Hierarchical summaries for primordial non-Gaussianities

¹ Laboratoire d’Annecy de Physique Theorique (LAPTh), CNRS/USMB, 99 Chemin de Bellevue BP110, Annecy, F-74941 Annecy Cedex, France
² CNRS & Sorbonne Université, Institut d’Astrophysique de Paris (IAP), UMR 7095, 98 bis bd Arago, F-75014 Paris, France
³ Department of Physics and Astronomy, Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218, USA
⁴ Department of Applied Mathematics and Statistics, Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218, USA
⁵ Center for Computational Astrophysics, Flatiron Institute, 162 5th Avenue, New York, NY 10010, USA

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 27 October 2025
Accepted: 15 April 2026

Abstract

The advent of Stage IV galaxy redshift surveys such as DESI and Euclid marks the beginning of an era of precision cosmology, with one key objective being the detection of primordial non-Gaussianities (PNG), which are potential signatures of inflationary physics. In particular, constraining the amplitude of local-type PNG, parametrised by f_NL, with σ_fNL ∼ 1, would provide a critical test of single-versus-multi-field inflation scenarios. While current large-scale structure and cosmic microwave background analyses have achieved σ_fNL ∼ 5–9, further improvements demand novel data compression strategies. We propose a hybrid estimator that hierarchically combines standard two-point and three-point statistics with a field-level neural summary, motivated by recent theoretical works that have indicated that such a combination is nearly optimal in effectively disentangling primordial from late-time non-Gaussianity. We employed PATCHNET, a convolutional neural network that extracts small-scale information from sub-volumes (i.e. patches) of the halo number density field, while large-scale information is retained via the power spectrum and bispectrum. Using QUIJOTE-PNG simulations, we evaluated the Fisher information of this combined estimator across various redshifts, halo mass cuts, and scale cuts. Our results demonstrate that the inclusion of patch-based field-level compression always enhances constraints on f_NL, reaching gains of 30–45% at low k_max (∼ 0.1h Mpc⁻¹) and of 15–25% when the standard summary statistics include k modes comparable to those probed by the patches (k_max ∼ 0.4 h Mpc ⁻¹). This shows that, even in this configuration, information from beyond the bispectrum can be captured. This approach offers a computationally efficient and scalable pathway to tightening the PNG constraints with forthcoming survey data.