Much work has been devoted to devising architectures that build group-equivariant representations, while invariance is often induced using simple global pooling mechanisms. Little work has been done on creating expressive layers that are invariant to given symmetries, despite the success of permutation invariant pooling in various molecular tasks. In this work, we present Group Invariant Global Pooling (GIGP), an invariant pooling layer that is provably sufficiently expressive to represent a large class of invariant functions. We validate GIGP on rotated MNIST and QM9, showing improvements for the latter while attaining identical results for the former. By making the pooling process group orbit-aware, this invariant aggregation method leads to improved performance, while performing well-principled group aggregation.

翻译：大量工作致力于设计能够构建群等变表示的架构，而不变性通常通过简单的全局池化机制诱导产生。尽管置换不变池化在各种分子任务中取得了成功，但在创建对给定对称性具有表达力的不变层方面的工作却很少。在这项工作中，我们提出了群不变全局池化（Group Invariant Global Pooling, GIGP），这是一种不变池化层，被证明具有足够的表现力，能够表示一大类不变函数。我们在旋转MNIST和QM9上验证了GIGP，结果显示后者性能有所提升，而前者获得了相同的结果。通过使池化过程具有群轨道感知能力，这种不变聚合方法在实现原则性群聚合的同时，带来了性能的提升。