Beyond the Laplacian: Interpolated Spectral Augmentation for Graph Neural Networks

• URL: http://arxiv.org/abs/2511.11928v1
• Date: Fri, 14 Nov 2025 23:11:22 GMT
• Title: Beyond the Laplacian: Interpolated Spectral Augmentation for Graph Neural Networks
• Abstract summary: Interpolated Laplacian Embeddings (ILEs) are derived from a simple yet expressive family of graph matrices.<n>Our work offers a straightforward and practical approach that broadens the practitioner's spectral augmentation toolkit when node features are limited.
• Score: 0.42970700836450476
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• Exact Computation of Any-Order Shapley Interactions for Graph Neural Networks [53.10674067060148]
  Shapley Interactions (SIs) quantify node contributions and interactions among multiple nodes.<n>By exploiting the GNN architecture, we show that the structure of interactions in node embeddings are preserved for graph prediction.<n>We introduce GraphSHAP-IQ, an efficient approach to compute any-order SIs exactly.
  arXiv  Detail & Related papers  (2025-01-28T13:37:44Z)
• Large-Scale Spectral Graph Neural Networks via Laplacian Sparsification: Technical Report [21.288230563135055]
  We propose a novel graph spectral sparsification method to approximate the propagation patterns of spectral Graph Neural Networks (GNNs)<n>Our method allows the application of linear layers on the input node features, enabling end-to-end training as well as the handling of raw features.
  arXiv  Detail & Related papers  (2025-01-08T15:36:19Z)
• Boosting Graph Neural Network Expressivity with Learnable Lanczos Constraints [7.605749412696919]
  Graph Neural Networks (GNNs) excel in handling graph-structured data but often underperform in link prediction tasks.<n>We present a novel method to enhance the expressivity of GNNs by embedding induced subgraphs into the graph Laplacian matrix's eigenbasis.<n>We demonstrate the ability to distinguish graphs that are indistinguishable by 2-WL, while maintaining efficient time complexity.
  arXiv  Detail & Related papers  (2024-08-22T12:22:00Z)
• Graph Kernel Neural Networks [53.91024360329517]
  We propose to use graph kernels, i.e. kernel functions that compute an inner product on graphs, to extend the standard convolution operator to the graph domain. This allows us to define an entirely structural model that does not require computing the embedding of the input graph. Our architecture allows to plug-in any type of graph kernels and has the added benefit of providing some interpretability.
  arXiv  Detail & Related papers  (2021-12-14T14:48:08Z)
• Pointspectrum: Equivariance Meets Laplacian Filtering for Graph Representation Learning [3.7875603451557063]
  Graph Representation Learning (GRL) has become essential for modern graph data mining and learning tasks. While Graph Neural Networks (GNNs) have been used in state-of-the-art GRL architectures, they have been shown to suffer from over smoothing. We propose PointSpectrum, a spectral method that incorporates a set equivariant network to account for a graph's structure.
  arXiv  Detail & Related papers  (2021-09-06T10:59:11Z)
• GraphMI: Extracting Private Graph Data from Graph Neural Networks [59.05178231559796]
  We present textbfGraph textbfModel textbfInversion attack (GraphMI), which aims to extract private graph data of the training graph by inverting GNN. Specifically, we propose a projected gradient module to tackle the discreteness of graph edges while preserving the sparsity and smoothness of graph features. We design a graph auto-encoder module to efficiently exploit graph topology, node attributes, and target model parameters for edge inference.
  arXiv  Detail & Related papers  (2021-06-05T07:07:52Z)
• GraphSVX: Shapley Value Explanations for Graph Neural Networks [81.83769974301995]
  Graph Neural Networks (GNNs) achieve significant performance for various learning tasks on geometric data. In this paper, we propose a unified framework satisfied by most existing GNN explainers. We introduce GraphSVX, a post hoc local model-agnostic explanation method specifically designed for GNNs.
  arXiv  Detail & Related papers  (2021-04-18T10:40:37Z)
• Graph Networks with Spectral Message Passing [1.0742675209112622]
  We introduce the Spectral Graph Network, which applies message passing to both the spatial and spectral domains. Our results show that the Spectral GN promotes efficient training, reaching high performance with fewer training iterations despite having more parameters.
  arXiv  Detail & Related papers  (2020-12-31T21:33:17Z)
• Robust Optimization as Data Augmentation for Large-scale Graphs [117.2376815614148]
  We propose FLAG (Free Large-scale Adversarial Augmentation on Graphs), which iteratively augments node features with gradient-based adversarial perturbations during training. FLAG is a general-purpose approach for graph data, which universally works in node classification, link prediction, and graph classification tasks.
  arXiv  Detail & Related papers  (2020-10-19T21:51:47Z)
• Training Sensitivity in Graph Isomorphism Network [2.487445341407889]
  Graph neural network (GNN) is a popular tool to learn the lower-dimensional representation of a graph. This paper studies various alternative functions for a respective module using a diverse set of benchmark datasets.
  arXiv  Detail & Related papers  (2020-08-19T03:50:28Z)
• Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networks [183.97265247061847]
  We leverage graph signal processing to characterize the representation space of graph neural networks (GNNs) We discuss the role of graph convolutional filters in GNNs and show that any architecture built with such filters has the fundamental properties of permutation equivariance and stability to changes in the topology. We also study the use of GNNs in recommender systems and learning decentralized controllers for robot swarms.
  arXiv  Detail & Related papers  (2020-03-08T13:02:15Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.