Implicit Graph Neural Diffusion Networks: Convergence, Generalization, and Over-Smoothing

• URL: http://arxiv.org/abs/2308.03306v2
• Date: Thu, 15 Feb 2024 09:05:30 GMT
• Title: Implicit Graph Neural Diffusion Networks: Convergence, Generalization, and Over-Smoothing
• Authors: Guoji Fu, Mohammed Haroon Dupty, Yanfei Dong, Lee Wee Sun
• Abstract summary: Implicit Graph Neural Networks (GNNs) have achieved significant success in addressing graph learning problems. We introduce a geometric framework for designing implicit graph diffusion layers based on a parameterized graph Laplacian operator. We show how implicit GNN layers can be viewed as the fixed-point equation of a Dirichlet energy minimization problem.
• Score: 7.984586585987328
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Implicit Graph Neural Networks (GNNs) have achieved significant success in addressing graph learning problems recently. However, poorly designed implicit GNN layers may have limited adaptability to learn graph metrics, experience over-smoothing issues, or exhibit suboptimal convergence and generalization properties, potentially hindering their practical performance. To tackle these issues, we introduce a geometric framework for designing implicit graph diffusion layers based on a parameterized graph Laplacian operator. Our framework allows learning the metrics of vertex and edge spaces, as well as the graph diffusion strength from data. We show how implicit GNN layers can be viewed as the fixed-point equation of a Dirichlet energy minimization problem and give conditions under which it may suffer from over-smoothing during training (OST) and inference (OSI). We further propose a new implicit GNN model to avoid OST and OSI. We establish that with an appropriately chosen hyperparameter greater than the largest eigenvalue of the parameterized graph Laplacian, DIGNN guarantees a unique equilibrium, quick convergence, and strong generalization bounds. Our models demonstrate better performance than most implicit and explicit GNN baselines on benchmark datasets for both node and graph classification tasks.

Related papers

• Spectral Greedy Coresets for Graph Neural Networks [61.24300262316091]
  The ubiquity of large-scale graphs in node-classification tasks hinders the real-world applications of Graph Neural Networks (GNNs) This paper studies graph coresets for GNNs and avoids the interdependence issue by selecting ego-graphs based on their spectral embeddings. Our spectral greedy graph coreset (SGGC) scales to graphs with millions of nodes, obviates the need for model pre-training, and applies to low-homophily graphs.
  arXiv  Detail & Related papers  (2024-05-27T17:52:12Z)
• Learning to Reweight for Graph Neural Network [63.978102332612906]
  Graph Neural Networks (GNNs) show promising results for graph tasks. Existing GNNs' generalization ability will degrade when there exist distribution shifts between testing and training graph data. We propose a novel nonlinear graph decorrelation method, which can substantially improve the out-of-distribution generalization ability.
  arXiv  Detail & Related papers  (2023-12-19T12:25:10Z)
• Robust Graph Neural Network based on Graph Denoising [10.564653734218755]
  Graph Neural Networks (GNNs) have emerged as a notorious alternative to address learning problems dealing with non-Euclidean datasets. This work proposes a robust implementation of GNNs that explicitly accounts for the presence of perturbations in the observed topology.
  arXiv  Detail & Related papers  (2023-12-11T17:43:57Z)
• Global Minima, Recoverability Thresholds, and Higher-Order Structure in GNNS [0.0]
  We analyze the performance of graph neural network (GNN) architectures from the perspective of random graph theory. We show how both specific higher-order structures in synthetic data and the mix of empirical structures in real data have dramatic effects on GNN performance.
  arXiv  Detail & Related papers  (2023-10-11T17:16:33Z)
• MentorGNN: Deriving Curriculum for Pre-Training GNNs [61.97574489259085]
  We propose an end-to-end model named MentorGNN that aims to supervise the pre-training process of GNNs across graphs. We shed new light on the problem of domain adaption on relational data (i.e., graphs) by deriving a natural and interpretable upper bound on the generalization error of the pre-trained GNNs.
  arXiv  Detail & Related papers  (2022-08-21T15:12:08Z)
• Reliable Representations Make A Stronger Defender: Unsupervised Structure Refinement for Robust GNN [36.045702771828736]
  Graph Neural Networks (GNNs) have been successful on flourish tasks over graph data. Recent studies have shown that attackers can catastrophically degrade the performance of GNNs by maliciously modifying the graph structure. We propose an unsupervised pipeline, named STABLE, to optimize the graph structure.
  arXiv  Detail & Related papers  (2022-06-30T10:02:32Z)
• Adaptive Kernel Graph Neural Network [21.863238974404474]
  Graph neural networks (GNNs) have demonstrated great success in representation learning for graph-structured data. In this paper, we propose a novel framework - i.e., namely Adaptive Kernel Graph Neural Network (AKGNN) AKGNN learns to adapt to the optimal graph kernel in a unified manner at the first attempt. Experiments are conducted on acknowledged benchmark datasets and promising results demonstrate the outstanding performance of our proposed AKGNN.
  arXiv  Detail & Related papers  (2021-12-08T20:23:58Z)
• ACE-HGNN: Adaptive Curvature Exploration Hyperbolic Graph Neural Network [72.16255675586089]
  We propose an Adaptive Curvature Exploration Hyperbolic Graph NeuralNetwork named ACE-HGNN to adaptively learn the optimal curvature according to the input graph and downstream tasks. Experiments on multiple real-world graph datasets demonstrate a significant and consistent performance improvement in model quality with competitive performance and good generalization ability.
  arXiv  Detail & Related papers  (2021-10-15T07:18:57Z)
• Training Robust Graph Neural Networks with Topology Adaptive Edge Dropping [116.26579152942162]
  Graph neural networks (GNNs) are processing architectures that exploit graph structural information to model representations from network data. Despite their success, GNNs suffer from sub-optimal generalization performance given limited training data. This paper proposes Topology Adaptive Edge Dropping to improve generalization performance and learn robust GNN models.
  arXiv  Detail & Related papers  (2021-06-05T13:20:36Z)
• Learning to Drop: Robust Graph Neural Network via Topological Denoising [50.81722989898142]
  We propose PTDNet, a parameterized topological denoising network, to improve the robustness and generalization performance of Graph Neural Networks (GNNs) PTDNet prunes task-irrelevant edges by penalizing the number of edges in the sparsified graph with parameterized networks. We show that PTDNet can improve the performance of GNNs significantly and the performance gain becomes larger for more noisy datasets.
  arXiv  Detail & Related papers  (2020-11-13T18:53:21Z)
• Implicit Graph Neural Networks [46.0589136729616]
  We propose a graph learning framework called Implicit Graph Neural Networks (IGNN) IGNNs consistently capture long-range dependencies and outperform state-of-the-art GNN models.
  arXiv  Detail & Related papers  (2020-09-14T06:04:55Z)

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.