SE(3) 具有完整本地框架的等同图形神经网络 (SE(3) Equivariant Graph Neural Networks with Complete Local Frames)

Group equivariance (e.g. SE(3) equivariance) is a critical physical symmetry in science, from classical and quantum physics to computational biology. It enables robust and accurate prediction under arbitrary reference transformations. In light of this, great efforts have been put on encoding this symmetry into deep neural networks, which has been shown to improve the generalization performance and data efficiency for downstream tasks. Constructing an equivariant neural network generally brings high computational costs to ensure expressiveness. Therefore, how to better trade-off the expressiveness and computational efficiency plays a core role in the design of the equivariant deep learning models. In this paper, we propose a framework to construct SE(3) equivariant graph neural networks that can approximate the geometric quantities efficiently. Inspired by differential geometry and physics, we introduce equivariant local complete frames to graph neural networks, such that tensor information at given orders can be projected onto the frames. The local frame is constructed to form an orthonormal basis that avoids direction degeneration and ensure completeness. Since the frames are built only by cross product operations, our method is computationally efficient. We evaluate our method on two tasks: Newton mechanics modeling and equilibrium molecule conformation generation. Extensive experimental results demonstrate that our model achieves the best or competitive performance in two types of datasets.

翻译：群体等同( 例如 SE(3) equality) 是科学中从古典和量子物理到计算生物学的关键物理对称。它使得在任意的参考转换下能够进行稳健和准确的预测。有鉴于此, 已经为将这种对称编码入深神经网络做出了巨大努力, 从而改进了下游任务的一般性能和数据效率。构建一个等同神经网络通常带来高计算成本以确保表达性。因此, 如何更好地权衡表达性和计算效率在设计等同深学习模型中扮演核心角色。在本文中, 我们提议了一个框架, 以构建 SE(3) 等等等异图形神经网络, 从而能够有效地接近几何数量。在不同的几何测量和物理学的启发下, 我们引入了等异的本地完全框架来绘制神经网络, 这样, 给定的阵列的阵列信息可以被预测到框架上。因此, 本地框架将形成一个或正态的基础, 避免方向下降和确保完整性。在本文中, 框架将构建成一个框架, 最佳的模型, 我们的模型只能通过双级的模型, 我们的模型, 我们的模型, 我们的模型, 我们的模型, 我们的模型, 我们的模型将实现我们的的模型, 我们的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的和的的的的的的的的和的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的和的的的的的的的的的的的的的的的的的的的