Landscape statistics of the binary perceptron

The landscape of the binary perceptron is studied by Simulated Annealing, exhaustive search and performing random walks on the landscape. We find that the number of local minima increases exponentially with the number of bonds, becoming deeper in the vicinity of a global minimum, but more and more shallow as we move away from it. The random walker detects a simple dependence on the size of the mapping, the architecture introducing a nontrivial dependence on the number of steps