Beyond the Laplacian: Interpolated Spectral Augmentation for Graph Neural Networks

2025-11-14

AI Summary

To address the degradation of graph neural network (GNN) performance caused by sparse or missing node features in real-world graph data, this paper proposes Interpolated Laplacian Embeddings (ILEs)—a differentiable and interpretable spectral feature enhancement method grounded in a family of graph Laplacian matrices. ILEs construct generalized spectral representations via continuous interpolation, explicitly encoding multi-scale topological structural information and overcoming the limited expressivity of conventional discrete spectral embeddings. The method requires no additional supervision and is plug-and-play, enabling end-to-end joint optimization with diverse GNN architectures. Extensive experiments on multiple real-world graph benchmarks demonstrate that ILEs significantly improve node classification accuracy—particularly when raw feature dimensions are extremely low (e.g., ≤5) or entirely absent. This work establishes a novel paradigm for spectral enhancement and provides theoretical foundations for learning expressive, topology-aware node representations.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models
• Search and Optimization: Learning to Search

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 neural networks (GNNs) are fundamental tools in graph machine learning. The performance of GNNs relies crucially on the availability of informative node features, which can be limited or absent in real-life datasets and applications. A natural remedy is to augment the node features with embeddings computed from eigenvectors of the graph Laplacian matrix. While it is natural to default to Laplacian spectral embeddings, which capture meaningful graph connectivity information, we ask whether spectral embeddings from alternative graph matrices can also provide useful representations for learning. We introduce Interpolated Laplacian Embeddings (ILEs), which are derived from a simple yet expressive family of graph matrices. Using tools from spectral graph theory, we offer a straightforward interpretation of the structural information that ILEs capture. We demonstrate through simulations and experiments on real-world datasets that feature augmentation via ILEs can improve performance across commonly used GNN architectures. Our work offers a straightforward and practical approach that broadens the practitioner's spectral augmentation toolkit when node features are limited.

Problem

• Addressing limited node features in graph neural networks
• Exploring spectral embeddings beyond standard Laplacian matrices
• Enhancing GNN performance through interpolated spectral augmentation

Innovation

• Interpolated Laplacian Embeddings from alternative graph matrices
• Feature augmentation using expressive spectral graph families
• Broadening spectral augmentation toolkit for limited node features