Data efficiency in graph networks through equivariance
This addresses data efficiency issues in graph networks for machine learning applications, though it appears incremental as it builds on existing equivariance concepts.
The authors tackled the problem of data inefficiency in graph networks by introducing a novel architecture that is equivariant to distance-preserving transformations in coordinate embeddings, specifically Euclidean and conformal orthogonal groups. They showed that their model achieves perfect generalization on unseen synthetic data with minimal training data, while standard models require much more data for comparable performance.
We introduce a novel architecture for graph networks which is equivariant to any transformation in the coordinate embeddings that preserves the distance between neighbouring nodes. In particular, it is equivariant to the Euclidean and conformal orthogonal groups in $n$-dimensions. Thanks to its equivariance properties, the proposed model is extremely more data efficient with respect to classical graph architectures and also intrinsically equipped with a better inductive bias. We show that, learning on a minimal amount of data, the architecture we propose can perfectly generalise to unseen data in a synthetic problem, while much more training data are required from a standard model to reach comparable performance.