Identifiability in Deep Evidential Regression: Scalar Boundaries and a Multivariate Gauge

Deep Evidential Regression (DER) gives single-pass uncertainty estimates, but different evidential parameters can induce exactly the same Student-$t$ predictive distribution while reporting different evidence and epistemic uncertainty. We characterize when architectural restrictions remove this ambiguity. If the evidence strength $\nu$ is shared across inputs, the parameters are identifiable exactly when no two distinct allowed scale functions $\beta$ are positive constant multiples of one another. If both $\nu (x)$ and $\beta (x)$ are represented by affine softplus heads on fixed features, they are jointly identifiable under an open-set density condition unless both heads are constant. For multivariate DER, we decompose the prior scale matrix into a normalized shape, which the predictive law identifies, and a scalar amplitude governed by the same scalar criterion. Experiments distinguish this structural property from finite-sample behavior. The corresponding heads yield more reproducible evidence strengths on CIFAR-rotation and UCI regression tasks, with predictive quality evaluated alongside stability. In a joint-feature QM9 experiment, the gauge-fixed parameterization reduces variation in the epistemic covariance trace relative to coupled and uncoupled Normal-Inverse-Wishart baselines at the final checkpoint. Together, these results show how architectural structure can make evidential parameters uniquely determined and more reproducible in practice.