Fisher-Consistent Evidential Learning under Prior Shift

Uncertainty representations are useful only when the decisions they induce remain coherent as prior beliefs change. Under long-tailed training, the mean–variance core of standard evidential deep learning (EDL) preserves the ordering of the training-prior posterior; under an explicit ordering-stability condition, its population-optimal classifier therefore inherits the training log-prior term. In a shared-covariance Gaussian model, this term yields a closed-form boundary displacement and can eliminate every neighborhood of a minority-class mean. We propose Fisher-Consistent Evidential Learning (FC-EDL), which transports a strictly proper mean risk to a chosen reference prior by importance weighting and controls Dirichlet concentration through a separate regularizer. The resulting mean branch is Fisher-consistent for the reference-prior posterior, while the concentration branch retains a valid Dirichlet uncertainty representation. Across diverse classification settings spanning vision, video, text, and fixed-label LLMs, FC-EDL consistently improves minority-class performance and calibration, substantially mitigates the adverse effects of explicit prior shift, and yields robust, more decisive uncertainty representations.