arXiv:2502.00048v2 Announce Type: replace-cross Abstract: Contextually Entangled Gradient Mapping (CEGM) introduces a new approach to gradient optimization, redefining the relationship between contextual embeddings and gradient updates to enhance semantic coherence and reasoning capabilities in neural architectures. By treating gradients as dynamic carriers of contextual dependencies rather than isolated numerical entities, the proposed methodology bridges critical gaps in existing optimization strategies. The integration of entangled gradient dynamics into a loss regularization framework demonstrated significant improvements in tasks involving long-form reasoning, contextual retention, and adaptability to unseen domains. Experimental evaluations showed that the CEGM-enhanced model consistently outperformed baseline approaches, achieving higher accuracy in token-level predictions and greater resilience to noisy inputs. Practical implementations involved modifications to training pipelines, introducing entanglement layers and dynamic coefficient adjustments that seamlessly align with existing architectures. Results further highlighted reductions in semantic drift during sequential transformations and improvements in embedding coherence across paraphrased sentences, showing the robustness and versatility of the proposed methodology. The findings demonstrate the broader implications of gradient entanglement for both theoretical advancements and practical applications in optimization strategies.