Simple Yet Effective Self-Supervised Graph Learning with Inverse Laplacian

Self-supervised learning (SSL) has become a powerful paradigm for graph representation learning. However, most existing methods operate in the graph topology domain and rely on complex data augmentations or contrastive objectives, which constrain them to local structural information and hinder the effective modeling of global or long-range dependencies. In this work, we propose the inverse-filter graph neural network (IF-GNN), an alternative spectral-based method for SSL. IF-GNN employs a fixed spectral operator (I+α(L^−I))−1 as a low-pass inverse filter, enabling efficient and label-free node representation learning in the spectral domain. The inverse filter can be interpreted as an infinite-order polynomial filter, allowing the model to aggregate high-order neighborhood information without layer stacking or explicit message passing. This design helps alleviate over-smoothing by avoiding repeated feature averaging and improves the interpretability of spectral SSL models. Extensive experiments on multiple benchmark datasets demonstrate that IF-GNN achieves competitive or superior performance compared to both spectral and self-supervised baselines, establishing inverse filtering as a new and effective spectral SSL paradigm.