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.

介绍了一种基于无限宽的 ReLU 神经网络随机特征内核的 3D 表面重建技术，它能够超越最近的神经网络技术和 Poisson 表面重建方法，提供了一种简单且易于分析的内核公式，并证明其为更高维度的三次样条插值的推广。

神经样条：用无限宽神经网络拟合三维曲面

Neural Splines: Fitting 3D Surfaces with Infinitely-Wide Neural Networks

On the space of probability densities, we extend the Wasserstein geodesics to
the case of higher-order interpolation such as cubic spline interpolation.
After presenting the natural extension of cubic splines to the Wasserstein
space, we propose a simpler approach based on the relaxation of the variational
problem on the path space. We explore two different numerical approaches, one
based on multi-marginal optimal transport and entropic regularization and the
other based on semi-discrete optimal transport.

在概率密度空间中，我们将 Wasserstein 测地线扩展到更高阶的插值，如三次样条插值。我们提出了一种基于路径空间上变分问题简化松弛的方法，并探索了两种不同的数值方法，一种基于多重边际最优运输和熵正则化，另一种基于半离散最优运输。