When Does Confidence-Based Cascade Deferral Suffice?

Cascades are a classical strategy to enable inference cost to vary adaptively across samples, wherein a sequence of classifiers are invoked in turn. A deferral rule determines whether to invoke the next classifier in the sequence, or to terminate prediction. One simple deferral rule employs the confidence of the current classifier, e.g., based on the maximum predicted softmax probability. Despite being oblivious to the structure of the cascade --- e.g., not modelling the errors of downstream models --- such confidence-based deferral often works remarkably well in practice. In this paper, we seek to better understand the conditions under which confidence-based deferral may fail, and when alternate deferral strategies can perform better.