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

Abihith Kothapalli, Ashkan Shahbazi, Xinran Liu, Robert Sheng, Soheil Kolouri
Proceedings of the Geometry-grounded Representation Learning and Generative Modeling Workshop (GRaM), PMLR 251:364-380, 2024.

Abstract

Learning from set-structured data, such as point clouds, has gained significant attention from the machine learning community. Geometric deep learning provides a blueprint for designing effective set neural networks that preserve the permutation symmetry of set-structured data. 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 equivariant backbones, the impact of the pooling layer 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. Our code is available at https://github.com/mint-vu/backbone_vs_pooling.

Cite this Paper

BibTeX
@InProceedings{pmlr-v251-kothapalli24a, title = {Equivariant vs. Invariant Layers: A Comparison of Backbone and Pooling for Point Cloud Classification}, author = {Kothapalli, Abihith and Shahbazi, Ashkan and Liu, Xinran and Sheng, Robert and Kolouri, Soheil}, booktitle = {Proceedings of the Geometry-grounded Representation Learning and Generative Modeling Workshop (GRaM)}, pages = {364--380}, year = {2024}, editor = {Vadgama, Sharvaree and Bekkers, Erik and Pouplin, Alison and Kaba, Sekou-Oumar and Walters, Robin and Lawrence, Hannah and Emerson, Tegan and Kvinge, Henry and Tomczak, Jakub and Jegelka, Stephanie}, volume = {251}, series = {Proceedings of Machine Learning Research}, month = {29 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v251/main/assets/kothapalli24a/kothapalli24a.pdf}, url = {https://proceedings.mlr.press/v251/kothapalli24a.html}, abstract = {Learning from set-structured data, such as point clouds, has gained significant attention from the machine learning community. Geometric deep learning provides a blueprint for designing effective set neural networks that preserve the permutation symmetry of set-structured data. 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 equivariant backbones, the impact of the pooling layer 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. Our code is available at https://github.com/mint-vu/backbone_vs_pooling.} }
Endnote
%0 Conference Paper %T Equivariant vs. Invariant Layers: A Comparison of Backbone and Pooling for Point Cloud Classification %A Abihith Kothapalli %A Ashkan Shahbazi %A Xinran Liu %A Robert Sheng %A Soheil Kolouri %B Proceedings of the Geometry-grounded Representation Learning and Generative Modeling Workshop (GRaM) %C Proceedings of Machine Learning Research %D 2024 %E Sharvaree Vadgama %E Erik Bekkers %E Alison Pouplin %E Sekou-Oumar Kaba %E Robin Walters %E Hannah Lawrence %E Tegan Emerson %E Henry Kvinge %E Jakub Tomczak %E Stephanie Jegelka %F pmlr-v251-kothapalli24a %I PMLR %P 364--380 %U https://proceedings.mlr.press/v251/kothapalli24a.html %V 251 %X Learning from set-structured data, such as point clouds, has gained significant attention from the machine learning community. Geometric deep learning provides a blueprint for designing effective set neural networks that preserve the permutation symmetry of set-structured data. 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 equivariant backbones, the impact of the pooling layer 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. Our code is available at https://github.com/mint-vu/backbone_vs_pooling.
APA
Kothapalli, A., Shahbazi, A., Liu, X., Sheng, R. & Kolouri, S.. (2024). Equivariant vs. Invariant Layers: A Comparison of Backbone and Pooling for Point Cloud Classification. Proceedings of the Geometry-grounded Representation Learning and Generative Modeling Workshop (GRaM), in Proceedings of Machine Learning Research 251:364-380 Available from https://proceedings.mlr.press/v251/kothapalli24a.html.

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