Symmetry-driven graph neural networks
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Abstract (arXiv)
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.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 29 of its 42 references that are in the map. First posted on arXiv 28 May 2021.
Builds on
29 of 42 references.
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17 more
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