提出可旋转卷积核的通用基底构造方法，免去复杂系数计算。
Bases of Steerable Kernels for Equivariant CNNs: From 2D Rotations to the Lorentz Group
- 基于对称点处的简单不变性，通过旋转变换生成任意点的核基底。
- 直接使用输入输出特征表示，跳过克莱布希-戈登系数的计算。
- 方法简洁通用，适合希望快速实现等变CNN的研究者。
本文提出一种求解可旋转卷积核约束的新方法，适用于不同对称群及任意张量类型的特征图。该方法的核心是先在某点 $x_0$ 构造满足简化不变性条件的核基底，再通过可旋转性定义方程将基底“旋动”至任意点 $x = g ullet x_0$。相比传统依赖克莱布希-戈登系数的数值或解析计算，本方法直接基于输入与输出特征的表示，大幅降低实现复杂度。尽管该思想早有提及，但此前未被深入推广。本文以最小技术门槛阐明其通用性，旨在使等变卷积神经网络的设计更易理解与应用。
原文摘要 · Abstract (English)
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.
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