We study constraint satisfaction problems on the domain \{-1,1\}, where the given constraints are homogeneous linear threshold predicates. That is, predicates of the form \mathrm{sgn}(w_1 x_1 + \cdots + w_n x_n) for some positive integer weights w_1, \dots, w_n. Despite their simplicity, current techniques fall short of providing a classification ... more >>>