We introduce Gatekeeper, a novel loss function that calibrates smaller models in cascade setups to confidently handle easy tasks while deferring complex ones, significantly improving deferral performance across diverse architectures and tasks.

We introduce a model of prediction with limited selectivity, and prove instance-dependent bounds on the optimal error rate.

We decompose the gap between selective classifiers and the ideal oracle into five measurable sources, showing that only non-monotone scoring methods can reduce it and improve reliability.