可旋转核的基础：从2D旋转到洛伦兹群的等变CNN
Bases of Steerable Kernels for Equivariant CNNs: From 2D Rotations to the Lorentz Group
AI总结：
本文提出了一种解决可旋转核约束的新方法，提供不同对称群和任意张量类型的特征图基础。该方法通过直接使用输入和输出特征图的表示，避免计算克莱布施-戈尔丹系数，简化了等变卷积神经网络的设计。
摘要：
我们提出了一种解决可旋转核约束的新方法，提供不同对称群和任意张量类型的特征图基础。该方法的主要优势是避免了计算克莱布施-戈尔丹系数的需要，直接使用输入和输出特征图的表示。策略是找到在某些点$x_0$处具有更简单不变性条件的核基，然后通过定义方程将该基旋转到任意点$x=g\cdot x_0$。这一想法已在文献中提及，但未深入探讨。本文通过最小的技术工具描述其工作原理，使其对一般受众易于理解。
英文摘要：
We present an alternative way of solving the steerable kernel constraint that appears in the design of steerable equivariant convolutional neural networks. We find explicit real and complex bases which are ready to use, for different symmetry groups and for feature maps of arbitrary tensor type. A major advantage of this method is that it bypasses the need to numerically or analytically compute Clebsch-Gordan coefficients and works directly with the representations of the input and output feature maps. The strategy is to find a basis of kernels that respect a simpler invariance condition at some point $x_0$, and then \textit{steer} it with the defining equation of steerability to move to some arbitrary point $x=g\cdot x_0$. This idea has already been mentioned in the literature before, but not advanced in depth and with some generality. Here we describe how it works with minimal technical tools to make it accessible for a general audience.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
