What Models Know, How Well They Know It: Knowledge-Weighted Fine-Tuning for Learning When to Say "I Don't Know"

While large language models (LLMs) demonstrate strong capabilities across diverse user queries, they still suffer from hallucinations, often arising from knowledge misalignment between pre-training and fine-tuning. To address this misalignment, we reliably estimate a fine-grained, instance-level knowledge score via multi-sampled inference. Using the knowledge score, we scale the learning signal according to the model's existing knowledge, while encouraging explicit "I don't know" responses for out-of-scope queries. Experimental results show that this approach allows the model to explicitly express uncertainty when it lacks knowledge, while maintaining accuracy on questions it can answer. Furthermore, we propose evaluation metrics for uncertainty, showing that accurate discrimination between known and unknown instances consistently improves performance.