Interpreting deep learning models for weak lensing

TL;DR

This paper demonstrates that deep neural networks can enhance cosmological parameter estimation from weak lensing data and interprets the features they use, highlighting the importance of extreme convergence regions.

Contribution

It shows that DNNs improve parameter constraints from weak lensing maps and provides insights into the features driving the network's decisions using saliency methods.

Findings

DNNs improve cosmological parameter constraints by 20% over traditional statistics.

Saliency analysis reveals the network focuses on extreme convergence regions.

Negative $ppa$ regions dominate in noiseless maps, while high convergence regions are key with shape noise.

Abstract

Deep Neural Networks (DNNs) are powerful algorithms that have been proven capable of extracting non-Gaussian information from weak lensing (WL) data sets. Understanding which features in the data determine the output of these nested, non-linear algorithms is an important but challenging task. We analyze a DNN that has been found in previous work to accurately recover cosmological parameters in simulated maps of the WL convergence ($\kappa$). We derive constraints on the cosmological parameter pair $(\Omega_m,\sigma_8)$ from a combination of three commonly used WL statistics (power spectrum, lensing peaks, and Minkowski functionals), using ray-traced simulated $\kappa$ maps. We show that the network can improve the inferred parameter constraints relative to this combination by $20\%$ even in the presence of realistic levels of shape noise. We apply a series of well established saliency methods to interpret the DNN and find that the most relevant pixels are those with extreme $\kappa$ values. For noiseless maps, regions with negative $\kappa$ account for $86-69\%$ of the attribution of the DNN output, defined as the square of the saliency in input space. In the presence of shape nose, the attribution concentrates in high convergence regions, with $36-68\%$ of the attribution in regions with $\kappa > 3 \sigma_{\kappa}$.