Intrinsic Inversion of Stochastic Kinematic Hyperfractals via Non-Commutative Tensor Deconvolution in Variational Latent Spaces

Abstract

This paper introduces a unified mathematical framework that formalizes explainability not as an external post-hoc approximation, but as an intrinsic geometric property of a deep variational state space. Traditional Explainable AI (XAI) methods rely on perturbative or gradient-based local surrogates, introducing high sampling noise, computational complexity, and structural misalignment when analyzing hierarchical representation spaces. To resolve this, we present an ad hoc variational optimization objective constrained by a non-commutative Kinematic Deconvolution Operator. This operator resolves the inverse problem of reconstructing a stochastic hyperfractal manifold embedded in R^(D+1) using only its degenerated, non-linearly compressed two-dimensional canvas projections. By analytically evaluating linear subtractions over ancestral lineages, our objective quantifies structural fidelity within deep latent representations via an exact quadratic residue metric, ensuring zero sampling variance. Furthermore, the adaptive view-frustum culling routine, governed by the finite geometric progression of a contractive Gauss-Markov angular dispersion process, is mathematically repurposed as a zero-cost deterministic feature attribution score. Empirical validation within a specialized Variational Autoencoder (SG-XAI-VAE) confirms that our formalism yields a 1.75x evaluation reduction under quaternary branching configurations while establishing stable gradient propagation and strict analytical fidelity.