# Evidential Deep Learning

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.

The work introduces a first statistical framework for epistemic uncertainty in node classification, comprising an information-growth experimental protocol and a consistency criterion, and uses projective graph data-generating processes to ensure nested graphs are coherent observations of the same process; the analysis shows that graph evidential deep learning (EDL) methods retain non-vanishing epistemic uncertainty at the population optimum and regulate epistemic and aleatoric uncertainty externally through hyperparameters, thus failing consistency, whereas graph bootstrap ensembles (GB-Ens) capture both data and procedural uncertainty through graph resampling and randomized training and exhibit epistemic uncertainty contraction beyond standard deep ensembles under the same protocol.

The work introduces a first statistical framework for epistemic uncertainty in node classification, comprising an information-growth experimental protocol and a consistency criterion, and uses projective graph data-generating processes to ensure nested graphs are coherent observations of the same process; the analysis shows that graph evidential deep learning (EDL) methods retain non-vanishing epistemic uncertainty at the population optimum and regulate epistemic and aleatoric uncertainty externally through hyperparameters, thus failing consistency, whereas graph bootstrap ensembles (GB-Ens) capture both data and procedural uncertainty through graph resampling and randomized training and exhibit epistemic uncertainty contraction beyond standard deep ensembles under the same protocol.

The authors introduce CLEAR, a lightweight, task-agnostic post-hoc method that uses held-out calibration data to characterize the group-conditioned geometry of the model's latent space, then at inference generates perturbation views directly in the latent space and measures their conflict relative to the calibrated geometry of the predicted group, selectively reducing evidential strength for latent-inconsistent inputs without retraining or altering the base prediction; on ImageNet→CUB it improves OOD and adversarial AUROC by 8.29 and 5.01 while running 17.4× faster than competing post-hoc methods, and preserves predictive performance across classification, regression, and object detection benchmarks.

The authors introduce CLEAR, a lightweight, task-agnostic post-hoc method that uses held-out calibration data to characterize the group-conditioned geometry of the model's latent space, then at inference generates perturbation views directly in the latent space and measures their conflict relative to the calibrated geometry of the predicted group, selectively reducing evidential strength for latent-inconsistent inputs without retraining or altering the base prediction; on ImageNet→CUB it improves OOD and adversarial AUROC by 8.29 and 5.01 while running 17.4× faster than competing post-hoc methods, and preserves predictive performance across classification, regression, and object detection benchmarks.