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arXiv · 2006.13782

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

Francis Williams·Matthew Trager·Joan Bruna·Denis Zorin
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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.

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Francis Williams, Matthew Trager, Joan Bruna, Denis Zorin. 2020-06-24. Neural Splines: Fitting 3D Surfaces with Infinitely-Wide Neural Networks. https://arxiv.org/abs/2006.13782

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