Scalars are universal: Equivariant machine learning, structured like classical physics

Villar, Soledad; Storey-Fisher, Kate; Yao, Weichi; Blum-Smith, Ben

doi:10.48550/arxiv.2106.06610

Cited by 6 publications

(4 citation statements)

References 53 publications

(75 reference statements)

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“…Symmetry under rotations can be built by using as features the distance and the scalar products of the directions of two vectors defining the edge (Villar et al 2021). Let us define the unit vectors…”

Section: Edge Featuresmentioning

confidence: 99%

Learning Cosmology and Clustering with Cosmic Graphs

Villanueva-Domingo

Villaescusa-Navarro

2022

ApJ

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We train deep-learning models on thousands of galaxy catalogs from the state-of-the-art hydrodynamic simulations of the Cosmology and Astrophysics with MachinE Learning Simulations (CAMELS) project to perform regression and inference. We employ Graph Neural Networks (GNNs), architectures designed to work with irregular and sparse data, like the distribution of galaxies in the universe. We first show that GNNs can learn to compute the power spectrum of galaxy catalogs with a few percent accuracy. We then train GNNs to perform likelihood-free inference at the galaxy-field level. Our models are able to infer the value of Ωm with a ∼12%–13% accuracy just from the positions of ∼1000 galaxies in a volume of ( 25 h − 1 Mpc ) 3 at z = 0 while accounting for astrophysical uncertainties as modeled in CAMELS. Incorporating information from galaxy properties, such as the stellar mass, stellar metallicity, and stellar radius, increases the accuracy to 4%–8%. Our models are built to be translation and rotation invariant, and they can extract information from any scale larger than the minimum distance between two galaxies. However, our models are not completely robust: testing on simulations run with a different subgrid physics than the ones used for training does not yield accurate results.

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Section: Edge Featuresmentioning

confidence: 99%

Learning Cosmology and Clustering with Cosmic Graphs

Villanueva-Domingo

Villaescusa-Navarro

2022

ApJ

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“…Symmetry under rotations can be built by using as features the distance and the scalar products of the directions of two vectors defining the edge (Villar et al 2021). Lets define the unit vectors…”

Section: Edge Featuresmentioning

confidence: 99%

Learning cosmology and clustering with cosmic graphs

Villanueva-Domingo,

Villaescusa-Navarro

2022

Preprint

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We train deep learning models on thousands of galaxy catalogues from the state-of-the-art hydrodynamic simulations of the CAMELS project to perform regression and inference. We employ Graph Neural Networks (GNNs), architectures designed to work with irregular and sparse data, like the distribution of galaxies in the Universe. We first show that GNNs can learn to compute the power spectrum of galaxy catalogues with a few percent accuracy. We then train GNNs to perform likelihood-free inference at the galaxy-field level. Our models are able to infer the value of Ω m with a ∼ 12% − 13% accuracy just from the positions of ∼ 1000 galaxies in a volume of (25 h −1 Mpc) 3 at z = 0 while accounting for astrophysical uncertainties as modelled in CAMELS. Incorporating information from galaxy properties, such as stellar mass, stellar metallicity, and stellar radius, increases the accuracy to 4% − 8%. Our models are built to be translational and rotational invariant, and they can extract information from any scale larger than the minimum distance between two galaxies. However, our models are not completely robust: testing on simulations run with a different subgrid physics than the ones used for training does not yield as accurate results.

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“…While finalizing this work, we were made aware of the concurrent papers [37,46], with an approach that is related to ours. In fact, Proposition 10 of [37] is similar to our Theorem 2 but for the group O(2) instead of SO(2) (in fact, they deal with a d-dimensional underlying space and the group O(d)). In particular, we make a more thorough description and analysis of neural network architectures.…”

Section: Related Workmentioning

confidence: 99%

ZZ-Net: A Universal Rotation Equivariant Architecture for 2D Point Clouds

Bökman¹,

Kahl²,

Flinth³

2021

Preprint

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In this paper, we are concerned with rotation equivariance on 2D point cloud data. We describe a particular set of functions able to approximate any continuous rotation equivariant and permutation invariant function. Based on this result, we propose a novel neural network architecture for processing 2D point clouds and we prove its universality for approximating functions exhibiting these symmetries.We also show how to extend the architecture to accept a set of 2D-2D correspondences as indata, while maintaining similar equivariance properties. Experiments are presented on the estimation of essential matrices in stereo vision. References

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Scalars are universal: Equivariant machine learning, structured like classical physics

Cited by 6 publications

References 53 publications

Learning Cosmology and Clustering with Cosmic Graphs

Learning Cosmology and Clustering with Cosmic Graphs

Learning cosmology and clustering with cosmic graphs

ZZ-Net: A Universal Rotation Equivariant Architecture for 2D Point Clouds

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