Statistical Coherence Alignment for Large Language Model Representation Learning Through Tensor Field Convergence

Abstract

Representation learning plays a central role in structuring internal embeddings to capture the statistical properties of language, influencing the coherence and contextual consistency of generated text. Statistical Coherence Alignment is introduced as a method to enforce structured token representations through tensor field convergence, guiding embeddings to reflect statistical dependencies inherent in linguistic data. A mathematical framework is established to quantify coherence alignment, integrating a loss function that optimizes representational consistency across training iterations. Empirical evaluations demonstrate that applying coherence constraints improves perplexity, enhances classification accuracy, and refines rare word embeddings, contributing to a more stable representation space. Comparative analyses with baseline models reveal that the proposed method fosters a more interpretable internal structure, ensuring that embeddings retain contextual dependencies while mitigating representation collapse. The impact on coherence score distributions suggests that the alignment mechanism strengthens semantic integrity across diverse linguistic constructs, leading to a more balanced organization of learned embeddings. Computational assessments indicate that while the method introduces additional memory and training costs, the structured optimization process justifies the trade-offs in applications requiring heightened contextual fidelity. Experimental results validate the effectiveness of coherence alignment in optimizing token representations, providing insights into how statistical dependencies can be leveraged to improve language model training.