论文标题
分层结构的模棱两可地图
Equivariant Maps for Hierarchical Structures
论文作者
论文摘要
在使用不变和模棱两可的地图时，可以将深度学习应用于一系列原始数据结构，而处理层次结构的形式主义是缺乏的。这是一个重要的问题，因为许多实用结构是简单构建基础的层次结构。一些示例包括集的序列，图形图或多分辨率图像。观察层次结构的对称性是构建块对称性的“花圈产物”，我们使用构建块的均值线性层的直观组合来表达层次结构的层次图。更笼统地，我们表明，任何层次结构的任何模棱两可的地图都有此形式。为了证明这种模型设计方法的有效性，我们考虑了其在点云数据的语义分割中的应用。通过对点云的素化，我们将翻译和置换对称性的层次结构施加在数据上，并在Semantic3d，S3DIS和Vkitti上报告最新的，其中包括一些最大的现实点云基准测试。
While using invariant and equivariant maps, it is possible to apply deep learning to a range of primitive data structures, a formalism for dealing with hierarchy is lacking. This is a significant issue because many practical structures are hierarchies of simple building blocks; some examples include sequences of sets, graphs of graphs, or multiresolution images. Observing that the symmetry of a hierarchical structure is the "wreath product" of symmetries of the building blocks, we express the equivariant map for the hierarchy using an intuitive combination of the equivariant linear layers of the building blocks. More generally, we show that any equivariant map for the hierarchy has this form. To demonstrate the effectiveness of this approach to model design, we consider its application in the semantic segmentation of point-cloud data. By voxelizing the point cloud, we impose a hierarchy of translation and permutation symmetries on the data and report state-of-the-art on Semantic3D, S3DIS, and vKITTI, that include some of the largest real-world point-cloud benchmarks.
