论文标题
神经花纹：与无限宽的神经网络拟合3D表面
Neural Splines: Fitting 3D Surfaces with Infinitely-Wide Neural Networks
论文作者
论文摘要
我们提出了神经花纹，这是一种基于无限宽浅层恢复网络引起的随机特征内核的3D表面重建技术。我们的方法实现了最新的结果，表现优于最新的基于神经网络的技术和广泛使用的泊松表面重建（正如我们所证明的那样，这也可以被视为一种核方法）。由于我们的方法基于简单的内核公式，因此很容易分析，并且可以通过为基于内核的学习设计的一般技术加速。我们为内核提供了明确的分析表达式，并认为我们的配方可以看作是对更高维度的立方样条插值的概括。特别是，与神经花纹有关的RKHS规范偏向光滑的插值。
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.
