A Cosmic-Scale Benchmark for Symmetry-Preserving Data Processing

Julia Balla, Siddharth Mishra-Sharma, Carolina Cuesta-Lazaro, Tommi Jaakkola, Tess Smidt
Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations, PMLR 282:1048-1066, 2026.

Abstract

Efficiently processing structured point cloud data while preserving multiscale information is a key challenge across domains, from graphics to atomistic modeling. Using a curated dataset of simulated galaxy positions and properties, represented as point clouds, we benchmark the ability of graph neural networks to simultaneously capture local clustering environments and long-range correlations. Given the homogeneous and isotropic nature of the Universe, the data exhibits a high degree of symmetry. We therefore focus on evaluating the performance of Euclidean symmetry-preserving ($E(3)$-equivariant) graph neural networks, showing that they can outperform non-equivariant counterparts and domain-specific information extraction techniques in downstream performance as well as simulation-efficiency.

Cite this Paper

BibTeX
@InProceedings{pmlr-v282-balla26a, title = {A Cosmic-Scale Benchmark for Symmetry-Preserving Data Processing}, author = {Balla, Julia and Mishra-Sharma, Siddharth and Cuesta-Lazaro, Carolina and Jaakkola, Tommi and Smidt, Tess}, booktitle = {Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations}, pages = {1048--1066}, year = {2026}, editor = {Acosta, Francisco and Azeglio, Simone and Tolooshams, Bahareh and van de Geijn, Chase and Shewmake, Christian and Sanborn, Sophia and Miolane, Nina}, volume = {282}, series = {Proceedings of Machine Learning Research}, month = {14 Dec 2024--07 Dec 2025}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v282/main/assets/balla26a/balla26a.pdf}, url = {https://proceedings.mlr.press/v282/balla26a.html}, abstract = {Efficiently processing structured point cloud data while preserving multiscale information is a key challenge across domains, from graphics to atomistic modeling. Using a curated dataset of simulated galaxy positions and properties, represented as point clouds, we benchmark the ability of graph neural networks to simultaneously capture local clustering environments and long-range correlations. Given the homogeneous and isotropic nature of the Universe, the data exhibits a high degree of symmetry. We therefore focus on evaluating the performance of Euclidean symmetry-preserving ($E(3)$-equivariant) graph neural networks, showing that they can outperform non-equivariant counterparts and domain-specific information extraction techniques in downstream performance as well as simulation-efficiency.} }
Endnote
%0 Conference Paper %T A Cosmic-Scale Benchmark for Symmetry-Preserving Data Processing %A Julia Balla %A Siddharth Mishra-Sharma %A Carolina Cuesta-Lazaro %A Tommi Jaakkola %A Tess Smidt %B Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations %C Proceedings of Machine Learning Research %D 2026 %E Francisco Acosta %E Simone Azeglio %E Bahareh Tolooshams %E Chase van de Geijn %E Christian Shewmake %E Sophia Sanborn %E Nina Miolane %F pmlr-v282-balla26a %I PMLR %P 1048--1066 %U https://proceedings.mlr.press/v282/balla26a.html %V 282 %X Efficiently processing structured point cloud data while preserving multiscale information is a key challenge across domains, from graphics to atomistic modeling. Using a curated dataset of simulated galaxy positions and properties, represented as point clouds, we benchmark the ability of graph neural networks to simultaneously capture local clustering environments and long-range correlations. Given the homogeneous and isotropic nature of the Universe, the data exhibits a high degree of symmetry. We therefore focus on evaluating the performance of Euclidean symmetry-preserving ($E(3)$-equivariant) graph neural networks, showing that they can outperform non-equivariant counterparts and domain-specific information extraction techniques in downstream performance as well as simulation-efficiency.
APA
Balla, J., Mishra-Sharma, S., Cuesta-Lazaro, C., Jaakkola, T. & Smidt, T.. (2026). A Cosmic-Scale Benchmark for Symmetry-Preserving Data Processing. Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations, in Proceedings of Machine Learning Research 282:1048-1066 Available from https://proceedings.mlr.press/v282/balla26a.html.

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