Title: GraphSpa: Self-supervised Graph Sparsification for robust generalization
Primary area: learning on graphs and other geometries & topologies
Keywords: Graph Sparsification, Self-Supervised Learning, Constrained Optimization

Abstract: Graph sparsification has emerged as a promising approach to improve efficiency and remove redundant or noisy edges in large-scale graphs. However, existing methods often rely on task-specific labels, limiting their applicability in label-scarce scenarios, and they rarely address the residual noise that persists after sparsification. In this work, we present GraphSpa, a self-supervised graph sparsification framework that learns to construct compact yet informative subgraphs without requiring labels, while explicitly mitigating the effect of residual noise. GraphSpa formulates sparsification with a target edge budget as a constrained optimization problem, modeling each edge as a differentiable Bernoulli random variable and employing the mutual information between sampled subgraphs and the original graph as a loss function to learn individual edge importance. To progressively impose sparsity with stability, GraphSpa adopts an augmented Lagrangian scheme with convergence guarantees. In addition, the encoder is trained in a flatness-aware manner using Sharpness-Aware Minimization (SAM), which reduces sensitivity to residual noise and improves generalization. Extensive experiments on benchmark datasets demonstrate that GraphSpa consistently outperforms baselines across different sparsity ratios, preserves cluster structures in
t-SNE visualizations, and remains robust even when noisy edges are injected after sparsification. These results highlight GraphSpa as a principled and reliable framework for graph sparsification without labels and under residual noise.