# New research at ICML: Reducing LLM hallucinations with mathematics Riemann geometry-based SRM-LoRA method reduces hallucinations by 32% - **Source:** [r/MachineLearning](https://www.reddit.com/r/MachineLearning) - **Published:** 2026-07-14 - **Topic:** [Data & AI](https://brifing.si/c/data-ai) - **Original article:** - **On Brifing:** https://brifing.si/s/ed7e867d-5575-4e31-b87f-e4750111b4fd ## The hallucination problem in LLMs Large language models sometimes generate unrealistic or inconsistent outputs (hallucinations). This research aims to solve this problem during LoRA fine-tuning using a mathematical approach. The method inspired by Riemann geometry reshapes model updates. ## Core principle of SRM-LoRA The method reshapes backpropagation gradients by constructing a Riemann metric in parameter space. This sensitivity-based metric suppresses high-cost update directions while leaving forward computation and inference costs unchanged, only optimizing the training process. ## Mathematical innovation The research's original contribution is building the metric based on the rate of parameter changes relative to the loss signal. Unlike traditional approaches, this sensitivity metric (gradient(loss)/gradient(parameter)) prevents overfitting to training data. ## Experimental results SRM-LoRA trained only on HaluEval-QA dataset significantly reduces hallucinations in both related and out-of-distribution benchmarks. It shows improvements up to 32% in factual accuracy metrics. ## Mathematical theory integration in AI The study provides an important example of how mathematical theories can be used more effectively in AI. Here the Riemann metric functions not just as a complex component but as a 'brake' mechanism for updates from training data. ## Advance in AI reliability This research represents a significant step toward making LLMs more reliable in real-world applications. Properly designed integration of mathematical theories has potential to enhance AI systems' generalization capabilities. ## Sources covering this story - https://www.reddit.com/r/MachineLearning/comments/1uw4j6a/llm_hallucination_paperusing_math_accepted_to/ — --- _Summary written by Brifing from the original reporting. Copyright in the original article belongs to its publisher; read the full piece at the link above._