Spectral Graph Neural Networks with Hermite Polynomials: A Comprehensive Study

arXiv:2609.28979 · cs.LG · Submitted 2026-09-24 · Read on arXiv

cs.LG

Submitted: 2026-09-24

Updated: 2026-09-24

Terminology

• Accuracy — 43× in this paper · explained in 1 episode
• Calibration — 26× in this paper · explained in 7 episodes
• Regularization — 20× in this paper · explained in 3 episodes
• Ablation — 9× in this paper · explained in 1 episode
• Benchmark — 8× in this paper · explained in 2 episodes
• Adam — 7× in this paper · explained in 2 episodes
• Alignment — 5× in this paper · explained in 1 episode
• GNNs — 3× in this paper · explained in 2 episodes
• Error Decomposition — 2× in this paper · explained in 3 episodes
• Sparsity — 2× in this paper · explained in 4 episodes
• Trace — 2× in this paper · explained in 2 episodes
• Aggregation — 1× in this paper · explained in 1 episode
• Contrastive Learning — 1× in this paper · explained in 5 episodes
• Graph Construction — 1× in this paper · explained in 3 episodes
• Over-smoothing — 1× in this paper · explained in 4 episodes
• Over-squashing — 1× in this paper · explained in 3 episodes
• Pruning — 1× in this paper · explained in 4 episodes

Sources

• Beyond Low-frequency Information in Graph Convolutional Networks
• Adaptive Universal Generalized PageRank Graph Neural Network
• Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering
• Stability Properties of Graph Neural Networks
• Predict then Propagate: Graph Neural Networks meet Personalized PageRank
• Graph Neural Networks with Learnable and Optimal Polynomial Bases
• Clenshaw Graph Neural Networks
• BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation
• Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited
• Optimizing Polynomial Graph Filters: A Novel Adaptive Krylov Subspace Approach
• Revisiting convolutional neural network on graphs with polynomial approximations of Laplace-Beltrami spectral filtering
• Semi-Supervised Classification with Graph Convolutional Networks
• Geom-GCN: Geometric Graph Convolutional Networks
• A critical look at the evaluation of GNNs under heterophily: Are we really making progress?
• PolyCF: Towards the Optimal Spectral Graph Filters for Collaborative Filtering
• Learning to Approximate Adaptive Kernel Convolution on Graphs
• ChebNet: Efficient and Stable Constructions of Deep Neural Networks with Rectified Power Units via Chebyshev Approximations
• User-friendly tail bounds for sums of random matrices
• How Powerful are Spectral Graph Neural Networks
• Shape-aware Graph Spectral Learning

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