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Learning from set-structured data, such as point clouds, has gainedsignificant attention from the community. Geometric deep learning provides ablueprint for designing effective set neural networks by incorporatingpermutation symmetry. Of our interest are permutation invariant networks, whichare composed of a permutation equivariant backbone, permutation invariantglobal pooling, and regression/classification head. While existing literaturehas focused on improving permutation equivariant backbones, the impact ofglobal pooling is often overlooked. In this paper, we examine the interplaybetween permutation equivariant backbones and permutation invariant globalpooling on three benchmark point cloud classification datasets. Our findingsreveal that: 1) complex pooling methods, such as transport-based orattention-based poolings, can significantly boost the performance of simplebackbones, but the benefits diminish for more complex backbones, 2) evencomplex backbones can benefit from pooling layers in low data scenarios, 3)surprisingly, the choice of pooling layers can have a more significant impacton the model's performance than adjusting the width and depth of the backbone,and 4) pairwise combination of pooling layers can significantly improve theperformance of a fixed backbone. Our comprehensive study provides insights forpractitioners to design better permutation invariant set neural networks.

Equivariant vs. Invariant Layers: A Comparison of Backbone and Pooling for Point Cloud Classification