SRM-LoRA: Sub-Riemannian-Style Updates for Mitigating LLM Hallucination in Low-Rank Adaptation

Hallucination remains a central challenge for deploying large language models in factual and knowledge-grounded settings, where post-training must correct unreliable generations with- out degrading reliable behavior. We propose SRM-LoRA, a low-rank adaptation method that views hallucination mitigation as selective control over update directions in LoRA adapter space. SRM-LoRA introduces a soft sub-Riemannian-style restriction on admissible parameter-space updates, encouraging factual correction while discouraging unreliable changes. This provides a geometric perspective on hallucination mitigation while preserving the standard forward LoRA computation. As a result, SRM-LoRA improves factual reliability without additional inference cost.