We investigate size-induced distribution shifts in graphs and assess their impact on the ability of graph neural networks (GNNs) to generalize to larger graphs relative to the training data. Existing literature presents conflicting conclusions on GNNs' size generalizability, primarily due to disparities in application domains and underlying assumptions concerning size-induced distribution shifts. Motivated by this, we take a data-driven approach: we focus on real biological datasets and seek to characterize the types of size-induced distribution shifts. Diverging from prior approaches, we adopt a spectral perspective and identify that spectrum differences induced by size are related to differences in subgraph patterns (e.g., average cycle lengths). While previous studies have identified that the inability of GNNs in capturing subgraph information negatively impacts their in-distribution generalization, our findings further show that this decline is more pronounced when evaluating on larger test graphs not encountered during training. Based on these spectral insights, we introduce a simple yet effective model-agnostic strategy, which makes GNNs aware of these important subgraph patterns to enhance their size generalizability. Our empirical results reveal that our proposed size-insensitive attention strategy substantially enhances graph classification performance on large test graphs, which are 2-10 times larger than the training graphs, resulting in an improvement in F1 scores by up to 8%.
Despite the increasing relevance of explainable AI, assessing the quality of explanations remains a challenging issue. Due to the high costs associated with human-subject experiments, various proxy metrics are often used to approximately quantify explanation quality. Generally, one possible interpretation of the quality of an explanation is its inherent value for teaching a related concept to a student. In this work, we extend artificial simulatability studies to the domain of graph neural networks. Instead of costly human trials, we use explanation-supervisable graph neural networks to perform simulatability studies to quantify the inherent usefulness of attributional graph explanations. We perform an extensive ablation study to investigate the conditions under which the proposed analyses are most meaningful. We additionally validate our methods applicability on real-world graph classification and regression datasets. We find that relevant explanations can significantly boost the sample efficiency of graph neural networks and analyze the robustness towards noise and bias in the explanations. We believe that the notion of usefulness obtained from our proposed simulatability analysis provides a dimension of explanation quality that is largely orthogonal to the common practice of faithfulness and has great potential to expand the toolbox of explanation quality assessments, specifically for graph explanations.
We aim to deepen the theoretical understanding of Graph Neural Networks (GNNs) on large graphs, with a focus on their expressive power. Existing analyses relate this notion to the graph isomorphism problem, which is mostly relevant for graphs of small sizes, or studied graph classification or regression tasks, while prediction tasks on nodes are far more relevant on large graphs. Recently, several works showed that, on very general random graphs models, GNNs converge to certains functions as the number of nodes grows. In this paper, we provide a more complete and intuitive description of the function space generated by equivariant GNNs for node-tasks, through general notions of convergence that encompass several previous examples. We emphasize the role of input node features, and study the impact of node Positional Encodings (PEs), a recent line of work that has been shown to yield state-of-the-art results in practice. Through the study of several examples of PEs on large random graphs, we extend previously known universality results to significantly more general models. Our theoretical results hint at some normalization tricks, which is shown numerically to have a positive impact on GNN generalization on synthetic and real data. Our proofs contain new concentration inequalities of independent interest.
Graph Neural Networks (GNNs) are gaining extensive attention for their application in graph data. However, the black-box nature of GNNs prevents users from understanding and trusting the models, thus hampering their applicability. Whereas explaining GNNs remains a challenge, most existing methods fall into approximation based and perturbation based approaches with suffer from faithfulness problems and unnatural artifacts, respectively. To tackle these problems, we propose DEGREE \degree to provide a faithful explanation for GNN predictions. By decomposing the information generation and aggregation mechanism of GNNs, DEGREE allows tracking the contributions of specific components of the input graph to the final prediction. Based on this, we further design a subgraph level interpretation algorithm to reveal complex interactions between graph nodes that are overlooked by previous methods. The efficiency of our algorithm can be further improved by utilizing GNN characteristics. Finally, we conduct quantitative and qualitative experiments on synthetic and real-world datasets to demonstrate the effectiveness of DEGREE on node classification and graph classification tasks.
