Efficient Long-Range Convolutions for Point Clouds
Efficient Long-Range Convolutions for Point Clouds
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DOI：
10.1016/j.jcp.2022.111692
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发表时间：
2020-10
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影响因子：
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通讯作者：
Yifan Peng;Lin Lin-Lin;Lexing Ying;Leonardo Zepeda-N'unez
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文献类型：
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作者：
Yifan Peng;Lin Lin-Lin;Lexing Ying;Leonardo Zepeda-N'unez
在许多科学机器学习应用中，有效处理点云的远程交互（LRI）是一个具有挑战性的问题。为了提取全局信息，通常需要大的窗口大小、大量的层和/或大量的通道。这通常会显着增加计算成本。在这项工作中，我们提出了一种新颖的神经网络层，它直接合并点云的远程信息。该层被称为远程卷积（LRC）层，利用卷积定理与非均匀傅里叶变换相结合。简而言之，LRC 层将点云软化为足够大小的规则网格，计算其傅里叶变换，将结果乘以一组可训练的傅里叶乘法器，计算逆傅里叶变换，最后将结果插值回点云。由此产生的全局全对全卷积运算可以在关于输入点的数量的近线性时间内渐进地执行。当与局部卷积结合时，LRC 层是一个特别强大的工具，因为它们一起提供了短程和长程交互的高效和无缝处理。我们通过引入一种神经网络架构来展示该框架，该架构将 LRC 层与短程卷积层相结合，以准确地学习与 N 体势相关的能量和力。我们还利用诱导的两级分解，并提出了一种有效的策略来训练具有减少样本数量的组合架构。
The efficient treatment of long-range interactions (LRIs) for point clouds is a challenging problem in many scientific machine learning applications. To extract global information, one usually needs a large window size, a large number of layers, and/or a large number of channels. This can often significantly increase the computational cost. In this work, we present a novel neural network layer that directly incorporates long-range information for a point cloud. This layer, dubbed thelong-range convolutional(LRC)-layer, leverages the convolutional theorem coupled with the non-uniform Fourier transform. In a nutshell, the LRC-layer mollifies the point cloud to an adequately sized regular grid, computes its Fourier transform, multiplies the result by a set of trainable Fourier multipliers, computes the inverse Fourier transform, and finally interpolates the result back to the point cloud. The resulting global all-to-all convolution operation can be performed in nearly-linear time asymptotically with respect to the number of input points. The LRC-layer is a particularly powerful tool when combined with local convolution as together they offer efficient and seamless treatment of both short- and long-range interactions. We showcase this framework by introducing a neural network architecture that combines LRC-layers with short-range convolutional layers to accurately learn the energy and force associated with aN-body potential. We also exploit the induced two-level decomposition and propose an efficient strategy to train the combined architecture with a reduced number of samples.