Controllable Generative AI: A Technical Review of Model Parameters for Hallucination Mitigation, Fine-Tuning, and Replicable Model Construction

Generative artificial intelligence (GenAI) systems, particularly large language models (LLMs), expose a dense and interacting set of architectural, optimization, and inference-time parameters that jointly determine factual reliability, adaptation quality, and reproducibility. This review develops an industry-oriented technical synthesis of those parameters under three operational goals: (i)~quantifying and reducing hallucination, (ii)~selecting fine-tuning controls for stable domain adaptation, and (iii)~constructing a functionally similar successor model. We formalize how temperature, nucleus and top-k sampling, repetition penalties, LoRA rank and scaling, learning-rate schedules, preference KL coefficients, retrieval depth, and context length reshape the predictive distribution. For each control we discuss mechanism, empirical failure modes, and recommended operating ranges. Parameter search is embedded inside the ModelSure validation methodology to enforce leakage-free train/validation/test discipline, metric selection under class imbalance, and bias--variance diagnosis. The paper concludes with consolidated tables, an algorithmic selection workflow, and a replication checklist suitable for industrial GenAI governance.