Neural Splines: Fitting 3D Surfaces with Infinitely-Wide Neural Networks
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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 Screened Poisson Surface Reconstruction and modern neural network based techniques. Because our approach is based on a simple kernel formulation, it is fast to run and easy to analyze. 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 our kernel biases toward smooth interpolants. Finally, we formulate Screened Poisson Surface Reconstruction as a kernel method and derive an analytic expression for its norm in the corresponding RKHS.
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