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

Abstract

ELVAE places an input-dependent normal--inverse-gamma (NIG) hierarchy at each VAE latent coordinate, separating location uncertainty $u_{\mathrm{epi}}=\beta /[\nu (\alpha -1)]$ from conditional variability $u_{\mathrm{var}}=\beta /(\alpha -1)$. The marginalized latent law, however, identifies only the three quotient coordinates $(\gamma ,\alpha ,c)$ with $c=\beta (1+1/\nu )$; reconstruction is blind to one $(\nu ,\beta )$ 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 ${\tau }_{\mathrm{epi}}=1$, the three-seed mean high/low-$u_{\mathrm{epi}}$ 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 $u_{\mathrm{epi}}$ and $u_{\mathrm{var}}$ fields and 1.69 (95\% interval 1.45--1.97) under a geometry-free isotropic field, whereas $u_{\mathrm{var}}$ reverses the isotropic ordering to 0.76. Under the experimental prior, canonical $1/{\nu }_{\mathrm{can}}$ is a strictly increasing transform of $T=c/[\alpha ({\gamma }^2+2)]$ and is bounded above by $3+\sqrt{10}$. 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.

31 pages, 5 figures, 7 tables. Substantially revised: expanded quotient/canonical analysis, added Fashion-MNIST and energy-matched/isotropic controls, added a canonical-closure ablation, and updated the discussion and conclusions