  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.
