מרחב קרן הילברט המכללי: פולינומים ומרחק IMQ

תקציר מקורי באנגליתarXiv:2605.03262v2 Announce Type: replace Abstract: Inverse-multiquadric (IMQ) kernel sections decay at infinity. Can polynomial alignment add persistent directional responses while preserving universal approximation? The \yat{} (Yat) kernel answers this question by multiplying IMQ distance by a biased squared inner product. With shared positive bias and regularization, its RKHS continuously contains the IMQ RKHS and is universal on every compact domain. Alignment strictly enlarges the global function space: Yat sections retain a quadratic directional trace at infinity. We quantify a second distinction through high-dimensional activation covariance. For a fixed number of orthogonal unit centers and fixed kernel parameters, isotropic Gaussian inputs yield a rank-one rescaled limiting covari