Steerable convolutional neural networks (CNNs) provide a general framework for building neural networks equivariant to translations and transformations of 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 $G$, implementing a kernel basis does not generalize to other symmetry transformations, complicating 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：可操控卷积神经网络（CNNs）提供了一个通用框架，用于构建对平移及原点保持群 $G$（如反射和旋转）的变换等变的神经网络。该框架依赖于通过解析求解施加于核空间的群特定等变约束而获得的 $G$-可操控核的标准卷积。由于该解是针对特定群 $G$ 定制的，实现一个核基无法推广到其他对称变换，从而增加了开发通用群等变模型的复杂性。我们提出使用基于多层感知器（MLPs）的隐式神经表示来参数化 $G$-可操控核。所提出的框架提供了一种简单灵活的方式来实现可操控CNNs，并能推广到任何可构建 $G$-等变MLP的群 $G$。我们通过多项任务（包括N体模拟、点云分类和分子性质预测）证明了我们方法的有效性。