  The surge in demand for efficient radio resource management has necessitated
the development of sophisticated yet compact neural network architectures. In
this paper, we introduce a novel approach to Graph Neural Networks (GNNs)
tailored for radio resource management by presenting a new architecture: the
Low Rank Message Passing Graph Neural Network (LR-MPGNN). The cornerstone of
LR-MPGNN is the implementation of a low-rank approximation technique that
substitutes the conventional linear layers with their low-rank counterparts.
This innovative design significantly reduces the model size and the number of
parameters. We evaluate the performance of the proposed LR-MPGNN model based on
several key metrics: model size, number of parameters, weighted sum rate of the
communication system, and the distribution of eigenvalues of weight matrices.
Our extensive evaluations demonstrate that the LR-MPGNN model achieves a
sixtyfold decrease in model size, and the number of model parameters can be
reduced by up to 98%. Performance-wise, the LR-MPGNN demonstrates robustness
with a marginal 2% reduction in the best-case scenario in the normalized
weighted sum rate compared to the original MPGNN model. Additionally, the
distribution of eigenvalues of the weight matrices in the LR-MPGNN model is
more uniform and spans a wider range, suggesting a strategic redistribution of
weights.
