On Learning Deep O(n)-Equivariant Hyperspheres
CoRR(2023)
摘要
In this paper, we utilize hyperspheres and regular n-simplexes and propose
an approach to learning deep features equivariant under the transformations of
nD reflections and rotations, encompassed by the powerful group of O(n).
Namely, we propose O(n)-equivariant neurons with spherical decision surfaces
that generalize to any dimension n, which we call Deep Equivariant
Hyperspheres. We demonstrate how to combine them in a network that directly
operates on the basis of the input points and propose an invariant operator
based on the relation between two points and a sphere, which as we show, turns
out to be a Gram matrix. Using synthetic and real-world data in nD, we
experimentally verify our theoretical contributions and find that our approach
is superior to the competing methods for O(n)-equivariant benchmark datasets
(classification and regression), demonstrating a favorable speed/performance
trade-off.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要