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

TL;DR

Neural Splines introduce a kernel-based method for 3D surface reconstruction using infinitely-wide neural networks, achieving state-of-the-art results and offering analytical insights into spline generalizations.

Contribution

The paper presents Neural Splines, a novel kernel formulation derived from infinitely-wide neural networks for 3D surface reconstruction, outperforming existing methods and enabling easier analysis.

Findings

Achieves state-of-the-art 3D surface reconstruction results.

Provides explicit kernel expressions and analytical insights.

Generalizes cubic spline interpolation to higher dimensions.

Abstract

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.