We introduce Graph-Induced Sum-Product Networks (GSPNs), a new probabilistic framework for graph representation learning that can tractably answer probabilistic queries. Inspired by the computational trees induced by vertices in the context of message-passing neural networks, we build hierarchies of sum-product networks (SPNs) where the parameters of a parent SPN are learnable transformations of the a-posterior mixing probabilities of its children's sum units. Due to weight sharing and the tree-shaped computation graphs of GSPNs, we obtain the efficiency and efficacy of deep graph networks with the additional advantages of a probabilistic model. We show the model's competitiveness on scarce supervision scenarios, under missing data, and for graph classification in comparison to popular neural models. We complement the experiments with qualitative analyses on hyper-parameters and the model's ability to answer probabilistic queries.
Message passing neural networks (MPNNs) have been shown to suffer from the phenomenon of over-squashing that causes poor performance for tasks relying on long-range interactions. This can be largely attributed to message passing only occurring locally, over a node's immediate neighbours. Rewiring approaches attempting to make graphs 'more connected', and supposedly better suited to long-range tasks, often lose the inductive bias provided by distance on the graph since they make distant nodes communicate instantly at every layer. In this paper we propose a framework, applicable to any MPNN architecture, that performs a layer-dependent rewiring to ensure gradual densification of the graph. We also propose a delay mechanism that permits skip connections between nodes depending on the layer and their mutual distance. We validate our approach on several long-range tasks and show that it outperforms graph Transformers and multi-hop MPNNs.
In contrastive learning, the choice of ``view'' controls the information that the representation captures and influences the performance of the model. However, leading graph contrastive learning methods generally produce views via random corruption or learning, which could lead to the loss of essential information and alteration of semantic information. An anchor view that maintains the essential information of input graphs for contrastive learning has been hardly investigated. In this paper, based on the theory of graph information bottleneck, we deduce the definition of this anchor view; put differently, \textit{the anchor view with essential information of input graph is supposed to have the minimal structural uncertainty}. Furthermore, guided by structural entropy, we implement the anchor view, termed \textbf{SEGA}, for graph contrastive learning. We extensively validate the proposed anchor view on various benchmarks regarding graph classification under unsupervised, semi-supervised, and transfer learning and achieve significant performance boosts compared to the state-of-the-art methods.
We present the analysis of the topological graph descriptor Local Degree Profile (LDP), which forms a widely used structural baseline for graph classification. Our study focuses on model evaluation in the context of the recently developed fair evaluation framework, which defines rigorous routines for model selection and evaluation for graph classification, ensuring reproducibility and comparability of the results. Based on the obtained insights, we propose a new baseline algorithm called Local Topological Profile (LTP), which extends LDP by using additional centrality measures and local vertex descriptors. The new approach provides the results outperforming or very close to the latest GNNs for all datasets used. Specifically, state-of-the-art results were obtained for 4 out of 9 benchmark datasets. We also consider computational aspects of LDP-based feature extraction and model construction to propose practical improvements affecting execution speed and scalability. This allows for handling modern, large datasets and extends the portfolio of benchmarks used in graph representation learning. As the outcome of our work, we obtained LTP as a simple to understand, fast and scalable, still robust baseline, capable of outcompeting modern graph classification models such as Graph Isomorphism Network (GIN). We provide open-source implementation at \href{https://github.com/j-adamczyk/LTP}{GitHub}.
