Graph Alignment via Dual-Pass Spectral Encoding and Latent Space Communication

Graph alignment, the problem of identifying corresponding nodes across multiple graphs, is fundamental to numerous applications. Most existing unsupervised methods embed node features into latent representations to enable cross-graph comparison without ground-truth correspondences. However, these methods suffer from two critical limitations: the degradation of node distinctiveness due to oversmoothing in GNN-based embeddings, and the misalignment of latent spaces across graphs caused by structural noise, feature heterogeneity, and training instability, ultimately leading to unreliable node correspondences. Our key insight is that rather than balancing these objectives purely in the feature space, a unified framework can simultaneously filter in both feature and map spaces. We propose a novel framework that employs a dual-pass encoder to inject high-frequency discriminability into node features, paired with a geometry-aware functional map module that operates on the correspondence itself. This functional map module learns bijective and isometric transformations that align latent spaces while acting as a low-pass filter on correspondences, enforcing smoothness and robustness as a structural prior in the map space. Extensive experiments on graph benchmarks demonstrate that our method consistently outperforms existing unsupervised alignment baselines, exhibiting superior robustness to structural inconsistencies and challenging alignment scenarios.