  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.
