提出可处理球面标量与矢量场的旋转等变神经网络，突破传统模型限制。
SO(3)-Equivariant Neural Networks for Learning from Scalar and Vector Fields on Spheres
- 基于SO(3)群傅里叶卷积构建等变架构，支持更丰富的卷积核与激活函数
- 在球面数据上性能优于标准CNN，多数任务接近或超越spherical CNN
- 适用于含不同自旋信息的多类型球面信号，适合气候、地理等科学建模
分析球面上的标量与矢量场（如地球温度或风速风向）具有挑战性。模型需同时尊重球面的旋转对称性及矢量场固有的对称性。现有等变模型通过三维旋转群（SO(3)）在傅里叶空间进行卷积，但受限于卷积核与非线性函数的选择。本文提出一种新深度学习架构，突破此限制，支持更丰富的卷积核与激活函数。该架构适用于包含标量和矢量场的球面信号，因其可被描述为SO(3)群上的等变信号。实验表明，该架构在多数任务上优于标准CNN，常达到或超过同等条件下spherical CNN的性能；然而优势并非在所有任务中一致，且在隐藏层引入不同自旋间交互可缩小与sCNN的差距。
原文摘要 · Abstract (English)
Analyzing scalar and vector fields on the sphere, such as temperature or wind speed and direction on Earth, is a difficult task. Models should respect both the rotational symmetries of the sphere and the inherent symmetries of the vector fields. A class of equivariant models has emerged, which process these spherical signals by applying group convolutions in Fourier space with respect to the three-dimensional rotation group. However, the proposed models are constrained in the choice of convolution kernels and nonlinearities in order to preserve the desired signal properties. In this paper, we introduce a deep learning architecture without these limitations, thus with a richer class of convolution kernels and activation functions. This architecture is suitable for signals consisting of both scalar and vector fields on the sphere, as they can be described as equivariant signals on the three-dimensional rotation group. Experiments show that this architecture generally outperforms standard CNNs and often matches or exceeds the performance of spherical CNNs trained under comparable conditions. However, the advantage over sCNNs is not uniform across all tasks and we observe that incorporating the interaction between different spins in the hidden layers narrows this gap.
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