  Supervised learning in a binary perceptron is able to classify an extensive
number of random patterns by a proper assignment of binary synaptic weights.
However, to find such assignments in practice, is quite a nontrivial task. The
relation between the weight space structure and the algorithmic hardness has
not yet been fully understood. To this end, we analytically derive the
Franz-Parisi potential for the binary preceptron problem, by starting from an
equilibrium solution of weights and exploring the weight space structure around
it. Our result reveals the geometrical organization of the weight
space\textemdash the weight space is composed of isolated solutions, rather
than clusters of exponentially many close-by solutions. The point-like clusters
far apart from each other in the weight space explain the previously observed
glassy behavior of stochastic local search heuristics.
