Manifold limit for the training of shallow graph convolutional neural networks

arXiv:2601.06025 · stat.ML, cs.LG, math.FA, math.OC · Submitted 2026-01-09 · Read on arXiv

stat.ML, cs.LG, math.FA, math.OC

Submitted: 2026-01-09

Updated: 2026-09-25

Terminology

• Consistency — 20× in this paper · explained in 3 episodes
• Spectral Gap — 10× in this paper · explained in 5 episodes
• Activation Function — 8× in this paper · explained in 1 episode
• Transferability — 8× in this paper · explained in 4 episodes
• Generalization — 6× in this paper · explained in 13 episodes
• Loss Function — 6× in this paper · explained in 2 episodes
• Semi-supervised Learning — 5× in this paper · explained in 4 episodes
• Clustering — 3× in this paper · explained in 2 episodes
• Hilbert Space — 3× in this paper · explained in 2 episodes
• Point Clouds — 3× in this paper · explained in 2 episodes
• Regularization — 3× in this paper · explained in 3 episodes
• Gradient Flow — 2× in this paper · explained in 2 episodes
• -convergence — 1× in this paper · explained in 1 episode
• Curse of Dimensionality — 1× in this paper · explained in 6 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• GNNs — 1× in this paper · explained in 2 episodes
• Generalization Bounds — 1× in this paper · explained in 2 episodes
• Hypernetwork — 1× in this paper · explained in 3 episodes
• Intrinsic Dimension — 1× in this paper · explained in 2 episodes
• Inverse Problem — 1× in this paper · explained in 2 episodes
• Optimal Transport — 1× in this paper · explained in 5 episodes
• Sparsity — 1× in this paper · explained in 4 episodes
• Spectral clustering — 1× in this paper · explained in 2 episodes
• Wasserstein Distance — 1× in this paper · explained in 4 episodes

Sources

• Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges
• Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators

Related papers

• Behavior of prediction performance metrics with rare events
• Optimal Estimation of Generic Dynamics by Path-Dependent Neural Jump ODEs
• A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priors
• One Permutation Is All You Need: Fast, Deterministic Feature Importance and Model Stress-Testing
• Online Conformal Prediction for Non-Exchangeable Panel Data
• Deep Time-Series Forecasting in 10 Years: A Survey