Most existing neural networks for learning graphs address permutation
invariance by conceiving of the network as a message passing scheme, where each
node sums the feature vectors coming from its neighbors. We argue that this
imposes a limitation on their representation power, and instead propose a new
general architecture for representing objects consisting of a hierarchy of
parts, which we call Covariant Compositional Networks (CCNs). Here, covariance
means that the activation of each neuron must transform in a specific way under
permutations, similarly to steerability in CNNs. We achieve covariance by
making each activation transform according to a tensor representation of the
permutation group, and derive the corresponding tensor aggregation rules that
each neuron must implement. Experiments show that CCNs can outperform competing
methods on standard graph learning benchmarks.

提出了一种新的用于表示图对象的协变组合网络 (Covariant Compositional Networks, CCNs) 模型，采用张量表示的置换群，并引入相应的张量聚合规则来实现协变。实验结果表明，CCN 模型在标准图学习基准测试中优于竞争算法。