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This paper develops a Fourier analysis framework to study data augmentation under group invariances, showing that partial augmentation can achieve the same minimax rates as full augmentation up to a vanishing approximation error, while also proving that exact invariance requires full group averaging.
This paper analyzes oversmoothing in Neural Sheaf Diffusion (NSD) as a representation degeneracy phenomenon using quiver theory and Geometric Invariant Theory. It proposes moment-map-inspired regularizers and explores non-uniform stalk dimensions to mitigate this issue in heterophilic graph benchmarks.