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1. When Do GNNs Work: Understanding and Improving Neighborhood Aggregation

   https://doi.org/10.24963/ijcai.2020/181  

   Xie, Yiqing; Li, Sha; Yang, Carl; Wong, Raymond Chi-Wing; Han, Jiawei (July 2020, IJCAI'20: Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence, {IJCAI} 2020)

   null (Ed.)

   Graph Neural Networks (GNNs) have been shown to be powerful in a wide range of graph-related tasks. While there exists various GNN models, a critical common ingredient is neighborhood aggregation, where the embedding of each node is updated by referring to the embedding of its neighbors. This paper aims to provide a better understanding of this mechanisms by asking the following question: Is neighborhood aggregation always necessary and beneficial? In short, the answer is no. We carve out two conditions under which neighborhood aggregation is not helpful: (1) when a node's neighbors are highly dissimilar and (2) when a node's embedding is already similar with that of its neighbors. We propose novel metrics that quantitatively measure these two circumstances and integrate them into an Adaptive-layer module. Our experiments show that allowing for node-specific aggregation degrees have significant advantage over current GNNs. 

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2. A Model-Agnostic Graph Neural Network for Integrating Local and Global Information

   https://doi.org/10.1080/01621459.2024.2404668  

   Zhou, Wenzhuo; Qu, Annie; Cooper, Keiland W; Fortin, Norbert; Shahbaba, Babak (November 2024, Journal of the American Statistical Association)

   Graph Neural Networks (GNNs) have achieved promising performance in a variety of graph-focused tasks. Despite their success, however, existing GNNs suffer from two significant limitations: a lack of interpretability in their results due to their black-box nature, and an inability to learn representations of varying orders. To tackle these issues, we propose a novel Model-agnostic Graph Neural Network (MaGNet) framework, which is able to effectively integrate information of various orders, extract knowledge from high-order neighbors, and provide meaningful and interpretable results by identifying influential compact graph structures. In particular, MaGNet consists of two components: an estimation model for the latent representation of complex relationships under graph topology, and an interpretation model that identifies influential nodes, edges, and node features. Theoretically, we establish the generalization error bound for MaGNet via empirical Rademacher complexity, and demonstrate its power to represent layer-wise neighborhood mixing. We conduct comprehensive numerical studies using simulated data to demonstrate the superior performance of MaGNet in comparison to several state-of-the-art alternatives. Furthermore, we apply MaGNet to a real-world case study aimed at extracting task-critical information from brain activity data, thereby highlighting its effectiveness in advancing scientific research. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work. 

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3. Hierarchical Multi Scale Graph Neural Networks: Scalable Heterophilous Learning with Oversmoothing and Oversquashing Mitigation

   Hossen, MD_Sazzad; Sahoo, Avimanyu (July 2026, 2026 International Conference on Machine Learning)

   Graphs with heterophily, where adjacent nodes carry different labels, are prevalent in real-world applications, from social networks to molecular interactions. However, existing spectral Graph Neural Network (GNN) approaches tailored for heterophilous graph classification suffer from hub-dominated (node with large degree) aggregation and oversmoothing, as their suboptimal polynomial filters introduce approximation errors and blend distant signals. To address the degree-biased aggregation and suboptimal polynomial filtering, we introduce a Hierarchical Multi‐view HAAR (HMH), a novel spectral graph‐learning framework that scales in near‑linear time . HMH first learns feature- and structure-aware \emph{signed} affinities via a heterophily-aware encoder, then constructs a soft graph hierarchy guided by these embeddings. At each hierarchical level, HMH constructs a sparse, orthonormal, and locality-aware Haar basis to apply learnable spectral filters in the frequency domain. Finally, skip-connection unpooling layers combine outputs from all hierarchical levels back into the original graph, effectively preventing hub domination and long-range signal bottleneck (over-squashing). Experimentation shows that HMH outperforms state‑of‑the‑art spectral baselines, achieving up to a 3 % improvement on node classification and 7% on graph classification datasets, all while maintaining linear scalability. 

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4. Adaptive Kernel Graph Neural Network

   https://doi.org/10.1609/aaai.v36i6.20664  

   Ju, Mingxuan; Hou, Shifu; Fan, Yujie; Zhao, Jianan; Ye, Yanfang; Zhao, Liang (June 2022, Proceedings of the AAAI Conference on Artificial Intelligence)

   Graph neural networks (GNNs) have demonstrated great success in representation learning for graph-structured data. The layer-wise graph convolution in GNNs is shown to be powerful at capturing graph topology. During this process, GNNs are usually guided by pre-defined kernels such as Laplacian matrix, adjacency matrix, or their variants. However, the adoptions of pre-defined kernels may restrain the generalities to different graphs: mismatch between graph and kernel would entail sub-optimal performance. For example, GNNs that focus on low-frequency information may not achieve satisfactory performance when high-frequency information is significant for the graphs, and vice versa. To solve this problem, in this paper, we propose a novel framework - i.e., namely Adaptive Kernel Graph Neural Network (AKGNN) - which learns to adapt to the optimal graph kernel in a unified manner at the first attempt. In the proposed AKGNN, we first design a data-driven graph kernel learning mechanism, which adaptively modulates the balance between all-pass and low-pass filters by modifying the maximal eigenvalue of the graph Laplacian. Through this process, AKGNN learns the optimal threshold between high and low frequency signals to relieve the generality problem. Later, we further reduce the number of parameters by a parameterization trick and enhance the expressive power by a global readout function. Extensive experiments are conducted on acknowledged benchmark datasets and promising results demonstrate the outstanding performance of our proposed AKGNN by comparison with state-of-the-art GNNs. The source code is publicly available at: https://github.com/jumxglhf/AKGNN. 

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5. Bridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural Networks

   https://doi.org/10.1145/3627816  

   Chen, Zhiqian; Chen, Fanglan; Zhang, Lei; Ji, Taoran; Fu, Kaiqun; Zhao, Liang; Chen, Feng; Wu, Lingfei; Aggarwal, Charu; Lu, Chang-Tien (May 2024, ACM Computing Surveys)

   Deep learning’s performance has been extensively recognized recently. Graph neural networks (GNNs) are designed to deal with graph-structural data that classical deep learning does not easily manage. Since most GNNs were created using distinct theories, direct comparisons are impossible. Prior research has primarily concentrated on categorizing existing models, with little attention paid to their intrinsic connections. The purpose of this study is to establish a unified framework that integrates GNNs based on spectral graph and approximation theory. The framework incorporates a strong integration between spatial- and spectral-based GNNs while tightly associating approaches that exist within each respective domain. 

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