Generative Semantic Exploration: A Mathematical Framework forControlled Creativity in Large Language Models

We present a comprehensive mathematical framework that reformulates large language model (LLM) generation as a controlled stochastic process in semantic state space.Generative Semantic Exploration (GSE) introduces explicit control parameters (novelty drive) and (coherence constraint) that dynamically modulate the trade-off between exploratory generation and faithful reproduction.By deriving from first principles of transformer architectures and information theory, we establish GSE as a principled approach for transforming uncontrolled "hallucination" into guided creative exploration.The framework provides theoretical guarantees, connects to existing sampling techniques, and enables fine-grained control over the creativity-factuality spectrum in text generation.Empirical validation confirms our theoretical predictions and demonstrates practical utility across diverse generation tasks.