Group Equivariant Conditional Neural Processes

Makoto Kawano, Wataru Kumagai, Akiyoshi Sannai, Yusuke Iwasawa, Yutaka Matsuo

Keywords: Neural Processes, Conditional Neural Processes, Stochastic Processes, Regression, Group Equivariance, Symmetry

Abstract: 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.

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One-sentence Summary: A model for regression that learns conditional distributions of a stochastic process, by incorporating group equivariance into Conditional Neural Processes.

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2102.08759/code)