A Cosmic-Scale Benchmark for Symmetry-Preserving Data Processing

TL;DR

This paper introduces a large-scale benchmark dataset of galaxy point clouds to evaluate Euclidean symmetry-preserving graph neural networks, highlighting their strengths and limitations in capturing local and long-range cosmic structures.

Contribution

It provides a curated galaxy dataset and benchmarks symmetry-preserving GNNs, demonstrating their advantages over non-equivariant models and identifying areas for architectural improvements.

Findings

Symmetry-preserving GNNs outperform non-equivariant models in local environment tasks.

Current architectures struggle with long-range correlation information.

The dataset enables standardized evaluation of symmetry-aware data processing methods.

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. However, we find that current architectures fail to capture information from long-range correlations as effectively as domain-specific baselines, motivating future work on architectures better suited for extracting long-range information.