ELVAE: Evidential Learning-Based Variational Autoencoder for Uncertainty-Aware Generation

ELVAE places an input-dependent normal--inverse-gamma (NIG) hierarchy at each VAE latent coordinate, separating location uncertainty uepi=β/[nu(α-1)] from conditional variability uvar=β/(α-1). The marginalized latent law, however, identifies only the three quotient coordinates (γ,α,c) with c=β(1+1/nu); reconstruction is blind to one (nu,β) fiber direction. A companion theoretical analysis shows that the complete NIG prior and forward KL select a unique prior-relative canonical representative on each fiber, so canonical inverse allocation is not a fourth independent information channel. Empirically, trained inverse evidence 1/nu remains the strongest sensitivity-ranking score. At τepi=1, the three-seed mean high/low-uepi semantic-transition ratios are 1.98 on MNIST and 1.66 on Fashion-MNIST, falling to 1.33 and 1.16 under scale-matched controls. In the 20-draw MNIST component study with equal per-anchor perturbation energy, 1/nu gives high/low ratios 1.69 and 1.65 under the uepi and uvar fields and 1.69 (95% interval 1.45--1.97) under a geometry-free isotropic field, whereas uvar reverses the isotropic ordering to 0.76. Under the experimental prior, canonical 1/nucan is a strictly increasing transform of T=c/[α(γ2+2)] and is bounded above by 3+√10. Thus ELVAE exposes a controllable sensitivity mechanism whose trained four-output realization is operationally informative, while the exact reconstruction-visible information remains three-dimensional and baseline image quality is a separate question.