Massive $\nu$s through the CNN lens: interpreting the field-level neutrino mass information in weak lensing

TL;DR

This study uses convolutional neural networks to analyze weak lensing maps, revealing that most neutrino mass information is contained in the 2-point correlation function, with the network's ability to extract additional info diminishing after removing 2-point data.

Contribution

It demonstrates that field-level neural network analysis largely confirms the dominance of 2-point information in neutrino mass constraints from weak lensing maps.

Findings

Neural networks improve neutrino mass detection at high redshifts and small scales.

Most information is captured by the 2-point correlation function.

Noise affects the extraction of information from underdense regions.

Abstract

Modern cosmological surveys probe the Universe deep into the nonlinear regime, where massive neutrinos suppress cosmic structure. Traditional cosmological analyses, which use the 2-point correlation function to extract information, are no longer optimal in the nonlinear regime, and there is thus much interest in extracting beyond-2-point information to improve constraints on neutrino mass. Quantifying and interpreting the beyond-2-point information is thus a pressing task. We study the field-level information in weak lensing convergence maps using convolution neural networks. We find that the network performance increases as higher source redshifts and smaller scales are considered -- investigating up to a source redshift of 2.5 and $\ell_{\rm max}\simeq10^4$ -- verifying that massive neutrinos leave a distinct effect on weak lensing. However, the performance of the network significantly drops after scaling out the 2-point information from the maps, implying that most of the field-level information can be found in the 2-point correlation function alone. We quantify these findings in terms of the likelihood ratio and also use Integrated Gradient saliency maps to interpret which parts of the map the network is learning the most from. We find that, in the absence of noise, the network extracts a similar amount of information from the most overdense and underdense regions. However, upon adding noise, the information in underdense regions is distorted as noise disproportionately washes out void-like structures.