Ad Hoc Geometric Probing and Deterministic Culling Attribution in Stochastic Kinematic Manifolds for Hierarchical Deep Learning XAI

Post-hoc explainability methods in deep learning typically rely on local linear approximations or stochastic gradient perturbations, introducing significant computational overhead and sampling noise. This paper introduces an intrinsic, ad hoc explainability framework that leverages the mathematical structure of continuous stochastic hyperfractal manifolds to perform exact feature attribution and geometric probing. By reversing the non-commutative matrix kinematics of ancestral lineages through a Kinematic Deconvolution Operator, we map latent representations directly onto homogeneous spaces R^(D+1), evaluating structural fidelity via exact quadratic residues. Furthermore, we repurpose the analytic Lipschitzian early-exit culling mechanism (originally designed for graphics optimization) into an overhead-free, deterministic feature attribution metric governed by the analytic covariance bounds of a contractive Gauss-Markov process. Empirical validation shows that our framework eliminates post-hoc sampling variance while naturally matching the 42.94% computational reduction bound established by the underlying geometric culling operator.