用几何方法重新推导可旋转卷积，更直观且抗噪更强。
A Geometric Approach to Steerable Convolutions
- 基于几何与模式匹配原理，直观推导可旋转卷积
- 提出基于插值核的新构造方式，提升对噪声数据的鲁棒性
- 解释了球谐基与克莱布施-戈登分解的几何来源
与多数论文采用的抽象群论方法不同，本文从几何角度出发，在d维空间中提供了一种更直观的可旋转卷积神经网络推导。该推导基于模式匹配的基本原理，直观解释了克莱布施-戈登分解和球谐基函数的出现原因。此外，我们提出一种基于插值核的新方法构建可旋转卷积层，相比现有实现具有更好的噪声鲁棒性。
原文摘要 · Abstract (English)
In contrast to the somewhat abstract, group theoretical approach adopted by many papers, our work provides a new and more intuitive derivation of steerable convolutional neural networks in $d$ dimensions. This derivation is based on geometric arguments and fundamental principles of pattern matching. We offer an intuitive explanation for the appearance of the Clebsch--Gordan decomposition and spherical harmonic basis functions. Furthermore, we suggest a novel way to construct steerable convolution layers using interpolation kernels that improve upon existing implementation, and offer greater robustness to noisy data.
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