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1. GRAND++: Graph Neural Diffusion with A Source Term

   Thorpe, Matthew; Xia, Hedi; Nguyen, Tan; Strohmer, Thomas; Bertozzi, Andrea; Osher, Stanley; Wang, Bao. (January 2022, International Conference on Learning Representations)

   We propose GRAph Neural Diffusion with a source term (GRAND++) for graph deep learning with a limited number of labeled nodes, i.e., low-labeling rate. GRAND++ is a class of continuous-depth graph deep learning architectures whose theoretical underpinning is the diffusion process on graphs with a source term. The source term guarantees two interesting theoretical properties of GRAND++: (i) the representation of graph nodes, under the dynamics of GRAND++, will not converge to a constant vector over all nodes even as the time goes to infinity, which mitigates the over-smoothing issue of graph neural networks and enables graph learning in very deep architectures. (ii) GRAND++ can provide accurate classification even when the model is trained with a very limited number of labeled training data. We experimentally verify the above two advantages on various graph deep learning benchmark tasks, showing a significant improvement over many existing graph neural networks. 

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2. Understanding Graph Neural Networks with Generalized Geometric Scattering Transforms

   https://doi.org/10.1137/21M1465056  

   Perlmutter, Michael; Tong, Alexander; Gao, Feng; Wolf, Guy; Hirn, Matthew (December 2023, SIAM Journal on Mathematics of Data Science)

   The scattering transform is a multilayered wavelet-based architecture that acts as a model of convolutional neural networks. Recently, several works have generalized the scattering transform to graph-structured data. Our work builds on these constructions by introducing windowed and nonwindowed geometric scattering transforms for graphs based on two very general classes wavelets, which are in most cases based on asymmetric matrices. We show that these transforms have many of the same theoretical guarantees as their symmetric counterparts. As a result, the proposed construction unifies and extends known theoretical results for many of the existing graph scattering architectures. Therefore, it helps bridge the gap between geometric scattering and other graph neural networks by introducing a large family of networks with provable stability and invariance guarantees. These results lay the groundwork for future deep learning architectures for graph-structured data that have learned filters and also provably have desirable theoretical properties. 

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3. Active Heterogeneous Graph Neural Networks with Per-step Meta-Q-Learning

   https://doi.org/10.1109/ICDM54844.2022.00176  

   Zhang, Yuheng; Xia, Yinglong; Zhu, Yan; Chi, Yuejie; Ying, Lei; Tong, Hanghang (November 2022, 2022 IEEE International Conference on Data Mining (ICDM))

   Recent years have witnessed the superior performance of heterogeneous graph neural networks (HGNNs) in dealing with heterogeneous information networks (HINs). Nonetheless, the success of HGNNs often depends on the availability of sufficient labeled training data, which can be very expensive to obtain in real scenarios. Active learning provides an effective solution to tackle the data scarcity challenge. For the vast majority of the existing work regarding active learning on graphs, they mainly focus on homogeneous graphs, and thus fall in short or even become inapplicable on HINs. In this paper, we study the active learning problem with HGNNs and propose a novel meta-reinforced active learning framework MetRA. Previous reinforced active learning algorithms train the policy network on labeled source graphs and directly transfer the policy to the target graph without any adaptation. To better exploit the information from the target graph in the adaptation phase, we propose a novel policy transfer algorithm based on meta-Q-learning termed per-step MQL. Empirical evaluations on HINs demonstrate the effectiveness of our proposed framework. The improvement over the best baseline is up to 7% in Micro-F1. 

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4. 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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5. Task-Adaptive Few-shot Node Classification

   https://doi.org/10.1145/3534678.3539265  

   Wang, Song; Ding, Kaize; Zhang, Chuxu; Chen, Chen; Li, Jundong (August 2022, Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining)

   Node classification is of great importance among various graph mining tasks. In practice, real-world graphs generally follow the long-tail distribution, where a large number of classes only consist of limited labeled nodes. Although Graph Neural Networks (GNNs) have achieved significant improvements in node classification, their performance decreases substantially in such a few-shot scenario. The main reason can be attributed to the vast generalization gap between meta-training and meta-test due to the task variance caused by different node/class distributions in meta-tasks (i.e., node-level and class-level variance). Therefore, to effectively alleviate the impact of task variance, we propose a task-adaptive node classification framework under the few-shot learning setting. Specifically, we first accumulate meta-knowledge across classes with abundant labeled nodes. Then we transfer such knowledge to the classes with limited labeled nodes via our proposed task-adaptive modules. In particular, to accommodate the different node/class distributions among meta-tasks, we propose three essential modules to perform node-level, class-level, and task-level adaptations in each meta-task, respectively. In this way, our framework can conduct adaptations to different meta-tasks and thus advance the model generalization performance on meta-test tasks. Extensive experiments on four prevalent node classification datasets demonstrate the superiority of our framework over the state-of-the-art baselines. Our code is provided at https://github.com/SongW-SW/TENT https://github.com/SongW-SW/TENT. 

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