Symmetry-driven graph neural networks
This work addresses the challenge of enhancing inductive biases and generalization for graph-based machine learning tasks, particularly in domains with geometric symmetries, though it is incremental in building on existing equivariance concepts.
The paper tackles the problem of improving generalization and data efficiency in graph neural networks by exploiting symmetries and invariance in data, introducing two architectures equivariant to Euclidean and conformal transformations, and demonstrates their capabilities on synthetic geometric datasets with increased data efficiency.
Exploiting symmetries and invariance in data is a powerful, yet not fully exploited, way to achieve better generalisation with more efficiency. In this paper, we introduce two graph network architectures that are equivariant to several types of transformations affecting the node coordinates. First, we build equivariance to any transformation in the coordinate embeddings that preserves the distance between neighbouring nodes, allowing for equivariance to the Euclidean group. Then, we introduce angle attributes to build equivariance to any angle preserving transformation - thus, to the conformal group. Thanks to their equivariance properties, the proposed models can be vastly more data efficient with respect to classical graph architectures, intrinsically equipped with a better inductive bias and better at generalising. We demonstrate these capabilities on a synthetic dataset composed of $n$-dimensional geometric objects. Additionally, we provide examples of their limitations when (the right) symmetries are not present in the data.