Boosting stops treating all errors alike: separate false-positive and false-negative guarantees get a geometric boostability line
Classical boosting theory counts all mistakes as one total, treating false positives and false negatives the same. A new formulation writes a weak learner's guarantee as a set of false-positive/false-negative error pairs and shows that whether that set can be boosted to arbitrarily high accuracy depends on whether its convex hull intersects the set of points reachable by random guessing. On this basis there is no middle ground between boostable and non-boostable, and boosting proceeds without knowing the set in advance.