Kernekoncepter
Graph neural networks struggle to reach Bayes-optimal rates in high-dimensional settings.
Resumé
The article explores the generalization properties of graph neural networks, focusing on single-layer graph convolutional networks (GCNs) trained on attributed stochastic block models (SBMs). The theoretical analysis predicts the performances of GCNs in high-dimensional limits, showing that while consistent, they do not achieve Bayes-optimal rates. The study compares different data models and loss functions, highlighting the impact of regularization on test accuracy. Additionally, it delves into convergence rates and the influence of signal-to-noise ratio on performance.
Introduction:
Theoretical understanding of generalization properties in graph neural networks.
Challenges in reaching Bayes-optimal rates for GCNs.
Data Models and Setup:
Attributed SBMs used for training GCNs.
Analysis of features and labels in CSBM and GLM-SBM models.
Analyzed GCN Architecture:
Single-layer GCN with specific transformations and regularization.
Empirical risk minimization approach for training.
Results and Rates:
Predicted test accuracies based on different loss functions and regularization strengths.
Comparison to Bayes-optimal performances.
Insights into learning rates at high signal-to-noise ratios.
Citater
"The long-term promise drives efforts to establish tight asymptotic analysis in broader settings."
"GCNs show practical applications but struggle to reach Bayes-optimal rates."