In this study we leveraged exercises and reference solutions from a Linear Control Systems course to build a supervised fine‑tuning dataset containing 360 system‑user‑assistant conversations. LoRA was applied to Qwen2.5-3B-Instruct and Qwen2.5-7B-Instruct with rank settings r=4, 8, and 16. Data splits, inference configurations, and evaluation protocols were kept identical to enable a fair comparison between base and fine‑tuned models.
Evaluation employed ROUGE, BERTScore, and structured‑output features to measure similarity to reference answers and the stability of the “Solution‑Method‑Teaching Points” format. Results show that LoRA improves both similarity and structured‑output stability for both model sizes. Notably, the 7B‑r16 model achieved the highest ROUGE‑L of 0.4093 and BERTScore‑F1 of 0.8643 on the current test set, while r=8 offered a better trade‑off between performance and parameter efficiency.
We further performed bootstrap resampling to obtain confidence intervals for the ROUGE‑L gains. The 3B‑r16 gain was 0.0764 [0.0613, 0.0915] and the 7B‑r16 gain was 0.0874 [0.0687, 0.1042]; both intervals exclude zero, indicating robust textual‑similarity improvements on the test set.
These findings suggest that LoRA can align open‑source instruction‑tuned models more closely with the language style and pedagogical organization of course reference answers. However, the metrics primarily capture textual similarity and formatting consistency, not domain‑specific reasoning or mathematical correctness, which still require expert assessment and task‑specific rubrics.
Review