Learning from set-structured data, such as point clouds, has gained significant attention from the community. Geometric deep learning provides a blueprint for designing effective set neural networks by incorporating permutation symmetry. Of our interest are permutation invariant networks, which are composed of a permutation equivariant backbone, permutation invariant global pooling, and regression/classification head. While existing literature has focused on improving permutation equivariant backbones, the impact of global pooling is often overlooked. In this paper, we examine the interplay between permutation equivariant backbones and permutation invariant global pooling on three benchmark point cloud classification datasets. Our findings reveal that: 1) complex pooling methods, such as transport-based or attention-based poolings, can significantly boost the performance of simple backbones, but the benefits diminish for more complex backbones, 2) even complex backbones can benefit from pooling layers in low data scenarios, 3) surprisingly, the choice of pooling layers can have a more significant impact on the model's performance than adjusting the width and depth of the backbone, and 4) pairwise combination of pooling layers can significantly improve the performance of a fixed backbone. Our comprehensive study provides insights for practitioners to design better permutation invariant set neural networks.

翻译：从集合结构数据（例如点云）中学习已引起学术界的广泛关注。几何深度学习通过融入置换对称性，为设计高效的集合神经网络提供了蓝图。我们关注的是置换不变网络，它由置换等变骨干网络、置换不变全局池化层以及回归/分类头组成。尽管现有研究侧重于改进置换等变骨干网络，但全局池化的影响常被忽视。本文在三个基准点云分类数据集上，系统考察了置换等变骨干网络与置换不变全局池化之间的相互作用。研究发现：1）基于输运或注意力等复杂池化方法能显著提升简单骨干网络的性能，但对于复杂骨干网络，这种增益会减弱；2）在低数据量场景下，即使复杂骨干网络也能从池化层中获益；3）令人惊讶的是，选择不同的池化层对模型性能的影响，可能比调整骨干网络的宽度和深度更为显著；4）将多个池化层进行组合配对，可显著提升固定骨干网络的性能。本研究为实践者设计更优的置换不变集合神经网络提供了系统性的见解。