The problem of efficiently training and evaluating image classifiers that can distinguish between a large number of object categories is considered. A novel metric, sharpness, is proposed which is defined as the fraction of object categories that are above a threshold accuracy. To estimate sharpness (along with a confidence value), a technique called fraction-accurate estimation is introduced which samples categories and samples instances from these categories. In addition, a technique called parity partition coding, a special type of error correcting output code, is introduced, increasing sharpness, while reducing the multi-class problem to a multi-label one with exponentially fewer outputs. We demonstrate that this approach outperforms the baseline model for both MultiMNIST and CelebA, while requiring fewer parameters and exceeding state of the art accuracy on individual labels.