{"ID":2838387,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.16871","arxiv_id":"2511.16871","title":"Aggregating Direct and Indirect Neighbors through Graph Linear Transformations","abstract":"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.","short_abstract":"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 operat...","url_abs":"https://arxiv.org/abs/2511.16871","url_pdf":"https://arxiv.org/pdf/2511.16871v2","authors":"[\"Marshall Rosenhoover\",\"Huaming Zhang\"]","published":"2025-11-21T00:43:14Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[\"Graph Neural Network\"]","has_code":false}