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We first prove spectral convergence of the random feature method (RFM) for multidimensional targets in Sobolev, Gevrey, ultra-analytic, and bandlimited classes. The analysis establishes general high-probability approximation estimates in the interpolation scale generated by a kernel integral operator. On a single event...
We establish sharp mixed spectral Barron regularity for eigenfunctions of molecular Coulomb Hamiltonians. The mixed norm is a Fourier $L^1$ norm with one isotropic weight and coordinate-product weights, and therefore detects regularity invisible to the isotropic Barron scale. For a nonempty set $I$ of electron indices...
It is proved that the Hypergraph Neural Network, an invariant architecture with 3-body message passing, is a universal approximator for potential energy surfaces and provides the first rigorous justification for the common practice of using multi-layer message passing with a per-layer cutoff smaller than the physical i...
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