The problem of out-of-distribution detection for graph classification is far from being solved. The existing models tend to be overconfident about OOD examples or completely ignore the detection task. In this work, we consider this problem from the uncertainty estimation perspective and perform the comparison of several recently proposed methods. In our experiment, we find that there is no universal approach for OOD detection, and it is important to consider both graph representations and predictive categorical distribution.
We present a novel graph neural network we call AgentNet, which is designed specifically for graph-level tasks. AgentNet is inspired by sublinear algorithms, featuring a computational complexity that is independent of the graph size. The architecture of AgentNet differs fundamentally from the architectures of traditional graph neural networks. In AgentNet, some trained \textit{neural agents} intelligently walk the graph, and then collectively decide on the output. We provide an extensive theoretical analysis of AgentNet: We show that the agents can learn to systematically explore their neighborhood and that AgentNet can distinguish some structures that are even indistinguishable by 2-WL. Moreover, AgentNet is able to separate any two graphs which are sufficiently different in terms of subgraphs. We confirm these theoretical results with synthetic experiments on hard-to-distinguish graphs and real-world graph classification tasks. In both cases, we compare favorably not only to standard GNNs but also to computationally more expensive GNN extensions.
The step function is one of the simplest and most natural activation functions for deep neural networks (DNNs). As it counts 1 for positive variables and 0 for others, its intrinsic characteristics (e.g., discontinuity and no viable information of subgradients) impede its development for several decades. Even if there is an impressive body of work on designing DNNs with continuous activation functions that can be deemed as surrogates of the step function, it is still in the possession of some advantageous properties, such as complete robustness to outliers and being capable of attaining the best learning-theoretic guarantee of predictive accuracy. Hence, in this paper, we aim to train DNNs with the step function used as an activation function (dubbed as 0/1 DNNs). We first reformulate 0/1 DNNs as an unconstrained optimization problem and then solve it by a block coordinate descend (BCD) method. Moreover, we acquire closed-form solutions for sub-problems of BCD as well as its convergence properties. Furthermore, we also integrate $\ell_{2,0}$-regularization into 0/1 DNN to accelerate the training process and compress the network scale. As a result, the proposed algorithm has a high performance on classifying MNIST and Fashion-MNIST datasets. As a result, the proposed algorithm has a desirable performance on classifying MNIST, FashionMNIST, Cifar10, and Cifar100 datasets.
With the development of graph kernels and graph representation learning, many superior methods have been proposed to handle scalability and oversmoothing issues on graph structure learning. However, most of those strategies are designed based on practical experience rather than theoretical analysis. In this paper, we use a particular dummy node connecting to all existing vertices without affecting original vertex and edge properties. We further prove that such the dummy node can help build an efficient monomorphic edge-to-vertex transform and an epimorphic inverse to recover the original graph back. It also indicates that adding dummy nodes can preserve local and global structures for better graph representation learning. We extend graph kernels and graph neural networks with dummy nodes and conduct experiments on graph classification and subgraph isomorphism matching tasks. Empirical results demonstrate that taking graphs with dummy nodes as input significantly boosts graph structure learning, and using their edge-to-vertex graphs can also achieve similar results. We also discuss the gain of expressive power from the dummy in neural networks.
Graph Neural Networks (GNNs) that are based on the message passing (MP) paradigm generally exchange information between 1-hop neighbors to build node representations at each layer. In principle, such networks are not able to capture long-range interactions (LRI) that may be desired or necessary for learning a given task on graphs. Recently, there has been an increasing interest in development of Transformer-based methods for graphs that can consider full node connectivity beyond the original sparse structure, thus enabling the modeling of LRI. However, MP-GNNs that simply rely on 1-hop message passing often fare better in several existing graph benchmarks when combined with positional feature representations, among other innovations, hence limiting the perceived utility and ranking of Transformer-like architectures. Here, we present the Long Range Graph Benchmark (LRGB) with 5 graph learning datasets: PascalVOC-SP, COCO-SP, PCQM-Contact, Peptides-func and Peptides-struct that arguably require LRI reasoning to achieve strong performance in a given task. We benchmark both baseline GNNs and Graph Transformer networks to verify that the models which capture long-range dependencies perform significantly better on these tasks. Therefore, these datasets are suitable for benchmarking and exploration of MP-GNNs and Graph Transformer architectures that are intended to capture LRI.
