A Simple and Universal Rotation Equivariant Point-Cloud Network

Ben Finkelshtein, Chaim Baskin, Haggai Maron, Nadav Dym
Proceedings of Topological, Algebraic, and Geometric Learning Workshops 2022, PMLR 196:107-115, 2022.

Abstract

Equivariance to permutations and rigid motions is an important inductive bias for various 3D learning problems. Recently it has been shown that the equivariant Tensor Field Network architecture is universal- it can approximate any equivariant function. In this paper we suggest a much simpler architecture, prove that it enjoys the same universality guarantees and evaluate its performance on Modelnet40.

Cite this Paper

BibTeX
@InProceedings{pmlr-v196-finkelshtein22a, title = {A Simple and Universal Rotation Equivariant Point-Cloud Network}, author = {Finkelshtein, Ben and Baskin, Chaim and Maron, Haggai and Dym, Nadav}, booktitle = {Proceedings of Topological, Algebraic, and Geometric Learning Workshops 2022}, pages = {107--115}, year = {2022}, editor = {Cloninger, Alexander and Doster, Timothy and Emerson, Tegan and Kaul, Manohar and Ktena, Ira and Kvinge, Henry and Miolane, Nina and Rieck, Bastian and Tymochko, Sarah and Wolf, Guy}, volume = {196}, series = {Proceedings of Machine Learning Research}, month = {25 Feb--22 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v196/finkelshtein22a/finkelshtein22a.pdf}, url = {https://proceedings.mlr.press/v196/finkelshtein22a.html}, abstract = { Equivariance to permutations and rigid motions is an important inductive bias for various 3D learning problems. Recently it has been shown that the equivariant Tensor Field Network architecture is universal- it can approximate any equivariant function. In this paper we suggest a much simpler architecture, prove that it enjoys the same universality guarantees and evaluate its performance on Modelnet40.} }
Endnote
%0 Conference Paper %T A Simple and Universal Rotation Equivariant Point-Cloud Network %A Ben Finkelshtein %A Chaim Baskin %A Haggai Maron %A Nadav Dym %B Proceedings of Topological, Algebraic, and Geometric Learning Workshops 2022 %C Proceedings of Machine Learning Research %D 2022 %E Alexander Cloninger %E Timothy Doster %E Tegan Emerson %E Manohar Kaul %E Ira Ktena %E Henry Kvinge %E Nina Miolane %E Bastian Rieck %E Sarah Tymochko %E Guy Wolf %F pmlr-v196-finkelshtein22a %I PMLR %P 107--115 %U https://proceedings.mlr.press/v196/finkelshtein22a.html %V 196 %X Equivariance to permutations and rigid motions is an important inductive bias for various 3D learning problems. Recently it has been shown that the equivariant Tensor Field Network architecture is universal- it can approximate any equivariant function. In this paper we suggest a much simpler architecture, prove that it enjoys the same universality guarantees and evaluate its performance on Modelnet40.
APA
Finkelshtein, B., Baskin, C., Maron, H. & Dym, N.. (2022). A Simple and Universal Rotation Equivariant Point-Cloud Network. Proceedings of Topological, Algebraic, and Geometric Learning Workshops 2022, in Proceedings of Machine Learning Research 196:107-115 Available from https://proceedings.mlr.press/v196/finkelshtein22a.html.

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