Sheaf Graph Neural Networks via PAC-Bayes Spectral Optimization

• URL: http://arxiv.org/abs/2508.00357v1
• Date: Fri, 01 Aug 2025 06:39:28 GMT
• Title: Sheaf Graph Neural Networks via PAC-Bayes Spectral Optimization
• Authors: Yoonhyuk Choi, Jiho Choi, Chong-Kwon Kim,
• Abstract summary: Over-smoothing in Graph Neural Networks (GNNs) causes collapse in distinct node features.<n>We introduce a novel scheme called SGPC (Sheaf GNNs with PAC-Bayes)<n>We show that SGPC outperforms state-of-the-art spectral and sheaf-based GNNs while providing certified confidence intervals on unseen nodes.
• Score: 3.2771631221674333
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Over-smoothing in Graph Neural Networks (GNNs) causes collapse in distinct node features, particularly on heterophilic graphs where adjacent nodes often have dissimilar labels. Although sheaf neural networks partially mitigate this problem, they typically rely on static or heavily parameterized sheaf structures that hinder generalization and scalability. Existing sheaf-based models either predefine restriction maps or introduce excessive complexity, yet fail to provide rigorous stability guarantees. In this paper, we introduce a novel scheme called SGPC (Sheaf GNNs with PAC-Bayes Calibration), a unified architecture that combines cellular-sheaf message passing with several mechanisms, including optimal transport-based lifting, variance-reduced diffusion, and PAC-Bayes spectral regularization for robust semi-supervised node classification. We establish performance bounds theoretically and demonstrate that the resulting bound-aware objective can be achieved via end-to-end training in linear computational complexity. Experiments on nine homophilic and heterophilic benchmarks show that SGPC outperforms state-of-the-art spectral and sheaf-based GNNs while providing certified confidence intervals on unseen nodes.

Related papers

• ReDiSC: A Reparameterized Masked Diffusion Model for Scalable Node Classification with Structured Predictions [64.17845687013434]
  We propose ReDiSC, a structured diffusion model for structured node classification.<n>We show that ReDiSC achieves superior or highly competitive performance compared to state-of-the-art GNN, label propagation, and diffusion-based baselines.<n> Notably, ReDiSC scales effectively to large-scale datasets on which previous structured diffusion methods fail due to computational constraints.
  arXiv  Detail & Related papers  (2025-07-19T04:46:53Z)
• Alleviating Structural Distribution Shift in Graph Anomaly Detection [70.1022676681496]
  Graph anomaly detection (GAD) is a challenging binary classification problem. Gallon neural networks (GNNs) benefit the classification of normals from aggregating homophilous neighbors. We propose a framework to mitigate the effect of heterophilous neighbors and make them invariant.
  arXiv  Detail & Related papers  (2024-01-25T13:07:34Z)
• Heterophily-Aware Graph Attention Network [42.640057865981156]
  Graph Neural Networks (GNNs) have shown remarkable success in graph representation learning. Existing heterophilic GNNs tend to ignore the modeling of heterophily of each edge, which is also a vital part in tackling the heterophily problem. We propose a novel Heterophily-Aware Graph Attention Network (HA-GAT) by fully exploring and utilizing the local distribution as the underlying heterophily.
  arXiv  Detail & Related papers  (2023-02-07T03:21:55Z)
• Simple and Efficient Heterogeneous Graph Neural Network [55.56564522532328]
  Heterogeneous graph neural networks (HGNNs) have powerful capability to embed rich structural and semantic information of a heterogeneous graph into node representations. Existing HGNNs inherit many mechanisms from graph neural networks (GNNs) over homogeneous graphs, especially the attention mechanism and the multi-layer structure. This paper conducts an in-depth and detailed study of these mechanisms and proposes Simple and Efficient Heterogeneous Graph Neural Network (SeHGNN)
  arXiv  Detail & Related papers  (2022-07-06T10:01:46Z)
• EvenNet: Ignoring Odd-Hop Neighbors Improves Robustness of Graph Neural Networks [51.42338058718487]
  Graph Neural Networks (GNNs) have received extensive research attention for their promising performance in graph machine learning. Existing approaches, such as GCN and GPRGNN, are not robust in the face of homophily changes on test graphs. We propose EvenNet, a spectral GNN corresponding to an even-polynomial graph filter.
  arXiv  Detail & Related papers  (2022-05-27T10:48:14Z)
• 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)
• Implicit vs Unfolded Graph Neural Networks [29.803948965931212]
  We show that implicit and unfolded GNNs can achieve strong node classification accuracy across disparate regimes.<n>While IGNN is substantially more memory-efficient, UGNN models support unique, integrated graph attention mechanisms and propagation rules.
  arXiv  Detail & Related papers  (2021-11-12T07:49:16Z)
• Stability of Neural Networks on Manifolds to Relative Perturbations [118.84154142918214]
  Graph Neural Networks (GNNs) show impressive performance in many practical scenarios. GNNs can scale well on large size graphs, but this is contradicted by the fact that existing stability bounds grow with the number of nodes.
  arXiv  Detail & Related papers  (2021-10-10T04:37:19Z)
• Graph Neural Networks Inspired by Classical Iterative Algorithms [28.528150667063876]
  We consider a new family of GNN layers designed to mimic and integrate the update rules of two classical iterative algorithms. A novel attention mechanism is explicitly anchored to an underlying end-toend energy function, contributing stability with respect to edge uncertainty.
  arXiv  Detail & Related papers  (2021-03-10T14:08:12Z)
• Stochastic Aggregation in Graph Neural Networks [9.551282469099887]
  Graph neural networks (GNNs) manifest pathologies including over-smoothing and limited power discriminating. We present a unifying framework for aggregation (STAG) in GNNs, where noise is (adaptively) injected into the aggregation process from the neighborhood to form node embeddings.
  arXiv  Detail & Related papers  (2021-02-25T02:52:03Z)
• Scattering GCN: Overcoming Oversmoothness in Graph Convolutional Networks [0.0]
  Graph convolutional networks (GCNs) have shown promising results in processing graph data by extracting structure-aware features. Here, we propose to augment conventional GCNs with geometric scattering transforms and residual convolutions. The former enables band-pass filtering of graph signals, thus alleviating the so-called oversmoothing often encountered in GCNs.
  arXiv  Detail & Related papers  (2020-03-18T18:03:08Z)

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.