Aggregating Direct and Indirect Neighbors through Graph Linear Transformations
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866915733689073664 |
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| author | Rosenhoover, Marshall Zhang, Huaming |
| author_facet | Rosenhoover, Marshall Zhang, Huaming |
| contents | Graph neural networks (GNN) typically rely on localized message passing, requiring increasing depth to capture long range dependencies. In this work, we introduce Graph Linear Transformations, a linear transformation that realizes direct and indirect feature mixing on graphs through a single, well-defined linear operator derived from the graph structure. By interpreting graphs as walk-summable Gaussian graphical models, we compute these transformations via Gaussian Belief Propagation, enabling each node to aggregate information from both direct and indirect neighbors without explicit enumeration of multi-hop paths. We show that different constructions of the underlying precision matrix induce distinct and interpretable propagation biases, ranging from selective edge-level interactions to uniform structural smoothing, and that Graph Linear Transformations can achieve competitive or superior performance compared to both local message-passing GNNs and dynamic neighborhood aggregation models across homophilic and heterophilic benchmark datasets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_16871 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Aggregating Direct and Indirect Neighbors through Graph Linear Transformations Rosenhoover, Marshall Zhang, Huaming Machine Learning I.2.6; I.5.1; G.3 Graph neural networks (GNN) typically rely on localized message passing, requiring increasing depth to capture long range dependencies. In this work, we introduce Graph Linear Transformations, a linear transformation that realizes direct and indirect feature mixing on graphs through a single, well-defined linear operator derived from the graph structure. By interpreting graphs as walk-summable Gaussian graphical models, we compute these transformations via Gaussian Belief Propagation, enabling each node to aggregate information from both direct and indirect neighbors without explicit enumeration of multi-hop paths. We show that different constructions of the underlying precision matrix induce distinct and interpretable propagation biases, ranging from selective edge-level interactions to uniform structural smoothing, and that Graph Linear Transformations can achieve competitive or superior performance compared to both local message-passing GNNs and dynamic neighborhood aggregation models across homophilic and heterophilic benchmark datasets. |
| title | Aggregating Direct and Indirect Neighbors through Graph Linear Transformations |
| topic | Machine Learning I.2.6; I.5.1; G.3 |
| url | https://arxiv.org/abs/2511.16871 |