Probabilistic Lexical Manifold Construction in Large Language Models via Hierarchical Vector Field Interpolation

Hierarchical vector field interpolation introduces a structured probabilistic framework for lexical representation, ensuring that word embeddings transition smoothly across a continuous manifold rather than being constrained to discrete token mappings. The proposed methodology constructs a probabilistic function space where word representations adhere to topological consistency, mitigating representational discontinuities commonly observed in transformer-based embeddings. Empirical evaluations reveal that probabilistic constraints enhance lexical coherence by refining contextual relationships, leading to improvements in semantic stability across multiple linguistic distributions. The application of divergence minimization techniques ensures that interpolated embeddings maintain probabilistic consistency while preserving computational feasibility for large-scale implementations. Experimental findings demonstrate that interpolated lexical manifolds improve representation density alignment, reducing anisotropic distortions in contextual embedding distributions. Comparative analyses with standard transformer-based models highlight that structured interpolation yields more stable representations, particularly in tasks requiring fine-grained semantic differentiation. The statistical evaluation of embedding divergence confirms that probabilistic lexical manifolds reduce representational inconsistencies while maintaining coherence across varying scales of contextual abstraction. An assessment of computational efficiency reveals that while interpolation introduces minor processing overhead, the structured representation learning approach remains scalable for practical deployment.