Group Equivariant Conditional Neural Processes
This work addresses the need for symmetry-aware models in machine learning, particularly for real-world data with inherent symmetries, though it appears incremental as it builds on existing conditional neural processes.
The authors tackled the problem of incorporating symmetry transformations like rotations and scalings into meta-learning models by introducing the group equivariant conditional neural process (EquivCNP), which achieves comparable performance to conventional CNPs in 1D regression and enables zero-shot generalization in image completion tasks.
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.