In this paper, we explore a novel model reusing task tailored for graph neural networks (GNNs), termed as "deep graph reprogramming". We strive to reprogram a pre-trained GNN, without amending raw node features nor model parameters, to handle a bunch of cross-level downstream tasks in various domains. To this end, we propose an innovative Data Reprogramming paradigm alongside a Model Reprogramming paradigm. The former one aims to address the challenge of diversified graph feature dimensions for various tasks on the input side, while the latter alleviates the dilemma of fixed per-task-per-model behavior on the model side. For data reprogramming, we specifically devise an elaborated Meta-FeatPadding method to deal with heterogeneous input dimensions, and also develop a transductive Edge-Slimming as well as an inductive Meta-GraPadding approach for diverse homogenous samples. Meanwhile, for model reprogramming, we propose a novel task-adaptive Reprogrammable-Aggregator, to endow the frozen model with larger expressive capacities in handling cross-domain tasks. Experiments on fourteen datasets across node/graph classification/regression, 3D object recognition, and distributed action recognition, demonstrate that the proposed methods yield gratifying results, on par with those by re-training from scratch.
This paper studies semi-supervised graph classification, a crucial task with a wide range of applications in social network analysis and bioinformatics. Recent works typically adopt graph neural networks to learn graph-level representations for classification, failing to explicitly leverage features derived from graph topology (e.g., paths). Moreover, when labeled data is scarce, these methods are far from satisfactory due to their insufficient topology exploration of unlabeled data. We address the challenge by proposing a novel semi-supervised framework called Twin Graph Neural Network (TGNN). To explore graph structural information from complementary views, our TGNN has a message passing module and a graph kernel module. To fully utilize unlabeled data, for each module, we calculate the similarity of each unlabeled graph to other labeled graphs in the memory bank and our consistency loss encourages consistency between two similarity distributions in different embedding spaces. The two twin modules collaborate with each other by exchanging instance similarity knowledge to fully explore the structure information of both labeled and unlabeled data. We evaluate our TGNN on various public datasets and show that it achieves strong performance.
Graph contrastive learning (GCL) has recently achieved substantial advancements. Existing GCL approaches compare two different ``views'' of the same graph in order to learn node/graph representations. The underlying assumption of these studies is that the graph augmentation strategy is capable of generating several different graph views such that the graph views are structurally different but semantically similar to the original graphs, and thus the ground-truth labels of the original and augmented graph/nodes can be regarded identical in contrastive learning. However, we observe that this assumption does not always hold. For instance, the deletion of a super-node within a social network can exert a substantial influence on the partitioning of communities for other nodes. Similarly, any perturbation to nodes or edges in a molecular graph will change the labels of the graph. Therefore, we believe that augmenting the graph, accompanied by an adaptation of the labels used for the contrastive loss, will facilitate the encoder to learn a better representation. Based on this idea, we propose ID-MixGCL, which allows the simultaneous interpolation of input nodes and corresponding identity labels to obtain soft-confidence samples, with a controllable degree of change, leading to the capture of fine-grained representations from self-supervised training on unlabeled graphs. Experimental results demonstrate that ID-MixGCL improves performance on graph classification and node classification tasks, as demonstrated by significant improvements on the Cora, IMDB-B, IMDB-M, and PROTEINS datasets compared to state-of-the-art techniques, by 3-29% absolute points.
Subgraph classification is an emerging field in graph representation learning where the task is to classify a group of nodes (i.e., a subgraph) within a graph. Subgraph classification has applications such as predicting the cellular function of a group of proteins or identifying rare diseases given a collection of phenotypes. Graph neural networks (GNNs) are the de facto solution for node, link, and graph-level tasks but fail to perform well on subgraph classification tasks. Even GNNs tailored for graph classification are not directly transferable to subgraph classification as they ignore the external topology of the subgraph, thus failing to capture how the subgraph is located within the larger graph. The current state-of-the-art models for subgraph classification address this shortcoming through either labeling tricks or multiple message-passing channels, both of which impose a computation burden and are not scalable to large graphs. To address the scalability issue while maintaining generalization, we propose Stochastic Subgraph Neighborhood Pooling (SSNP), which jointly aggregates the subgraph and its neighborhood (i.e., external topology) information without any computationally expensive operations such as labeling tricks. To improve scalability and generalization further, we also propose a simple data augmentation pre-processing step for SSNP that creates multiple sparse views of the subgraph neighborhood. We show that our model is more expressive than GNNs without labeling tricks. Our extensive experiments demonstrate that our models outperform current state-of-the-art methods (with a margin of up to 2%) while being up to 3X faster in training.