Graph Neural Networks (GNNs) have been shown to achieve competitive results to tackle graph-related tasks, such as node and graph classification, link prediction and node and graph clustering in a variety of domains. Most GNNs use a message passing framework and hence are called MPNNs. Despite their promising results, MPNNs have been reported to suffer from over-smoothing, over-squashing and under-reaching. Graph rewiring and graph pooling have been proposed in the literature as solutions to address these limitations. However, most state-of-the-art graph rewiring methods fail to preserve the global topology of the graph, are neither differentiable nor inductive, and require the tuning of hyper-parameters. In this paper, we propose DiffWire, a novel framework for graph rewiring in MPNNs that is principled, fully differentiable and parameter-free by leveraging the Lov\'asz bound. The proposed approach provides a unified theory for graph rewiring by proposing two new, complementary layers in MPNNs: CT-Layer, a layer that learns the commute times and uses them as a relevance function for edge re-weighting; and GAP-Layer, a layer to optimize the spectral gap, depending on the nature of the network and the task at hand. We empirically validate the value of each of these layers separately with benchmark datasets for graph classification. We also perform preliminary studies on the use of CT-Layer for homophilic and heterophilic node classification tasks. DiffWire brings together the learnability of commute times to related definitions of curvature, opening the door to creating more expressive MPNNs.
Node classification and graph classification are two graph learning problems that predict the class label of a node and the class label of a graph respectively. A node of a graph usually represents a real-world entity, e.g., a user in a social network, or a document in a document citation network. In this work, we consider a more challenging but practically useful setting, in which a node itself is a graph instance. This leads to a hierarchical graph perspective which arises in many domains such as social network, biological network and document collection. We study the node classification problem in the hierarchical graph where a 'node' is a graph instance. As labels are usually limited, we design a novel semi-supervised solution named SEAL-CI. SEAL-CI adopts an iterative framework that takes turns to update two modules, one working at the graph instance level and the other at the hierarchical graph level. To enforce a consistency among different levels of hierarchical graph, we propose the Hierarchical Graph Mutual Information (HGMI) and further present a way to compute HGMI with theoretical guarantee. We demonstrate the effectiveness of this hierarchical graph modeling and the proposed SEAL-CI method on text and social network data.
Output reachability and adversarial robustness are among the most relevant safety properties of neural networks. We show that in the context of Message Passing Neural Networks (MPNN), a common Graph Neural Network (GNN) model, formal verification is impossible. In particular, we show that output reachability of graph-classifier MPNN, working over graphs of unbounded size, non-trivial degree and sufficiently expressive node labels, cannot be verified formally: there is no algorithm that answers correctly (with yes or no), given an MPNN, whether there exists some valid input to the MPNN such that the corresponding output satisfies a given specification. However, we also show that output reachability and adversarial robustness of node-classifier MPNN can be verified formally when a limit on the degree of input graphs is given a priori. We discuss the implications of these results, for the purpose of obtaining a complete picture of the principle possibility to formally verify GNN, depending on the expressiveness of the involved GNN models and input-output specifications.
Graph Neural Networks (GNNs) have been widely applied to various fields for learning over graph-structured data. They have shown significant improvements over traditional heuristic methods in various tasks such as node classification and graph classification. However, since GNNs heavily rely on smoothed node features rather than graph structure, they often show poor performance than simple heuristic methods in link prediction where the structural information, e.g., overlapped neighborhoods, degrees, and shortest paths, is crucial. To address this limitation, we propose Neighborhood Overlap-aware Graph Neural Networks (Neo-GNNs) that learn useful structural features from an adjacency matrix and estimate overlapped neighborhoods for link prediction. Our Neo-GNNs generalize neighborhood overlap-based heuristic methods and handle overlapped multi-hop neighborhoods. Our extensive experiments on Open Graph Benchmark datasets (OGB) demonstrate that Neo-GNNs consistently achieve state-of-the-art performance in link prediction. Our code is publicly available at https://github.com/seongjunyun/Neo_GNNs.
Many modern deep-learning techniques do not work without enormous datasets. At the same time, several fields demand methods working in scarcity of data. This problem is even more complex when the samples have varying structures, as in the case of graphs. Graph representation learning techniques have recently proven successful in a variety of domains. Nevertheless, the employed architectures perform miserably when faced with data scarcity. On the other hand, few-shot learning allows employing modern deep learning models in scarce data regimes without waiving their effectiveness. In this work, we tackle the problem of few-shot graph classification, showing that equipping a simple distance metric learning baseline with a state-of-the-art graph embedder allows to obtain competitive results on the task. While the simplicity of the architecture is enough to outperform more complex ones, it also allows straightforward additions. To this end, we show that additional improvements may be obtained by encouraging a task-conditioned embedding space. Finally, we propose a MixUp-based online data augmentation technique acting in the latent space and show its effectiveness on the task.
