Unverified50% confidenceFactExact time
The paper proves that the eigenpair convergence rate of a manifold-agnostic graph Laplacian estimator to the tensorized Laplace-Beltrami operator is n^{-1/(2.5d-1)} (ignoring logarithmic factors).
1
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50%
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Long-term
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10/14/2026
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Related Claims
UnverifiedThe eigenvalues and eigenvectors of the graph Laplacian matrix converge to the spectrum of the Laplace-Beltrami operator on the manifold as the sample size tends to infinity.70% similarUnverifiedFor polynomial activation functions and arbitrary compact input sets, this lifting gives a rate of m^{-1/2} under the supremum norm, with an explicit constant.65% similarUnverifiedThe paper proves that the logarithmic factor appearing in previous risk bounds is not essential and can be completely eliminated, thereby improving the convergence rate to O(1/√N), consistent with the classical law of large numbers.63% similarUnverifiedThe error bound in this paper holds for all Wasserstein-p distances with p ≥ 1, rather than being limited to a specific metric.63% similarUnverifiedWhen d is much greater than n, the minimum-norm solution can be selected via the Moore-Penrose pseudoinverse X^T(XX^T)⁻¹y, and the stability of the solution is improved.62% similar
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