  We present the group equivariant conditional neural process (EquivCNP), a
meta-learning 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.
