  We present Neural Splines, a technique for 3D surface reconstruction that is
based on random feature kernels arising from infinitely-wide shallow ReLU
networks. Our method achieves state-of-the-art results, outperforming recent
neural network-based techniques and widely used Poisson Surface Reconstruction
(which, as we demonstrate, can also be viewed as a type of kernel method).
Because our approach is based on a simple kernel formulation, it is easy to
analyze and can be accelerated by general techniques designed for kernel-based
learning. We provide explicit analytical expressions for our kernel and argue
that our formulation can be seen as a generalization of cubic spline
interpolation to higher dimensions. In particular, the RKHS norm associated
with Neural Splines biases toward smooth interpolants.
