Data efficiency in graph networks through equivariance

TL;DR

This paper presents a new graph network architecture that is equivariant to geometric transformations, significantly improving data efficiency and generalization in learning tasks involving spatial data.

Contribution

The paper introduces a novel equivariant graph network architecture that handles transformations like Euclidean and conformal groups, enhancing data efficiency and inductive bias.

Findings

The model is highly data-efficient, requiring less training data to generalize.

It achieves perfect generalization on synthetic tasks with minimal data.

Compared to standard models, it needs much less data for similar performance.

Abstract

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.