mlsanityData to 7 Oct 2026

Permutation Equivariant Graph Framelets for Heterophilous Graph Learning

arXiv 2306.04265 ↗First posted 7 Jun 2023cs.LG cs.AI cs.SIcited by 19

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Abstract (arXiv)

The nature of heterophilous graphs is significantly different from that of homophilous graphs, which causes difficulties in early graph neural network models and suggests aggregations beyond the 1-hop neighborhood. In this paper, we develop a new way to implement multi-scale extraction via constructing Haar-type graph framelets with desired properties of permutation equivariance, efficiency, and sparsity, for deep learning tasks on graphs. We further design a graph framelet neural network model PEGFAN (Permutation Equivariant Graph Framelet Augmented Network) based on our constructed graph framelets. The experiments are conducted on a synthetic dataset and 9 benchmark datasets to compare performance with other state-of-the-art models. The result shows that our model can achieve the best performance on certain datasets of heterophilous graphs (including the majority of heterophilous datasets with relatively larger sizes and denser connections) and competitive performance on the remaining.

Key facts. Cited by 19 papers in the map (data through 7 Oct 2026). Builds on 34 of its 61 references that are in the map. First posted on arXiv 7 Jun 2023.

Builds on

34 of 61 references.

References · 34

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22 more
  1. 2018Deep Learning on Graphs: A Surveycited by 393
  2. 2018Invariant and Equivariant Graph Networkscited by 339
  3. 2021Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methodscited by 309
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  6. 2021Is Homophily a Necessity for Graph Neural Networks?cited by 182
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  17. 2019Fast Haar Transforms for Graph Neural Networkscited by 20
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 11; 2025: 5; 2026: 1.

19 papers.

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  1. 2024SpeGCL: Self-supervised Graph Spectrum Contrastive Learning without Positive Samplescited by 20
  2. 2025Uncertainty-Aware Graph Neural Networks: A Multi-Hop Evidence Fusion Approachcited by 14
  3. 2025BP-SGCN: Behavioral Pseudo-Label Informed Sparse Graph Convolution Network for Pedestrian and Heterogeneous Trajectory Predictioncited by 9
  4. 2023HAGNN: Hybrid Aggregation for Heterogeneous Graph Neural Networkscited by 4
  5. 2024SympGNNs: Symplectic Graph Neural Networks for identifiying high-dimensional Hamiltonian systems and node classificationcited by 4
  6. 2024Rethinking Spectral Graph Neural Networks with Spatially Adaptive Filteringcited by 3
  7. 2024Flexible Diffusion Scopes with Parameterized Laplacian for Heterophilic Graph Learningcited by 3
  8. 2024Derivation of Back-propagation for Graph Convolutional Networks using Matrix Calculus and its Application to Explainable Artificial Intelligencecited by 1
  9. 2024MALADY: Multiclass Active Learning with Auction Dynamics on Graphscited by 1
  10. 2024PromptGCN: Bridging Subgraph Gaps in Lightweight GCNscited by 1
  11. 2024Graph Signal Adaptive Message Passingcited by 1
  12. 2023Data-Adaptive Graph Framelets with Generalized Vanishing Moments for Graph Machine Learningcited by 0
7 more
  1. 2024A Hierarchical Framework with Spatio-Temporal Consistency Learning for Emergence Detection in Complex Adaptive Systemscited by 0
  2. 2024Generative-Contrastive Heterogeneous Graph Neural Networkcited by 0
  3. 2024Heterophilous Distribution Propagation for Graph Neural Networkscited by 0
  4. 2025Adaptive Backdoor Attacks with Reasonable Constraints on Graph Neural Networkscited by 0
  5. 2025Learning from Heterophilic Graphs: A Spectral Theory Perspective on the Impact of Self-Loops and Parallel Edgescited by 0
  6. 2025DGTEN: A Robust Deep Gaussian based Graph Neural Network for Dynamic Trust Evaluation with Uncertainty-Quantification Supportcited by 0
  7. 2026Group-Invariant Unsupervised Skill Discovery: Symmetry-aware Skill Representations for Generalizable Behaviorcited by 0