  We show that minimum-norm interpolation in the Reproducing Kernel Hilbert
Space corresponding to the Laplace kernel is not consistent if input dimension
is constant. The lower bound holds for any choice of kernel bandwidth, even if
selected based on data. The result supports the empirical observation that
minimum-norm interpolation (that is, exact fit to training data) in RKHS
generalizes well for some high-dimensional datasets, but not for
low-dimensional ones.
