An improved cosmological parameter inference scheme motivated by deep learning

Dark matter cannot be observed directly, but its weak gravitational lensing slightly distorts the apparent shapes of background galaxies, making weak lensing one of the most promising probes of cosmology. Several observational studies have measured the effect, and there are currently running, and planned efforts to provide even larger, and higher resolution weak lensing maps. Due to nonlinearities on small scales, the traditional analysis with two-point statistics does not fully capture all the underlying information. Multiple inference methods were proposed to extract more details based on higher order statistics, peak statistics, Minkowski functionals and recently convolutional neural networks (CNN). Here we present an improved convolutional neural network that gives significantly better estimates of $\Omega_m$ and $\sigma_8$ cosmological parameters from simulated convergence maps than the state of art methods and also is free of systematic bias. We show that the network exploits information in the gradients around peaks, and with this insight, we construct a new, easy-to-understand, and robust peak counting algorithm based on the 'steepness' of peaks, instead of their heights. The proposed scheme is even more accurate than the neural network on high-resolution noiseless maps. With shape noise and lower resolution its relative advantage deteriorates, but it remains more accurate than peak counting.