Interpreting deep learning models for weak lensing

Abstract

Deep neural networks (DNNs) are powerful algorithms that have been proven capable of extracting non-Gaussian information from weak lensing (WL) datasets. Understanding which features in the data determine the output of these nested, nonlinear 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 ($\ensuremath{\kappa}$). We derive constraints on the cosmological parameter pair $({\mathrm{\ensuremath{\Omega}}}_{m},{\ensuremath{\sigma}}_{8})$ from a combination of three commonly used WL statistics (power spectrum, lensing peaks, and Minkowski functionals), using ray-traced simulated $\ensuremath{\kappa}$ 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 $\ensuremath{\kappa}$ values. For noiseless maps, regions with negative $\ensuremath{\kappa}$ account for 69%--89%. of the attribution of the DNN output, defined as the square of the saliency in input space. In the presence of shape noise, the attribution concentrates in high-convergence regions, with 36%--68% of the attribution in regions with $\ensuremath{\kappa}>3{\ensuremath{\sigma}}_{\ensuremath{\kappa}}$.