Learning from deep learning: better cosmological parameter inference from weak lensing maps

Gravitational weak lensing is one of the most promising probes of cosmology. 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 CNN 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. Going beyond "black box" style predictions, the investigation of the features learned by a high performing CNN revealed interesting insights. Without direct human assistance, only from the training data, the CNN discovered two familiar convolutional operators: the discrete Laplace operator and a Roberts cross kernel, which both characterize the steepness of the peaks. Using this insight we constructed a new, easy-to-understand, and robust peak counting algorithm which uses these operators, instead of the heights of the peaks. The new scheme significantly reduced prediction errors, and turned out to be even more accurate than the neural network.

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