发表机构
NVIDIA Corporation; California Institute of Technology（英伟达公司; 加州理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对球面数据处理的机器学习需求，提出torch-harmonics库，提供高效可微的球谐变换、卷积和注意力机制，支持可扩展的旋转感知学习。
AI 中文摘要
嵌入三维欧几里得空间中的二维球面S2，在地球物理学、行星科学、大地测量学、大气物理学、量子化学、宇宙学以及虚拟现实等众多科学与工程领域中扮演着核心角色。随着机器学习日益渗透到这些领域，对能够处理球面上函数并建模、同时尊重该域固有拓扑和对称性质的稳健工具的需求不断增长。我们提出了torch-harmonics，这是一个全面的库，为球面数据提供高效、可微的先进信号处理和机器学习（ML）方法的实现。这些方法包括球谐变换（SHT），即傅里叶变换的球面对应物、矢量球谐函数、离散-连续和谱卷积，以及全局和邻域球面注意力机制。除了传统表示之外，torch-harmonics还为最先进的球面ML架构（如球面变换器）提供了构建模块，以在现代科学与工程应用中实现可扩展的、具有旋转感知的学习和推理。
英文摘要
The two-dimensional sphere embedded in three-dimensional Euclidean space S2, plays a central role in a variety of scientific and engineering domains, including geophysics, planetary science, geodesy, atmospheric physics, quantum chemistry, cosmology, and virtual reality, among many others. As machine learning increasingly permeates these fields, the demand grows for robust tools that process and model functions on the sphere, while respecting the inherent topological and symmetry properties of the domain. We present torch-harmonics, a comprehensive library that offers efficient, differentiable implementations of advanced signal processing and machine learning (ML) methods for spherical data. These include the spherical harmonic transform (SHT), the spherical analogue of the Fourier transform, vector spherical harmonics, discrete-continuous and spectral convolutions, as well as both global and neighborhood spherical attention mechanisms. Beyond traditional representations, torch-harmonics provides the building blocks for state-of-the-art spherical ML architectures such as spherical transformers in order to enable scalable, rotationally-aware learning and inference in modern scientific and engineering applications.
