  Cross Entropy (CE) has an important role in machine learning and, in
particular, in neural networks. It is commonly used in neural networks as the
cost between the known distribution of the label and the Softmax/Sigmoid
output. In this paper we present a new cost function called the Amended Cross
Entropy (ACE). Its novelty lies in its affording the capability to train
multiple classifiers while explicitly controlling the diversity between them.
We derived the new cost by mathematical analysis and "reverse engineering" of
the way we wish the gradients to behave, and produced a tailor-made, elegant
and intuitive cost function to achieve the desired result. This process is
similar to the way that CE cost is picked as a cost function for the
Softmax/Sigmoid classifiers for obtaining linear derivatives. By choosing the
optimal diversity factor we produce an ensemble which yields better results
than the vanilla one. We demonstrate two potential usages of this outcome, and
present empirical results. Our method works for classification problems
analogously to Negative Correlation Learning (NCL) for regression problems.
