论文标题
谎言代数网络的计算表示
Computing Representations for Lie Algebraic Networks
论文作者
论文摘要
最近的工作构建了神经网络，这些神经网络与连续的对称群（例如2D和3D旋转）构建。这是使用明确的谎言组表示来得出模棱两可的内核和非线性的。我们提出了三个贡献，这些贡献是由旋转和翻译超出旋转和翻译的边界应用的三个贡献。首先，我们使用一种新颖的算法放宽了对仅考虑相关谎言代数的结构常数的新算法的显式谎言组表示的要求。其次，我们提供了一种使用这些表示形式来构建Lie-efivariant神经网络的独立方法和软件。第三，我们贡献了一个新颖的基准数据集，用于从相对论点云中分类对象，并应用我们的方法来构建与庞加莱组相等的第一个对象跟踪模型。
Recent work has constructed neural networks that are equivariant to continuous symmetry groups such as 2D and 3D rotations. This is accomplished using explicit Lie group representations to derive the equivariant kernels and nonlinearities. We present three contributions motivated by frontier applications of equivariance beyond rotations and translations. First, we relax the requirement for explicit Lie group representations with a novel algorithm that finds representations of arbitrary Lie groups given only the structure constants of the associated Lie algebra. Second, we provide a self-contained method and software for building Lie group-equivariant neural networks using these representations. Third, we contribute a novel benchmark dataset for classifying objects from relativistic point clouds, and apply our methods to construct the first object-tracking model equivariant to the Poincaré group.
