aiqbench analysis
ELVAE introduces an input-dependent normal-inverse-gamma hierarchy into Variational Autoencoders to explicitly separate location uncertainty from conditional variability. Theoretical analysis confirms that while the model exposes a controllable sensitivity mechanism, the canonical inverse allocation does not function as a fourth independent information channel beyond the three quotient coordinates identified by the marginalized latent law. This work advances generative modeling by providing a rigorous framework for quantifying and ranking sensitivity in latent spaces without inflating the effective dimensionality of the reconstruction.
ELVAE: Evidential Learning-Based Variational Autoencoder for Uncertainty-Aware Generation
arXiv:2608.10398v2 Announce Type: replace-cross 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.
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
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2608.10398 [cs.LG]
(or arXiv:2608.10398v2 [cs.LG] for this version)
From: Ge Wang Dr. [view email] [v1] Tue, 11 Aug 2026 02:45:59 UTC (259 KB) [v2] Thu, 20 Aug 2026 18:04:11 UTC (901 KB)
Full text under the publisher's open licence · 263 words
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