“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.