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.

通过引入一种新颖的图网络架构，它对于保持相邻节点距离的所有坐标嵌入的任何变换都具有等变性，特别是在 $n$- 维中具有欧几里得和共形正交群等变性，从而使得所提出的模型相对于传统图形架构更加数据高效，并且本质上配备了更好的归纳偏差。我们表明，通过少量数据的学习，我们提出的架构可以完全推广到合成问题中的未见数据，而标准模型需要更多的训练数据才能达到可比较的性能。