Selective Ordinal Gating Network: Structure-Gated Training via the External Reference Principle

Existing methods for selective regression often estimate reliability from model predictions or learned representations. We propose an alternative approach that uses a learned ordinal structure of the target to identify samples with concentrated and coherent conditional target distributions. Our Selective Ordinal Gating Network (SOGN) combines an ordinal auxiliary head with a differentiable concentration–coherence gate and a stop-gradient weighted regression objective. We theoretically analyze how coherent ordinal probabilities can imply a narrow region in target space, and characterize the assumptions under which this implication holds. Across multiple benchmark datasets, SOGN consistently improves selective-regression performance at low coverage compared with uncertainty-based and rejection-based baselines. These results show that ordinal target structure can provide an effective signal for selective regression.