# Multidimensional Graph Neural Networks for Wireless Communications

arXiv: https://arxiv.org/abs/2212.11531 · HTML: https://mlsanity.com/paper/2212.11531/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Dec 2022.

## Built on by (most cited first, 7 of 7)

- [Learning Resource Allocation Policy: Vertex-GNN or Edge-GNN?](https://mlsanity.com/paper/2307.12480/) (2023)
- [Precoder Learning for Weighted Sum Rate Maximization](https://mlsanity.com/paper/2503.04497/) (2025)
- [Precoder Learning by Leveraging Unitary Equivariance Property](https://mlsanity.com/paper/2503.09398/) (2025)
- [Precoder Design in Multi-User FDD Systems with VQ-VAE and GNN](https://mlsanity.com/paper/2510.09495/) (2025)
- [GNN-Enabled Robust Hybrid Beamforming with Score-Based CSI Generation and Denoising](https://mlsanity.com/paper/2511.06663/) (2025)
- [A General Deep Learning Framework for Wireless Resource Allocation under Discrete Constraints](https://mlsanity.com/paper/2603.19322/) (2026)
- [Efficient Graph Neural Networks for Multicarrier Wideband Hybrid Beamforming Optimization](https://mlsanity.com/paper/2609.09708/) (2026)

## Abstract (arXiv)

Graph neural networks (GNNs) have been shown promising in improving the efficiency of learning communication policies by leveraging their permutation properties. Nonetheless, existing works design GNNs only for specific wireless policies, lacking a systematical approach for modeling graph and selecting structure. Based on the observation that the mismatched permutation property from the policies and the information loss during the update of hidden representations have large impact on the learning performance and efficiency, in this paper we propose a unified framework to learn permutable wireless policies with multidimensional GNNs. To avoid the information loss, the GNNs update the hidden representations of hyper-edges. To exploit all possible permutations of a policy, we provide a method to identify vertices in a graph. We also investigate the permutability of wireless channels that affects the sample efficiency, and show how to trade off the training, inference, and designing complexities of GNNs. We take precoding in different systems as examples to demonstrate how to apply the framework. Simulation results show that the proposed GNNs can achieve close performance to numerical algorithms, and require much fewer training samples and trainable parameters to achieve the same learning performance as the commonly used convolutional neural networks.