Advanced deep learning methods, especially graph neural networks (GNNs), are increasingly expected to learn from brain functional network data and predict brain disorders. In this paper, we proposed a novel Transformer and snowball encoding networks (TSEN) for brain functional network classification, which introduced Transformer architecture with graph snowball connection into GNNs for learning whole-graph representation. TSEN combined graph snowball connection with graph Transformer by snowball encoding layers, which enhanced the power to capture multi-scale information and global patterns of brain functional networks. TSEN also introduced snowball graph convolution as position embedding in Transformer structure, which was a simple yet effective method for capturing local patterns naturally. We evaluated the proposed model by two large-scale brain functional network datasets from autism spectrum disorder and major depressive disorder respectively, and the results demonstrated that TSEN outperformed the state-of-the-art GNN models and the graph-transformer based GNN models.
Graph neural networks (GNNs) have demonstrated a significant success in various graph learning tasks, from graph classification to anomaly detection. There recently has emerged a number of approaches adopting a graph pooling operation within GNNs, with a goal to preserve graph attributive and structural features during the graph representation learning. However, most existing graph pooling operations suffer from the limitations of relying on node-wise neighbor weighting and embedding, which leads to insufficient encoding of rich topological structures and node attributes exhibited by real-world networks. By invoking the machinery of persistent homology and the concept of landmarks, we propose a novel topological pooling layer and witness complex-based topological embedding mechanism that allow us to systematically integrate hidden topological information at both local and global levels. Specifically, we design new learnable local and global topological representations Wit-TopoPool which allow us to simultaneously extract rich discriminative topological information from graphs. Experiments on 11 diverse benchmark datasets against 18 baseline models in conjunction with graph classification tasks indicate that Wit-TopoPool significantly outperforms all competitors across all datasets.
Graph machine learning (GML) has made great progress in node classification, link prediction, graph classification and so on. However, graphs in reality are often structurally imbalanced, that is, only a few hub nodes have a denser local structure and higher influence. The imbalance may compromise the robustness of existing GML models, especially in learning tail nodes. This paper proposes a selective graph augmentation method (SAug) to solve this problem. Firstly, a Pagerank-based sampling strategy is designed to identify hub nodes and tail nodes in the graph. Secondly, a selective augmentation strategy is proposed, which drops the noisy neighbors of hub nodes on one side, and discovers the latent neighbors and generates pseudo neighbors for tail nodes on the other side. It can also alleviate the structural imbalance between two types of nodes. Finally, a GNN model will be retrained on the augmented graph. Extensive experiments demonstrate that SAug can significantly improve the backbone GNNs and achieve superior performance to its competitors of graph augmentation methods and hub/tail aware methods.
Managing the threat posed by malware requires accurate detection and classification techniques. Traditional detection strategies, such as signature scanning, rely on manual analysis of malware to extract relevant features, which is labor intensive and requires expert knowledge. Function call graphs consist of a set of program functions and their inter-procedural calls, providing a rich source of information that can be leveraged to classify malware without the labor intensive feature extraction step of traditional techniques. In this research, we treat malware classification as a graph classification problem. Based on Local Degree Profile features, we train a wide range of Graph Neural Network (GNN) architectures to generate embeddings which we then classify. We find that our best GNN models outperform previous comparable research involving the well-known MalNet-Tiny Android malware dataset. In addition, our GNN models do not suffer from the overfitting issues that commonly afflict non-GNN techniques, although GNN models require longer training times.
