Enabling the Application of Graph Neural Networks on Graphs With Unknown Connectivity

Abstract

Graph Neural Networks (GNNs) have proven to be reliable methods for working with graph-structured data. However, it is common to find graphs with partially or fully inaccessible connectivity patterns, hindering the direct application of GNNs to the task at hand. To tackle this problem, several Graph Structure Learning (GSL) methods have been proposed, with the objective of jointly optimizing both the graph structure and the GNN model by adding loss terms that enforce desired graph properties. These properties, such as sparseness and connectivity of similar nodes, can have a drastic impact on the performance of a GNN. However, current methods offer little control on the desired degree of sparseness, which may lead to non-optimal connectivity and reduced efficiency. In this paper, we propose a new method called Adaptative Sparsification Graph Learning (ASGL), which enables finegrained, linear control over the total number of edges in the resulting learned graph via a novel perturbation-based loss term. ASGL not only provides flexibility in sparsity control but also improves both accuracy and computational efficiency, outperforming state-of-the-art methods in most benchmarks. We demonstrate its robustness through extensive experiments and highlight how adjusting sparsity enables optimizing the trade-off between accuracy, complexity, and interpretability.