Spatio-Spectral Graph Neural Networks

• URL: http://arxiv.org/abs/2405.19121v2
• Date: Sun, 2 Jun 2024 18:03:44 GMT
• Title: Spatio-Spectral Graph Neural Networks
• Authors: Simon Geisler, Arthur Kosmala, Daniel Herbst, Stephan Günnemann,
• Abstract summary: We propose Spatio-Spectral Graph Networks (S$2$GNNs) S$2$GNNs combine spatially and spectrally parametrized graph filters. We show that S$2$GNNs vanquish over-squashing and yield strictly tighter approximation-theoretic error bounds than MPGNNs.
• Score: 50.277959544420455
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Spatial Message Passing Graph Neural Networks (MPGNNs) are widely used for learning on graph-structured data. However, key limitations of l-step MPGNNs are that their "receptive field" is typically limited to the l-hop neighborhood of a node and that information exchange between distant nodes is limited by over-squashing. Motivated by these limitations, we propose Spatio-Spectral Graph Neural Networks (S$^2$GNNs) -- a new modeling paradigm for Graph Neural Networks (GNNs) that synergistically combines spatially and spectrally parametrized graph filters. Parameterizing filters partially in the frequency domain enables global yet efficient information propagation. We show that S$^2$GNNs vanquish over-squashing and yield strictly tighter approximation-theoretic error bounds than MPGNNs. Further, rethinking graph convolutions at a fundamental level unlocks new design spaces. For example, S$^2$GNNs allow for free positional encodings that make them strictly more expressive than the 1-Weisfeiler-Lehman (WL) test. Moreover, to obtain general-purpose S$^2$GNNs, we propose spectrally parametrized filters for directed graphs. S$^2$GNNs outperform spatial MPGNNs, graph transformers, and graph rewirings, e.g., on the peptide long-range benchmark tasks, and are competitive with state-of-the-art sequence modeling. On a 40 GB GPU, S$^2$GNNs scale to millions of nodes.

Related papers

• Training Graph Neural Networks on Growing Stochastic Graphs [114.75710379125412]
  Graph Neural Networks (GNNs) rely on graph convolutions to exploit meaningful patterns in networked data. We propose to learn GNNs on very large graphs by leveraging the limit object of a sequence of growing graphs, the graphon.
  arXiv  Detail & Related papers  (2022-10-27T16:00:45Z)
• From Local to Global: Spectral-Inspired Graph Neural Networks [28.858773653743075]
  Graph Neural Networks (GNNs) are powerful deep learning methods for Non-Euclidean data. MPNNs are message-passing algorithms that aggregate and combine signals in a local graph neighborhood. MPNNs can suffer from issues like over-smoothing or over-squashing.
  arXiv  Detail & Related papers  (2022-09-24T17:19:00Z)
• Transferability Properties of Graph Neural Networks [125.71771240180654]
  Graph neural networks (GNNs) are provably successful at learning representations from data supported on moderate-scale graphs. We study the problem of training GNNs on graphs of moderate size and transferring them to large-scale graphs. Our results show that (i) the transference error decreases with the graph size, and (ii) that graph filters have a transferability-discriminability tradeoff that in GNNs is alleviated by the scattering behavior of the nonlinearity.
  arXiv  Detail & Related papers  (2021-12-09T00:08:09Z)
• $p$-Laplacian Based Graph Neural Networks [27.747195341003263]
  Graph networks (GNNs) have demonstrated superior performance for semi-supervised node classification on graphs. We propose a new $p$-Laplacian based GNN model, termed as $p$GNN, whose message passing mechanism is derived from a discrete regularization framework. We show that the new message passing mechanism works simultaneously as low-pass and high-pass filters, thus making $p$GNNs effective on both homophilic and heterophilic graphs.
  arXiv  Detail & Related papers  (2021-11-14T13:16:28Z)
• Graph Neural Networks with Local Graph Parameters [1.8600631687568656]
  Local graph parameters can be added to any Graph Neural Networks (GNNs) architecture. Our results connect GNNs with deep results in finite model theory and finite variable logics.
  arXiv  Detail & Related papers  (2021-06-12T07:43:51Z)
• A Unified Lottery Ticket Hypothesis for Graph Neural Networks [82.31087406264437]
  We present a unified GNN sparsification (UGS) framework that simultaneously prunes the graph adjacency matrix and the model weights. We further generalize the popular lottery ticket hypothesis to GNNs for the first time, by defining a graph lottery ticket (GLT) as a pair of core sub-dataset and sparse sub-network.
  arXiv  Detail & Related papers  (2021-02-12T21:52:43Z)
• Graph Neural Networks: Architectures, Stability and Transferability [176.3960927323358]
  Graph Neural Networks (GNNs) are information processing architectures for signals supported on graphs. They are generalizations of convolutional neural networks (CNNs) in which individual layers contain banks of graph convolutional filters.
  arXiv  Detail & Related papers  (2020-08-04T18:57:36Z)
• 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)
• Generalization and Representational Limits of Graph Neural Networks [46.20253808402385]
  We prove that several important graph properties cannot be computed by graph neural networks (GNNs) that rely entirely on local information. We provide the first data dependent generalization bounds for message passing GNNs. Our bounds are much tighter than existing VC-dimension based guarantees for GNNs, and are comparable to Rademacher bounds for recurrent neural networks.
  arXiv  Detail & Related papers  (2020-02-14T18:10:14Z)

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.