Graph transformers have emerged as a promising architecture for a variety of graph learning and representation tasks. Despite their successes, though, it remains challenging to scale graph transformers to large graphs while maintaining accuracy competitive with message-passing networks. In this paper, we introduce Exphormer, a framework for building powerful and scalable graph transformers. Exphormer consists of a sparse attention mechanism based on two mechanisms: virtual global nodes and expander graphs, whose mathematical characteristics, such as spectral expansion, pseduorandomness, and sparsity, yield graph transformers with complexity only linear in the size of the graph, while allowing us to prove desirable theoretical properties of the resulting transformer models. We show that incorporating Exphormer into the recently-proposed GraphGPS framework produces models with competitive empirical results on a wide variety of graph datasets, including state-of-the-art results on three datasets. We also show that Exphormer can scale to datasets on larger graphs than shown in previous graph transformer architectures. Code can be found at \url{https://github.com/hamed1375/Exphormer}.
Graph Neural networks (GNNs) have recently become a powerful technique for many graph-related tasks including graph classification. Current GNN models apply different graph pooling methods that reduce the number of nodes and edges to learn the higher-order structure of the graph in a hierarchical way. All these methods primarily rely on the one-hop neighborhood. However, they do not consider the higher- order structure of the graph. In this work, we propose a multi-channel Motif-based Graph Pooling method named (MPool) captures the higher-order graph structure with motif and local and global graph structure with a combination of selection and clustering-based pooling operations. As the first channel, we develop node selection-based graph pooling by designing a node ranking model considering the motif adjacency of nodes. As the second channel, we develop cluster-based graph pooling by designing a spectral clustering model using motif adjacency. As the final layer, the result of each channel is aggregated into the final graph representation. We perform extensive experiments on eight benchmark datasets and show that our proposed method shows better accuracy than the baseline methods for graph classification tasks.
In this work, we develop an Aligned Entropic Reproducing Kernel (AERK) for graph classification. We commence by performing the Continuous-time Quantum Walk (CTQW) on each graph structure, and computing the Averaged Mixing Matrix (AMM) to describe how the CTQW visit all vertices from a starting vertex. More specifically, we show how this AMM matrix allows us to compute a quantum Shannon entropy for each vertex of a graph. For pairwise graphs, the proposed AERK kernel is defined by computing a reproducing kernel based similarity between the quantum Shannon entropies of their each pair of aligned vertices. The analysis of theoretical properties reveals that the proposed AERK kernel cannot only address the shortcoming of neglecting the structural correspondence information between graphs arising in most existing R-convolution graph kernels, but also overcome the problem of neglecting the structural differences between pairs of aligned vertices arising in existing vertex-based matching kernels. Moreover, unlike existing classical graph kernels that only focus on the global or local structural information of graphs, the proposed AERK kernel can simultaneously capture both global and local structural information through the quantum Shannon entropies, reflecting more precise kernel based similarity measures between pairs of graphs. The above theoretical properties explain the effectiveness of the proposed kernel. The experimental evaluation on standard graph datasets demonstrates that the proposed AERK kernel is able to outperform state-of-the-art graph kernels for graph classification tasks.
Two main families of node feature augmentation schemes have been explored for enhancing GNNs: random features and spectral positional encoding. Surprisingly, however, there is still no clear understanding of the relation between these two augmentation schemes. Here we propose a novel family of positional encoding schemes which draws a link between the above two approaches and improves over both. The new approach, named Random Feature Propagation (RFP), is inspired by the power iteration method and its generalizations. It concatenates several intermediate steps of an iterative algorithm for computing the dominant eigenvectors of a propagation matrix, starting from random node features. Notably, these propagation steps are based on graph-dependent propagation operators that can be either predefined or learned. We explore the theoretical and empirical benefits of RFP. First, we provide theoretical justifications for using random features, for incorporating early propagation steps, and for using multiple random initializations. Then, we empirically demonstrate that RFP significantly outperforms both spectral PE and random features in multiple node classification and graph classification benchmarks.