Superiority of GNN over NN in generalizing bandlimited functions
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We constructively show, via rigorous mathematical arguments, that GNN architectures outperform those of NN in approximating bandlimited functions on compact d-dimensional Euclidean grids. We show that the former only need ℳ sampled functional values in order to achieve a uniform approximation error of O_d(2^-ℳ^1/d) and that this error rate is optimal, in the sense that, NNs might achieve worse.
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