Canonization produces generalization bounds ranging from invariant-optimal to non-invariant depending on regularity, with Hilbert-curve ordering proven to give polynomial covering-number growth for point clouds while lexicographic sorting gives exponential growth.
Survey on generaliza- tion theory for graph neural networks
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A new PAC-Bayesian framework for GCNs derives a family of generalization bounds that embed graph topology via structured sensitivity matrices from spatial and spectral perspectives, recovering prior bounds as special cases while claiming tighter results.
ALL-IN projects node features to a random shared space and uses covariance operators to produce representations invariant to input feature permutations and orthogonal transformations, enabling transfer across graph datasets.
The authors develop a two-stage orthogonal learning framework using graph neural networks to estimate heterogeneous direct and spillover causal effects on networks, along with bootstrap-based uncertainty quantification.
A probabilistic graphical model framework with graph neural network inference computes Bayesian posteriors for discrete structural states, claimed to match traditional Bayesian results while scaling to high-dimensional problems via topology-informed learning and scale-adaptive training.
citing papers explorer
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When and How to Canonize: A Generalization Perspective
Canonization produces generalization bounds ranging from invariant-optimal to non-invariant depending on regularity, with Hilbert-curve ordering proven to give polynomial covering-number growth for point clouds while lexicographic sorting gives exponential growth.
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Topology-Aware PAC-Bayesian Generalization Analysis for Graph Neural Networks
A new PAC-Bayesian framework for GCNs derives a family of generalization bounds that embed graph topology via structured sensitivity matrices from spatial and spectral perspectives, recovering prior bounds as special cases while claiming tighter results.
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Bridging Input Feature Spaces Towards Graph Foundation Models
ALL-IN projects node features to a random shared space and uses covariance operators to produce representations invariant to input feature permutations and orthogonal transformations, enabling transfer across graph datasets.
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Estimating Heterogeneous Causal Effect on Networks via Orthogonal Learning
The authors develop a two-stage orthogonal learning framework using graph neural networks to estimate heterogeneous direct and spillover causal effects on networks, along with bootstrap-based uncertainty quantification.
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Probabilistic Graphical Model using Graph Neural Networks for Bayesian Inversion of Discrete Structural Component States
A probabilistic graphical model framework with graph neural network inference computes Bayesian posteriors for discrete structural states, claimed to match traditional Bayesian results while scaling to high-dimensional problems via topology-informed learning and scale-adaptive training.