“Sudden” transition to perfect generalization in binary perceptrons is investigated. Building on recent theoretical works of Gardner and Derrida (1989) and Baum and Lyuu (1991), we show the following: for α > α_c = 1.44797 …, if α n examples are drawn from the uniform distribution on {+1, −1}ⁿ and classified according to a target perceptron w_t ∈ {+1, −1}ⁿ as positive if w_t · x ≥ 0 and negative otherwise, then the expected number of nontarget perceptrons consistent with the examples is 2^−⊖(√n); the same number, however, grows exponentially 2^⊖(n) if α < α_c. Numerical calculations for n up to 1,000,002 are reported.