Energy-Weighted Conformal Classification: Efficiency Failure Modes and Cost-Bounded Adaptation

Energy weighting adapts conformal prediction sets using information beyond class probabilities, yet coverage alone leaves set size uncontrolled. We show that exact joint density can be dominated by label-independent nuisance features, while nearly constant weights can overwhelm narrow temperature-scaled score gaps; both effects survive recalibration. To protect efficiency, we introduce pooled cost projection (PCP), which measures score displacement in labels per input, clips it, and symmetrically recalibrates for each query. Under exchangeability, PCP preserves marginal coverage and bounds expected additions to the same separately calibrated base by a chosen budget B. A half-label budget repairs a nonempty construction from a raw-target lower bound of 47.583 labels to at most 2.5 + ε. On an energy-fine-tuned WRN and two ImageNetV2 target architectures, PCP reduces mean set size by 5.36–8.68% relative to adaptive linear shrinkage at the same formal budget. Label-count protection thus provides a principled interface between informative scores and efficient calibrated sets.