Residual connections provably mitigate oversmoothing in graph neural networks

• URL: http://arxiv.org/abs/2501.00762v2
• Date: Sat, 04 Jan 2025 03:14:11 GMT
• Title: Residual connections provably mitigate oversmoothing in graph neural networks
• Authors: Ziang Chen, Zhengjiang Lin, Shi Chen, Yury Polyanskiy, Philippe Rigollet,
• Abstract summary: Graph neural networks (GNNs) have achieved remarkable empirical success in processing and representing graph-structured data. However, a significant challenge known as "oversmoothing" persists, where expressive features become nearly indistinguishable in deep GNNs. In this work, we analyze the oversmoothing rates of deep GNNs with and without residual connections.
• Score: 33.548465692402765
• License:
• Abstract: Graph neural networks (GNNs) have achieved remarkable empirical success in processing and representing graph-structured data across various domains. However, a significant challenge known as "oversmoothing" persists, where vertex features become nearly indistinguishable in deep GNNs, severely restricting their expressive power and practical utility. In this work, we analyze the asymptotic oversmoothing rates of deep GNNs with and without residual connections by deriving explicit convergence rates for a normalized vertex similarity measure. Our analytical framework is grounded in the multiplicative ergodic theorem. Furthermore, we demonstrate that adding residual connections effectively mitigates or prevents oversmoothing across several broad families of parameter distributions. The theoretical findings are strongly supported by numerical experiments.

Related papers

• Rethinking Oversmoothing in Graph Neural Networks: A Rank-Based Perspective [5.482832675034467]
  We show that rank-based metrics consistently capture oversmoothing, whereas energy-based metrics often fail. Notably, we reveal that a significant drop in the rank aligns closely with performance degradation, even in scenarios where energy metrics remain unchanged.
  arXiv  Detail & Related papers  (2025-02-07T00:55:05Z)
• Consistency of augmentation graph and network approximability in contrastive learning [3.053989095162017]
  We analyze the pointwise and spectral consistency of the augmentation graph Laplacian. We show that Laplacian converges to a weighted Laplace-Beltrami operator on the natural data manifold. These consistency results ensure that the graph Laplacian spectrum effectively captures the manifold geometry.
  arXiv  Detail & Related papers  (2025-02-06T18:55:51Z)
• Spiking Graph Neural Network on Riemannian Manifolds [51.15400848660023]
  Graph neural networks (GNNs) have become the dominant solution for learning on graphs. Existing spiking GNNs consider graphs in Euclidean space, ignoring the structural geometry. We present a Manifold-valued Spiking GNN (MSG) MSG achieves superior performance to previous spiking GNNs and energy efficiency to conventional GNNs.
  arXiv  Detail & Related papers  (2024-10-23T15:09:02Z)
• A Survey on Oversmoothing in Graph Neural Networks [27.898197360068146]
  Node features of graph neural networks (GNNs) tend to become more similar with the increase of the network depth. We axiomatically define as the exponential convergence of suitable similarity measures on the node features. We empirically demonstrate this behavior for several over-smoothing measures on different graphs. We extend our definition of over-smoothing to the rapidly emerging field of continuous-time GNNs.
  arXiv  Detail & Related papers  (2023-03-20T10:21:29Z)
• Understanding Oversquashing in GNNs through the Lens of Effective Resistance [9.640594614636047]
  We develop an algorithm to identify edges to be added to an input graph to minimize the total effective resistance, thereby alleviating oversquashing. We provide empirical evidence of the effectiveness of our total effective resistance based rewiring strategies for improving the performance of GNNs.
  arXiv  Detail & Related papers  (2023-02-14T05:16:12Z)
• MGNNI: Multiscale Graph Neural Networks with Implicit Layers [53.75421430520501]
  implicit graph neural networks (GNNs) have been proposed to capture long-range dependencies in underlying graphs. We introduce and justify two weaknesses of implicit GNNs: the constrained expressiveness due to their limited effective range for capturing long-range dependencies, and their lack of ability to capture multiscale information on graphs at multiple resolutions. We propose a multiscale graph neural network with implicit layers (MGNNI) which is able to model multiscale structures on graphs and has an expanded effective range for capturing long-range dependencies.
  arXiv  Detail & Related papers  (2022-10-15T18:18:55Z)
• Relation Embedding based Graph Neural Networks for Handling Heterogeneous Graph [58.99478502486377]
  We propose a simple yet efficient framework to make the homogeneous GNNs have adequate ability to handle heterogeneous graphs. Specifically, we propose Relation Embedding based Graph Neural Networks (RE-GNNs), which employ only one parameter per relation to embed the importance of edge type relations and self-loop connections.
  arXiv  Detail & Related papers  (2022-09-23T05:24:18Z)
• Deep Architecture Connectivity Matters for Its Convergence: A Fine-Grained Analysis [94.64007376939735]
  We theoretically characterize the impact of connectivity patterns on the convergence of deep neural networks (DNNs) under gradient descent training. We show that by a simple filtration on "unpromising" connectivity patterns, we can trim down the number of models to evaluate.
  arXiv  Detail & Related papers  (2022-05-11T17:43:54Z)
• Wide Graph Neural Networks: Aggregation Provably Leads to Exponentially Trainability Loss [17.39060566854841]
  Graph convolutional networks (GCNs) and their variants have achieved great success in dealing with graph-structured data. It is well known that deep GCNs will suffer from over-smoothing problem. Few theoretical analyses have been conducted to study the expressivity and trainability of deep GCNs.
  arXiv  Detail & Related papers  (2021-03-03T11:06:12Z)
• How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks [80.55378250013496]
  We study how neural networks trained by gradient descent extrapolate what they learn outside the support of the training distribution. Graph Neural Networks (GNNs) have shown some success in more complex tasks.
  arXiv  Detail & Related papers  (2020-09-24T17:48:59Z)
• Optimization and Generalization Analysis of Transduction through Gradient Boosting and Application to Multi-scale Graph Neural Networks [60.22494363676747]
  It is known that the current graph neural networks (GNNs) are difficult to make themselves deep due to the problem known as over-smoothing. Multi-scale GNNs are a promising approach for mitigating the over-smoothing problem. We derive the optimization and generalization guarantees of transductive learning algorithms that include multi-scale GNNs.
  arXiv  Detail & Related papers  (2020-06-15T17:06:17Z)

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.