Inductive Biases in Field-Level Cosmological Inference from Galaxy Catalogs
Abstract
We perform field-level likelihood-free inference of the matter density parameter Ωm from simulated galaxy catalogs using machine learning models with differing inductive biases. Using hydrodynamic simulations from CAMELS, we examine how observable choice and architecture govern cosmological information extraction. We consider galaxy positions and line-of-sight peculiar velocities, separately and jointly, and compare permutation-invariant Deep Sets, implemented with either multilayer perceptrons (MLPs) or Kolmogorov-Arnold Networks (KANs), to graph neural networks (GNNs), which explicitly encode spatial relations. We test in-distribution and out-of-distribution (OOD) performance across simulations with different subgrid galaxy-formation prescriptions. Deep Sets infer Ωm from velocities alone with mean relative errors of approximately 18% in-distribution and ∼25% OOD, with KANs and MLPs achieving comparable performance. In contrast, the same set-based approach does not yield useful σ8 predictions in either in-distribution or cross-suite tests. Adding positions does not improve Deep Sets, while GNNs infer Ωm with mean relative errors of about 10% in-distribution and $10−−17\%$ OOD. These results indicate that peculiar velocities provide the dominant source of Ωm information for set-based models in this setting, while spatial information is most effectively used by architectures that explicitly encode galaxy-galaxy relations. Because the velocity inputs are exact simulated peculiar velocities, applications to survey data will require validation under realistic velocity-measurement noise, selection effects, and survey geometry.
Versions
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BibTeX
@misc{baldwin2026inductive,
title = {{Inductive Biases in Field-Level Cosmological Inference from Galaxy Catalogs}},
author = {James O. Baldwin and Shy Genel and Francisco Villaescusa-Navarro},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09504},
eprint = {2609.09504},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09504},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Inductive Biases in Field-Level Cosmological Inference from Galaxy Catalogs
AU - James O. Baldwin
AU - Shy Genel
AU - Francisco Villaescusa-Navarro
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.09504
UR - https://arxiv.org/abs/2609.09504
AB - We perform field-level likelihood-free inference of the matter density parameter Ω_m from simulated galaxy catalogs using machine learning models with differing inductive biases. Using hydrodynamic simulations from CAMELS, we examine how observable choice and architecture govern cosmological information extraction. We consider galaxy positions and line-of-sight peculiar velocities, separately and jointly, and compare permutation-invariant Deep Sets, implemented with either multilayer perceptrons (MLPs) or Kolmogorov-Arnold Networks (KANs), to graph neural networks (GNNs), which explicitly encode spatial relations. We test in-distribution and out-of-distribution (OOD) performance across simulations with different subgrid galaxy-formation prescriptions. Deep Sets infer Ω_m from velocities alone with mean relative errors of approximately 18% in-distribution and ∼25% OOD, with KANs and MLPs achieving comparable performance. In contrast, the same set-based approach does not yield useful σ_8 predictions in either in-distribution or cross-suite tests. Adding positions does not improve Deep Sets, while GNNs infer Ω_m with mean relative errors of about 10% in-distribution and $10−−17\%$ OOD. These results indicate that peculiar velocities provide the dominant source of Ω_m information for set-based models in this setting, while spatial information is most effectively used by architectures that explicitly encode galaxy-galaxy relations. Because the velocity inputs are exact simulated peculiar velocities, applications to survey data will require validation under realistic velocity-measurement noise, selection effects, and survey geometry.
ER -