Group Equivariant Conditional Neural Processes
Group Equivariant Conditional Neural Processes
复制标题
DOI：
--
复制
发表时间：
2021-02
期刊：
影响因子：
--
通讯作者：
M. Kawano;Wataru Kumagai;Akiyoshi Sannai;Yusuke Iwasawa;Y. Matsuo
中科院分区：
文献类型：
--
作者：
M. Kawano;Wataru Kumagai;Akiyoshi Sannai;Yusuke Iwasawa;Y. Matsuo
提出了群等变条件神经过程（equivariant conditional neural process, EquivCNP），这种元学习方法在数据集上与传统条件神经过程一样具有排列不变性，并且在数据空间上具有变换等变性。结合群等方差，如旋转和缩放等方差，提供了一种考虑真实世界数据对称性的方法。我们给出了置换不变映射和群等变映射的分解定理，从而构造了具有无限维潜在空间的等变映射来处理群对称。在本文中，我们使用李群卷积层来构建架构以进行实际实现。我们表明，在一维回归任务中，具有平移等方差的EquivCNP达到了与传统cnp相当的性能。此外，我们证明了结合适当的李群等方差，EquivCNP能够通过选择适当的李群等方差对图像补全任务进行零次泛化。
We present the group equivariant conditional neural process (EquivCNP), a metalearning method with permutation invariance in a data set as in conventional conditional neural processes (CNPs), and it also has transformation equivariance in data space. Incorporating group equivariance, such as rotation and scaling equivariance, provides a way to consider the symmetry of real-world data. We give a decomposition theorem for permutation-invariant and group-equivariant maps, which leads us to construct EquivCNPs with an infinite-dimensional latent space to handle group symmetries. In this paper, we build architecture using Lie group convolutional layers for practical implementation. We show that EquivCNP with translation equivariance achieves comparable performance to conventional CNPs in a 1D regression task. Moreover, we demonstrate that incorporating an appropriate Lie group equivariance, EquivCNP is capable of zero-shot generalization for an image-completion task by selecting an appropriate Lie group equivariance.