Group Invariant Global Pooling
This work addresses a gap in developing invariant layers for symmetry-aware machine learning, offering a principled method with potential domain-specific benefits, though it appears incremental relative to existing permutation invariant pooling.
The paper tackled the problem of creating expressive invariant pooling layers for group-equivariant representations, introducing Group Invariant Global Pooling (GIGP) and showing improvements on QM9 while matching results on rotated MNIST.
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.