In deep neural networks, better results can often be obtained by increasing the complexity of previously developed basic models. However, it is unclear whether there is a way to boost performance by decreasing the complexity of such models. Intuitively, given a problem, a simpler data structure comes with a simpler algorithm. Here, we investigate the feasibility of improving graph classification performance while simplifying the learning process. Inspired by structural entropy on graphs, we transform the data sample from graphs to coding trees, which is a simpler but essential structure for graph data. Furthermore, we propose a novel message passing scheme, termed hierarchical reporting, in which features are transferred from leaf nodes to root nodes by following the hierarchical structure of coding trees. We then present a tree kernel and a convolutional network to implement our scheme for graph classification. With the designed message passing scheme, the tree kernel and convolutional network have a lower runtime complexity of $O(n)$ than Weisfeiler-Lehman subtree kernel and other graph neural networks of at least $O(hm)$. We empirically validate our methods with several graph classification benchmarks and demonstrate that they achieve better performance and lower computational consumption than competing approaches.
Frequent and structurally related subgraphs, also known as network motifs, are valuable features of many graph datasets. However, the high computational complexity of identifying motif sets in arbitrary datasets (motif mining) has limited their use in many real-world datasets. By automatically leveraging statistical properties of datasets, machine learning approaches have shown promise in several tasks with combinatorial complexity and are therefore a promising candidate for network motif mining. In this work we seek to facilitate the development of machine learning approaches aimed at motif mining. We propose a formulation of the motif mining problem as a node labelling task. In addition, we build benchmark datasets and evaluation metrics which test the ability of models to capture different aspects of motif discovery such as motif number, size, topology, and scarcity. Next, we propose MotiFiesta, a first attempt at solving this problem in a fully differentiable manner with promising results on challenging baselines. Finally, we demonstrate through MotiFiesta that this learning setting can be applied simultaneously to general-purpose data mining and interpretable feature extraction for graph classification tasks.
Most graph neural network models rely on a particular message passing paradigm, where the idea is to iteratively propagate node representations of a graph to each node in the direct neighborhood. While very prominent, this paradigm leads to information propagation bottlenecks, as information is repeatedly compressed at intermediary node representations, which causes loss of information, making it practically impossible to gather meaningful signals from distant nodes. To address this, we propose shortest path message passing neural networks, where the node representations of a graph are propagated to each node in the shortest path neighborhoods. In this setting, nodes can directly communicate between each other even if they are not neighbors, breaking the information bottleneck and hence leading to more adequately learned representations. Our framework generalizes message passing neural networks, resulting in a class of more expressive models, including some recent state-of-the-art models. We verify the capacity of a basic model of this framework on dedicated synthetic experiments, and on real-world graph classification and regression benchmarks, and obtain state-of-the art results.
Graph kernels are conventional methods for computing graph similarities. However, the existing R-convolution graph kernels cannot resolve both of the two challenges: 1) Comparing graphs at multiple different scales, and 2) Considering the distributions of substructures when computing the kernel matrix. These two challenges limit their performances. To mitigate both of the two challenges, we propose a novel graph kernel called the Multi-scale Wasserstein Shortest-Path graph kernel (MWSP), at the heart of which is the multi-scale shortest-path node feature map, of which each element denotes the number of occurrences of the shortest path around a node. The shortest path is represented by the concatenation of all the labels of nodes in it. Since the shortest-path node feature map can only compare graphs at local scales, we incorporate into it the multiple different scales of the graph structure, which are captured by the truncated BFS trees of different depths rooted at each node in a graph. We use the Wasserstein distance to compute the similarity between the multi-scale shortest-path node feature maps of two graphs, considering the distributions of shortest paths. We empirically validate MWSP on various benchmark graph datasets and demonstrate that it achieves state-of-the-art performance on most datasets.
Current Graph Neural Networks (GNN) architectures generally rely on two important components: node features embedding through message passing, and aggregation with a specialized form of pooling. The structural (or topological) information is implicitly taken into account in these two steps. We propose in this work a novel point of view, which places distances to some learnable graph templates at the core of the graph representation. This distance embedding is constructed thanks to an optimal transport distance: the Fused Gromov-Wasserstein (FGW) distance, which encodes simultaneously feature and structure dissimilarities by solving a soft graph-matching problem. We postulate that the vector of FGW distances to a set of template graphs has a strong discriminative power, which is then fed to a non-linear classifier for final predictions. Distance embedding can be seen as a new layer, and can leverage on existing message passing techniques to promote sensible feature representations. Interestingly enough, in our work the optimal set of template graphs is also learnt in an end-to-end fashion by differentiating through this layer. After describing the corresponding learning procedure, we empirically validate our claim on several synthetic and real life graph classification datasets, where our method is competitive or surpasses kernel and GNN state-of-the-art approaches. We complete our experiments by an ablation study and a sensitivity analysis to parameters.
