Interpreting deep learning models for weak lensing

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 (κ). We derive constraints on the cosmological parameter pair (Ωm,σ8) from a combination of three commonly used WL statistics (power spectrum, lensing peaks, and Minkowski functionals), using ray-traced simulated κ 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 κ values. For noiseless maps, regions with negative κ 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 κ>3σκ.