用于可操控CNN的隐式卷积核
Implicit Convolutional Kernels for Steerable CNNs
AI总结：
本文提出用隐式神经表示（MLP）参数化G-可操控核，使可操控CNN能灵活推广到任意可构建等变MLP的群，并在N体模拟、点云分类和分子性质预测等任务上验证了有效性。
摘要：
可操控卷积神经网络（CNN）为构建对平移和保持原点群$G$（如反射和旋转）的变换具有等变性的神经网络提供了一个通用框架。它们依赖于标准卷积与$G$-可操控核，这些核通过解析求解施加在核空间上的群特定等变约束而获得。由于该解是针对特定群$G$定制的，实现核基无法推广到其他对称变换，这使通用群等变模型的开发变得复杂。我们提出使用通过多层感知机（MLP）实现的隐式神经表示来参数化$G$-可操控核。由此产生的框架为可操控CNN的实现提供了一种简单灵活的方式，并可推广到任何能够构建$G$-等变MLP的群$G$。我们在多个任务上证明了该方法的有效性，包括N体模拟、点云分类和分子性质预测。
英文摘要：
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.
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。