Graph neural architecture search has sparked much attention as Graph Neural Networks (GNNs) have shown powerful reasoning capability in many relational tasks. However, the currently used graph search space overemphasizes learning node features and neglects mining hierarchical relational information. Moreover, due to diverse mechanisms in the message passing, the graph search space is much larger than that of CNNs. This hinders the straightforward application of classical search strategies for exploring complicated graph search space. We propose Automatic Relation-aware Graph Network Proliferation (ARGNP) for efficiently searching GNNs with a relation-guided message passing mechanism. Specifically, we first devise a novel dual relation-aware graph search space that comprises both node and relation learning operations. These operations can extract hierarchical node/relational information and provide anisotropic guidance for message passing on a graph. Second, analogous to cell proliferation, we design a network proliferation search paradigm to progressively determine the GNN architectures by iteratively performing network division and differentiation. The experiments on six datasets for four graph learning tasks demonstrate that GNNs produced by our method are superior to the current state-of-the-art hand-crafted and search-based GNNs. Codes are available at https://github.com/phython96/ARGNP.
Graph similarity learning refers to calculating the similarity score between two graphs, which is required in many realistic applications, such as visual tracking, graph classification, and collaborative filtering. As most of the existing graph neural networks yield effective graph representations of a single graph, little effort has been made for jointly learning two graph representations and calculating their similarity score. In addition, existing unsupervised graph similarity learning methods are mainly clustering-based, which ignores the valuable information embodied in graph pairs. To this end, we propose a contrastive graph matching network (CGMN) for self-supervised graph similarity learning in order to calculate the similarity between any two input graph objects. Specifically, we generate two augmented views for each graph in a pair respectively. Then, we employ two strategies, namely cross-view interaction and cross-graph interaction, for effective node representation learning. The former is resorted to strengthen the consistency of node representations in two views. The latter is utilized to identify node differences between different graphs. Finally, we transform node representations into graph-level representations via pooling operations for graph similarity computation. We have evaluated CGMN on eight real-world datasets, and the experiment results show that the proposed new approach is superior to the state-of-the-art methods in graph similarity learning downstream tasks.
We propose a recipe on how to build a general, powerful, scalable (GPS) graph Transformer with linear complexity and state-of-the-art results on a diverse set of benchmarks. Graph Transformers (GTs) have gained popularity in the field of graph representation learning with a variety of recent publications but they lack a common foundation about what constitutes a good positional or structural encoding, and what differentiates them. In this paper, we summarize the different types of encodings with a clearer definition and categorize them as being $\textit{local}$, $\textit{global}$ or $\textit{relative}$. The prior GTs are constrained to small graphs with a few hundred nodes, here we propose the first architecture with a complexity linear in the number of nodes and edges $O(N+E)$ by decoupling the local real-edge aggregation from the fully-connected Transformer. We argue that this decoupling does not negatively affect the expressivity, with our architecture being a universal function approximator on graphs. Our GPS recipe consists of choosing 3 main ingredients: (i) positional/structural encoding, (ii) local message-passing mechanism, and (iii) global attention mechanism. We provide a modular framework $\textit{GraphGPS}$ that supports multiple types of encodings and that provides efficiency and scalability both in small and large graphs. We test our architecture on 16 benchmarks and show highly competitive results in all of them, show-casing the empirical benefits gained by the modularity and the combination of different strategies.
This paper studies asynchronous message passing (AMP), a new paradigm for applying neural network based learning to graphs. Existing graph neural networks use the synchronous distributed computing model and aggregate their neighbors in each round, which causes problems such as oversmoothing and limits their expressiveness. On the other hand, AMP is based on the asynchronous model, where nodes react to messages of their neighbors individually. We prove that (i) AMP can simulate synchronous GNNs and that (ii) AMP can theoretically distinguish any pair of graphs. We experimentally validate AMP's expressiveness. Further, we show that AMP might be better suited to propagate messages over large distances in graphs and performs well on several graph classification benchmarks.
Graph Neural Networks (GNNs) are attracting growing attention due to their effectiveness and flexibility in modeling a variety of graph-structured data. Exiting GNN architectures usually adopt simple pooling operations (eg. sum, average, max) when aggregating messages from a local neighborhood for updating node representation or pooling node representations from the entire graph to compute the graph representation. Though simple and effective, these linear operations do not model high-order non-linear interactions among nodes. We propose the Tensorized Graph Neural Network (tGNN), a highly expressive GNN architecture relying on tensor decomposition to model high-order non-linear node interactions. tGNN leverages the symmetric CP decomposition to efficiently parameterize permutation-invariant multilinear maps for modeling node interactions. Theoretical and empirical analysis on both node and graph classification tasks show the superiority of tGNN over competitive baselines. In particular, tGNN achieves the most solid results on two OGB node classification datasets and one OGB graph classification dataset.