Carlos Patricio Valenzuela Astaburuaga

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

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-bas...

Stochastic Morphogenetic Extensions of Autonomous Fractal Trees in D-Dimensional Spaces and Their Optical Rendering via Cascaded Perspective Projection with Lipschitzian Culling Stabilization

Traditional algorithmic frameworks for morphological synthesis, such as discrete L-systems, frequently induce structural dissociation under stochastic perturbation regimes due to the absence of geometric inheritance across ancestral lineages. This paper employs a novel algebraic...

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 leverag...

New Semantic Unit Operations: A Graph-Theoretical Metamodel for Sequential Fallback and Spatial Branching in Valuation Networks.

In classical first-order model theory, semantic valuations are traditionally restricted to static, univalent functional mappings (v: V to M). This abstraction fails to account for the discrete topological state transitions that occur during recursive evaluation and quantifier sat...

New Algebraic Modeling of Autonomous Fractal Trees in D-Dimensional Spaces and Their Optical Rendering via Cascaded Perspective Projection.

This paper introduces a unified algebraic framework for the generation and visualization of complex binary, ternary, and quaternary fractal branching structures embedded in arbitrary D-dimensional Euclidean spaces (R^D). While traditional fractal tree algorithms rely on discrete...

New Semantic Unit Operations: A Graph-Theoretical Metamodel for Sequential Fallback and Spatial Branching in Valuation Networks.

In classical first-order model theory, semantic valuations are traditionally restricted to static, univalent functional mappings (v: V to M). This abstraction fails to account for the discrete topological state transitions that occur during recursive evaluation and quantifier sat...

New Semantic Unit Operations: A Graph-Theoretical Metamodel for Recursive Fallback and Spatial Branching in Valuation Networks.

In classical first-order model theory, semantic valuations are traditionally restricted to static, univalent functional mappings (v: V to M). This abstraction fails to account for the discrete topological state transitions that occur during recursive evaluation and quantifier sat...

Semantic Unit Operations: A Graph-Theoretical Metamodel for Recursive Fallback and Spatial Branching in Valuation Networks.

In classical first-order model theory, semantic valuations are traditionally restricted to static, univalent functional mappings (v: V -> M). This abstraction fails to account for the discrete topological state transitions that occur during recursive evaluation and quantifier sat...

Stochastic Morphogenetic Extensions of Autonomous Fractal Trees in D-Dimensional Spaces and Their Optical Rendering via Cascaded Perspective Projection with Lipschitzian Culling Stabilization

Traditional algorithmic frameworks for morphological synthesis, such as discrete L-systems, frequently induce structural dissociation under stochastic perturbation regimes due to the absence of geometric inheritance across ancestral lineages. This paper employs a novel algebraic...

New Algebraic Modeling of Autonomous Fractal Trees in D-Dimensional Spaces and Their Optical Rendering via Cascaded Perspective Projection.

This paper introduces a unified algebraic framework for the generation and visualization of complex binary, ternary, and quaternary fractal branching structures embedded in arbitrary D-dimensional Euclidean spaces (R^D). While traditional fractal tree algorithms rely on discrete...