However, by examining the Algorithm 4.2: Perceptron with local and non-local features (parameters: if y 1 ̸ = yi * then (y 1 represents the best in {y n }) proofs in Collins (2002a), we can see that the essential condition for convergence is that the weights are always updated using some y (̸ = y * ) that satisfies: • α ≤ 0 (≤ C in the case of a perceptron with a margin).
2y does not necessarily need to be the exact best candidate or the exact second-best candidate.