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. We propose a novel framework employing a dual-pass encoder to inject high-frequency discriminability into node features, paired with a geometry-aware functional map module that learns bijective and isometric transformations to align latent spaces while acting as a low-pass filter on correspondences, enforcing smoothness and robustness as a structural prior in 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. The implementation is available at https://github.com/maysambehmanesh/GADL.

Many real-world problems require finding which nodes in one network correspond to which nodes in another, for example, matching users across different social platforms, or aligning scientific collaboration networks. This is called graph alignment, and solving it without any labeled examples is particularly challenging. Current automatic methods struggle with two key problems. First, the algorithms used to represent network nodes tend to make similar nodes look identical, losing the fine-grained differences needed to tell them apart. Second, even when two networks are embedded into a mathematical space for comparison, those spaces often end up geometrically incompatible, making reliable matching difficult. We propose a new method that tackles both problems at once. We use two complementary filters, one that captures the broad structure of the network, and one that preserves the subtle differences between individual nodes, and combine their outputs to get the best of both worlds. We then add a mathematical module inspired by geometry that explicitly brings the two network spaces into alignment, making corresponding nodes easier to find. Our method consistently outperforms existing approaches across a range of challenging benchmarks, and also works beyond traditional networks, successfully matching visual and language representations in multimodal AI settings.