Beyond permutation equivariance in graph networks
This work addresses a foundational issue in graph neural networks for researchers, but it is incremental as it builds on existing equivariance concepts without proven results.
The authors tackled the problem of designing graph networks that are equivariant to the Euclidean group in n-dimensions, introducing a novel architecture that includes existing variants as special cases and is expected to improve data efficiency and inductive bias, though these claims are not yet validated.
In this draft paper, we introduce a novel architecture for graph networks which is equivariant to the Euclidean group in $n$-dimensions. The model is designed to work with graph networks in their general form and can be shown to include particular variants as special cases. Thanks to its equivariance properties, we expect the proposed model to be more data efficient with respect to classical graph architectures and also intrinsically equipped with a better inductive bias. We defer investigating this matter to future work.