Steerable convolutional neural networks (CNNs) provide a general framework for building neural networks equivariant to translations and other transformations belonging to an origin-preserving group $G$, such as reflections and rotations. They rely on standard convolutions with $G$-steerable kernels obtained by analytically solving the group-specific equivariance constraint imposed onto the kernel space. As the solution is tailored to a particular group $G$, the implementation of a kernel basis does not generalize to other symmetry transformations, which complicates the development of general group equivariant models. We propose using implicit neural representation via multi-layer perceptrons (MLPs) to parameterize $G$-steerable kernels. The resulting framework offers a simple and flexible way to implement Steerable CNNs and generalizes to any group $G$ for which a $G$-equivariant MLP can be built. We prove the effectiveness of our method on multiple tasks, including N-body simulations, point cloud classification and molecular property prediction.

翻译：可转向卷积神经网络（CNN）为构建对平移及其他属于原点保持群$G$（如反射和旋转）等变换等变的神经网络提供了通用框架。该框架通过解析求解施加于核空间上的群特定等变性约束，得到标准卷积所需的$G$可转向核。由于解是针对特定群$G$定制的，核基底的实现无法泛化至其他对称变换，这使通用群等变模型的开发变得复杂。我们提出通过多层感知机（MLP）使用隐式神经表示来参数化$G$可转向核。所得框架提供了一种简单灵活的实现可转向CNN的方法，并能泛化至任何可构建$G$等变MLP的群$G$。我们通过多项任务（包括N体模拟、点云分类和分子属性预测）证明了该方法的有效性。