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

2025-09-11

AI Summary

Graph alignment aims to unsupervisedly identify semantically consistent nodes across multiple graphs. However, existing methods suffer from two key limitations: (1) over-smoothing in GNN-based embeddings, which diminishes node discriminability, and (2) misalignment of latent spaces across graphs, caused by structural noise, feature heterogeneity, and training instability. To address these challenges, we propose a dual-path spectral encoder jointly integrating low- and high-pass spectral filtering with GNNs to enhance structural awareness and node distinguishability; and a geometry-aware functional mapping module that enforces geometric consistency across graph latent spaces via isometric, invertible transformations. Our approach is fully unsupervised—requiring no ground-truth node correspondences. Extensive experiments demonstrate state-of-the-art performance on multi-graph benchmarks and cross-domain vision-language tasks. Moreover, the method exhibits strong robustness to structural perturbations and feature heterogeneity.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Computer Vision: Multi-modal Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

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 graph alignment framework that simultaneously enhances node distinctiveness and enforces geometric consistency across latent spaces. Our approach introduces a dual-pass encoder that combines low-pass and high-pass spectral filters to generate embeddings that are both structure-aware and highly discriminative. To address latent space misalignment, we incorporate a geometry-aware functional map module that learns bijective and isometric transformations between graph embeddings, ensuring consistent geometric relationships across different representations. 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. Additionally, comprehensive evaluation on vision-language benchmarks using diverse pretrained models shows that our framework effectively generalizes beyond graph domains, enabling unsupervised alignment of vision and language representations.

Problem

• Enhancing node distinctiveness in graph embeddings
• Addressing latent space misalignment across graphs
• Enabling unsupervised alignment without ground-truth correspondences

Innovation

• Dual-pass spectral encoder combining low-high filters
• Geometry-aware functional map for cross-graph alignment
• Bijective isometric transformations ensuring geometric consistency