# Aggregating Direct and Indirect Neighbors through Graph Linear Transformations

arXiv: https://arxiv.org/abs/2511.16871 · HTML: https://mlsanity.com/paper/2511.16871/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 17 references that are in the map.
- First posted on arXiv 21 Nov 2025.

## Builds on (most cited first, 10 of 10)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [Structure-Aware Transformer for Graph Representation Learning](https://mlsanity.com/paper/2202.03036/) (2022)
- [Graph Neural Ordinary Differential Equations](https://mlsanity.com/paper/1911.07532/) (2019)
- [Continuous Graph Neural Networks](https://mlsanity.com/paper/1912.00967/) (2019)
- [A visual introduction to Gaussian Belief Propagation](https://mlsanity.com/paper/2107.02308/) (2021)

## Abstract (arXiv)

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.