Improving convolutional neural networks for cosmological fields with random permutation

Convolutional neural networks (CNNs) have recently been applied to cosmological fields---weak lensing mass maps and Galaxy maps. However, cosmological maps differ in several ways from the vast majority of images that CNNs have been tested on: they are stochastic, typically low signal-to-noise per pixel, and with correlations on all scales. Further, the cosmology goal is a regression problem aimed at inferring posteriors on parameters that must be unbiased. We explore simple CNN architectures and present a novel approach of regularization and data augmentation to improve its performance for lensing mass maps. We find robust improvement by using a mixture of pooling and shuffling of the pixels in the deep layers. The random permutation regularizes the network in the low signal-to-noise regime and effectively augments the existing data. We use simulation-based inference to show that the model outperforms CNN designs in the literature. Including systematic uncertainties such as intrinsic alignments, we find a 30% improvement over unoptimized CNNs and power spectrum in the constraints of the S₈ parameter for simulated Stage-III surveys. We explore various statistical errors corresponding to next-generation surveys and find comparable improvements. We expect that our approach will have applications to other cosmological fields as well, such as Galaxy maps or 21-cm maps.