ADOQ: Predefined Analytical Regions for Selective Classification

Selective classification usually treats confidence scores as ranking devices and relies on held-out data to determine operating thresholds for specific coverage or risk targets. ADOQ introduces a different construction in which a single learned score organizes the latent decision space into successive predefined analytical shells around fixed class centers, combining a prescribed ${\chi }_d^2$ numerical scale with an ordering driven by discriminative difficulty. Once training and model selection are complete, the encoder, class geometry, score scales, and the entire continuous family of shell boundaries are fixed analytically, without empirical threshold estimation or per-operating-point recalibration, and certification is performed only afterward on these frozen regions. A single unlabeled certification sample provides distribution-free occupancy bounds uniformly over the predefined shell family, labeled observations provide exact reliability bounds for each fixed shell, and a new prediction is thus assigned to a region carrying an independently certified reliability bound rather than only the classifier's global accuracy or an arbitrary confidence score. Experiments on CIFAR-10, SVHN, Imagenette, and CIFAR-100 show that successive analytical shells strongly stratify predictive reliability, with inner and intermediate regions remaining substantially more reliable than the outer tail even when global performance or score-law fidelity is markedly weaker. Thus, a globally imperfect classifier, which would typically be discarded or retrained outright, may still contain substantial predefined regions with independently certified population-level predictive reliability, while less reliable outer regions are explicitly isolated for deferral.