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arXiv AI By Pingbing Ming, Hao Yu

Spectral Convergence of Random Feature Method in Multiple Dimensions

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The paper proves spectral convergence of the random feature method (RFM) for multidimensional targets across various function classes, providing high‑probability approximation estimates that hold simultaneously for all admissible error norms. It extends these results to strong‑ and weak‑form RFM discretizations, yielding convergence guarantees for multidimensional second‑order elliptic boundary value and eigenvalue problems. Additionally, it demonstrates super‑exponential singular‑value decay for Fourier features and exponential decay for tanh features, while establishing corresponding condition‑number lower bounds, highlighting a trade‑off between accuracy and ill‑conditioning.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv AI.

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