end representation learning model to construct an adaptive kernel matrix for graphs. To this end, we commence by leveraging a novel feature-channel attention mechanism to capture the interdependencies between different substructure invariants of original graphs. The proposed AKBR model can thus effectively identify the structural importance of different substructures, and compute the R-convolution kernel between pairwise graphs associated with the more significant substructures specified by their structural attentions. Since each row of the resulting kernel matrix can be theoretically seen as the embedding vector of a sample graph, the proposed AKBR model is able to directly employ the resulting kernel matrix as the graph feature matrix and input it into the classifier for classification (i.e., the SoftMax layer), naturally providing an end-to-end learning architecture between the kernel computation as well as the classifier. Experimental results show that the proposed AKBR model outperforms existing state-of-the-art graph kernels and deep learning methods on standard graph benchmarks.
Graph Neural Networks (GNN) have emerged as a popular and standard approach for learning from graph-structured data. The literature on GNN highlights the potential of this evolving research area and its widespread adoption in real-life applications. However, most of the approaches are either new in concept or derived from specific techniques. Therefore, the potential of more than one approach in hybrid form has not been studied extensively, which can be well utilized for sequenced data or static data together. We derive a hybrid approach based on two established techniques as generalized aggregation networks and topology adaptive graph convolution networks that solve our purpose to apply on both types of sequenced and static nature of data, effectively. The proposed method applies to both node and graph classification. Our empirical analysis reveals that the results are at par with literature results and better for handwritten strokes as sequenced data, where graph structures have not been explored.
Our work introduces an innovative approach to graph learning by leveraging Hyperdimensional Computing. Graphs serve as a widely embraced method for conveying information, and their utilization in learning has gained significant attention. This is notable in the field of chemoinformatics, where learning from graph representations plays a pivotal role. An important application within this domain involves the identification of cancerous cells across diverse molecular structures. We propose an HDC-based model that demonstrates comparable Area Under the Curve results when compared to state-of-the-art models like Graph Neural Networks (GNNs) or the Weisfieler-Lehman graph kernel (WL). Moreover, it outperforms previously proposed hyperdimensional computing graph learning methods. Furthermore, it achieves noteworthy speed enhancements, boasting a 40x acceleration in the training phase and a 15x improvement in inference time compared to GNN and WL models. This not only underscores the efficacy of the HDC-based method, but also highlights its potential for expedited and resource-efficient graph learning.
Graph-based anomaly detection is currently an important research topic in the field of graph neural networks (GNNs). We find that in graph anomaly detection, the homophily distribution differences between different classes are significantly greater than those in homophilic and heterophilic graphs. For the first time, we introduce a new metric called Class Homophily Variance, which quantitatively describes this phenomenon. To mitigate its impact, we propose a novel GNN model named Homophily Edge Generation Graph Neural Network (HedGe). Previous works typically focused on pruning, selecting or connecting on original relationships, and we refer to these methods as modifications. Different from these works, our method emphasizes generating new relationships with low class homophily variance, using the original relationships as an auxiliary. HedGe samples homophily adjacency matrices from scratch using a self-attention mechanism, and leverages nodes that are relevant in the feature space but not directly connected in the original graph. Additionally, we modify the loss function to punish the generation of unnecessary heterophilic edges by the model. Extensive comparison experiments demonstrate that HedGe achieved the best performance across multiple benchmark datasets, including anomaly detection and edgeless node classification. The proposed model also improves the robustness under the novel Heterophily Attack with increased class homophily variance on other graph classification tasks.
Graph Neural Networks (GNNs) have achieved impressive results in graph classification tasks, but they struggle to generalize effectively when faced with out-of-distribution (OOD) data. Several approaches have been proposed to address this problem. Among them, one solution is to diversify training distributions in vanilla classification by modifying the data environment, yet accessing the environment information is complex. Besides, another promising approach involves rationalization, extracting invariant rationales for predictions. However, extracting rationales is difficult due to limited learning signals, resulting in less accurate rationales and diminished predictions. To address these challenges, in this paper, we propose a Cooperative Classification and Rationalization (C2R) method, consisting of the classification and the rationalization module. Specifically, we first assume that multiple environments are available in the classification module. Then, we introduce diverse training distributions using an environment-conditional generative network, enabling robust graph representations. Meanwhile, the rationalization module employs a separator to identify relevant rationale subgraphs while the remaining non-rationale subgraphs are de-correlated with labels. Next, we align graph representations from the classification module with rationale subgraph representations using the knowledge distillation methods, enhancing the learning signal for rationales. Finally, we infer multiple environments by gathering non-rationale representations and incorporate them into the classification module for cooperative learning. Extensive experimental results on both benchmarks and synthetic datasets demonstrate the effectiveness of C2R. Code is available at https://github.com/yuelinan/Codes-of-C2R.
In recent times, a plethora of hardware accelerators have been put forth for graph learning applications such as vertex classification and graph classification. However, previous works have paid little attention to Knowledge Graph Completion (KGC), a task that is well-known for its significantly higher algorithm complexity. The state-of-the-art KGC solutions based on graph convolution neural network (GCN) involve extensive vertex/relation embedding updates and complicated score functions, which are inherently cumbersome for acceleration. As a result, existing accelerator designs are no longer optimal, and a novel algorithm-hardware co-design for KG reasoning is needed. Recently, brain-inspired HyperDimensional Computing (HDC) has been introduced as a promising solution for lightweight machine learning, particularly for graph learning applications. In this paper, we leverage HDC for an intrinsically more efficient and acceleration-friendly KGC algorithm. We also co-design an acceleration framework named HDReason targeting FPGA platforms. On the algorithm level, HDReason achieves a balance between high reasoning accuracy, strong model interpretability, and less computation complexity. In terms of architecture, HDReason offers reconfigurability, high training throughput, and low energy consumption. When compared with NVIDIA RTX 4090 GPU, the proposed accelerator achieves an average 10.6x speedup and 65x energy efficiency improvement. When conducting cross-models and cross-platforms comparison, HDReason yields an average 4.2x higher performance and 3.4x better energy efficiency with similar accuracy versus the state-of-the-art FPGA-based GCN training platform.