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1. Identity-Aware Graph Neural Networks

   You, Jiaxuan; Gomes-Selman, Jonathan; Ying, Rex; Leskovec, Jure. (January 2021, Conference on Artificial Intelligence (AAAI))

   null (Ed.)

   Message passing Graph Neural Networks (GNNs) provide a powerful modeling framework for relational data. However, the expressive power of existing GNNs is upper-bounded by the 1-Weisfeiler-Lehman (1-WL) graph isomorphism test, which means GNNs that are not able to predict node clustering coefficients and shortest path distances, and cannot differentiate between different d regular graphs. Here we develop a class of message passing GNNs, named Identity-aware Graph Neural Networks (ID-GNNs), with greater expressive power than the 1-WL test. ID-GNN offers a minimal but powerful solution to limitations of existing GNNs. ID-GNN extends existing GNN architectures by inductively considering nodes’ identities during message passing. To embed a given node, IDGNN first extracts the ego network centered at the node, then conducts rounds of heterogeneous message passing, where different sets of parameters are applied to the center node than to other surrounding nodes in the ego network. We further propose a simplified but faster version of ID-GNN that injects node identity information as augmented node features. Altogether, both versions of ID GNN represent general extensions of message passing GNNs, where experiments show that transforming existing GNNs to ID-GNNs yields on average 40% accuracy improvement on challenging node, edge, and graph property prediction tasks; 3% accuracy improvement on node and graph classification benchmarks; and 15% ROC AUC improvement on real-world link prediction tasks. Additionally, ID-GNNs demonstrate improved or comparable performance over other task-specific graph networks. 

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2. Identity-aware Graph Neural Networks

   You, Jiaxuan; Gomes-Selman, Jonathan; Ying, Rex; Leskovec, Jure (January 2021, Proceedings of the AAAI Conference on Artificial Intelligence)

   null (Ed.)

   Message passing Graph Neural Networks (GNNs) provide a powerful modeling framework for relational data. However, the expressive power of existing GNNs is upper-bounded by the 1-Weisfeiler-Lehman (1-WL) graph isomorphism test, which means GNNs that are not able to predict node clustering coefficients and shortest path distances, and cannot differentiate between different d-regular graphs. Here we develop a class of message passing GNNs, named Identity-aware Graph Neural Networks (ID-GNNs), with greater expressive power than the 1-WL test. ID-GNN offers a minimal but powerful solution to limitations of existing GNNs. ID-GNN extends existing GNN architectures by inductively considering nodes’ identities during message passing. To embed a given node, IDGNN first extracts the ego network centered at the node, then conducts rounds of heterogeneous message passing, where different sets of parameters are applied to the center node than to other surrounding nodes in the ego network. We further propose a simplified but faster version of ID-GNN that injects node identity information as augmented node features. Altogether, both versions of ID-GNN represent general extensions of message passing GNNs, where experiments show that transforming existing GNNs to ID-GNNs yields on average 40% accuracy improvement on challenging node, edge, and graph property prediction tasks; 3% accuracy improvement on node and graph classification benchmarks; and 15% ROC AUC improvement on real-world link prediction tasks. Additionally, ID-GNNs demonstrate improved or comparable performance over other task-specific graph networks. 

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3. Half-Hop: A graph upsampling approach for slowing down message passing

   Mehdi Azabou, Venkataramana Ganesh (January 2023, Proceedings of the 40th International Conference on Machine Learning)

   Message passing neural networks have shown a lot of success on graph-structured data. However, there are many instances where message passing can lead to over-smoothing or fail when neighboring nodes belong to different classes. In this work, we introduce a simple yet general framework for improving learning in message passing neural networks. Our approach essentially upsamples edges in the original graph by adding “slow nodes” at each edge that can mediate com- munication between a source and a target node. Our method only modifies the input graph, making it plug-and-play and easy to use with existing models. To understand the benefits of slowing down message passing, we provide theoretical and empirical analyses. We report results on several supervised and self-supervised benchmarks, and show improvements across the board, notably in heterophilic conditions where adjacent nodes are more likely to have different labels. Finally, we show how our approach can be used to generate augmentations for self-supervised learning, where slow nodes are randomly introduced into different edges in the graph to generate multi-scale views with variable path lengths. 

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4. Message passing on networks with loops

   https://doi.org/10.1073/pnas.1914893116  

   Cantwell, George T.; Newman, M. E. (November 2019, Proceedings of the National Academy of Sciences)

   Message passing is a fundamental technique for performing calculations on networks and graphs with applications in physics, computer science, statistics, and machine learning, including Bayesian inference, spin models, satisfiability, graph partitioning, network epidemiology, and the calculation of matrix eigenvalues. Despite its wide use, however, it has long been recognized that the method has a fundamental flaw: It works poorly on networks that contain short loops. Loops introduce correlations that can cause the method to give inaccurate answers or to fail completely in the worst cases. Unfortunately, most real-world networks contain many short loops, which limits the usefulness of the message-passing approach. In this paper we demonstrate how to rectify this shortcoming and create message-passing methods that work on any network. We give 2 example applications, one to the percolation properties of networks and the other to the calculation of the spectra of sparse matrices. 

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5. Belief propagation for networks with loops

   https://doi.org/10.1126/sciadv.abf1211  

   Kirkley, Alec; Cantwell, George T.; Newman, M. E. (April 2021, Science Advances)

   null (Ed.)

   Belief propagation is a widely used message passing method for the solution of probabilistic models on networks such as epidemic models, spin models, and Bayesian graphical models, but it suffers from the serious shortcoming that it works poorly in the common case of networks that contain short loops. Here, we provide a solution to this long-standing problem, deriving a belief propagation method that allows for fast calculation of probability distributions in systems with short loops, potentially with high density, as well as giving expressions for the entropy and partition function, which are notoriously difficult quantities to compute. Using the Ising model as an example, we show that our approach gives excellent results on both real and synthetic networks, improving substantially on standard message passing methods. We also discuss potential applications of our method to a variety of other problems. 

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