# Hybrid Compact-Core Newton

Evidential deep learning represents classification uncertainty through Dirichlet parameters, but the standard objective shows evidence contraction at high confidence. This work analyzes the optimization landscape of the regularized Dirichlet likelihood on a box domain, proves that the second-order sufficient conditions reduce to a scalar self-consistency derivative being positive, and gives an enumeration algorithm with a finite-convergence guarantee. On logits from a ResNet-18 trained on CIFAR-10, total evidence rises monotonically with confidence yet never exceeds a theoretical threshold near 19.75, while the active set shrinks from about 2.05 classes to one.

Evidential deep learning represents classification uncertainty through Dirichlet parameters, but the standard objective shows evidence contraction at high confidence. This work analyzes the optimization landscape of the regularized Dirichlet likelihood on a box domain, proves that the second-order sufficient conditions reduce to a scalar self-consistency derivative being positive, and gives an enumeration algorithm with a finite-convergence guarantee. On logits from a ResNet-18 trained on CIFAR-10, total evidence rises monotonically with confidence yet never exceeds a theoretical threshold near 19.75, while the active set shrinks from about 2.05 classes to one.