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Research questionHow can random-feature spaces achieve spectral accuracy for multidimensional targets and elliptic PDEs while controlling ill-conditioning?Increasing feature richness can produce very rapid approximation of smooth multidimensional functions, but the resulting random-feature matrices may become severely ill-conditioned. The same spectral behavior therefore affects both function approximation and discretized elliptic PDE solutions.
Machine Learning
Neural and Evolutionary Computing
Research Paper
Statistical Machine Learning
Latest papersRecent research connected to this question, newest first.Spectral Convergence of Random Feature Method in Multiple DimensionsThe results concern random feature methods for Sobolev, Gevrey, ultra-analytic, and bandlimited multidimensional targets. They provide high-probability approximation estimates, strong- and weak-form discretization bounds for second-order elliptic problems, and singular-value decay and condition-number lower bounds for Fourier and tanh features under regularity-adapted and uniform growing-window distributions. The evidence is theoretical and does not specify empirical deployment behavior.research paper · Sep 3, 2026
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