LoRA Fine-Tuned Models for Control Systems Course Q&A: A Multidimensional Evaluation of Model Scale and Rank Effects

We investigate whether commonly available LoRA variants have an advantage over basic LoRA in multilingual instruction tuning. Experiments involving LoRA and four other variants on two datasets across diverse target languages show that there is no significant advantage in using more complex LoRA variants instead of basic LoRA, with respect to balancing cross-lingual transfer and knowledge retention. An analysis of hidden embeddings reveal that layer-wise language representation remains largely similar across LLMs fine-tuned with different LoRA techniques, suggesting that architectural novelty of LoRA techniques may not translate into better cross-lingual adaptation.

Recent literature on fine-tuning Large Language Models highlights a fundamental debate. While Full Fine-Tuning (FFT) provides greater representational plasticity, Low-Rank Adaptation (LoRA) can match or surpass FFT performance while constraining updates to a low-rank space and potentially benefiting from additional regularization. Through empirical evaluation across diverse tasks (SQL, Medical QA, and Counterfactual Knowledge) and varying language models (Gemma-3-1B, Qwen2.5-1.5B, and Qwen2.5-3B), we observe both trends and find that the better static architecture depends on the task and model. Spectral and truncation analyses further show that endpoint compressibility alone does not explain these task differences, suggesting task-score sensitivity and constrained optimization trajectories as possible explanations. To address this challenge, we propose a Mixture of LoRA and Full (MoLF) Fine-Tuning, a unified framework that enables continuous navigation between both training regimes. MoLF dynamically routes updates between FFT and LoRA at the optimizer level to ensure that exact gradient signals are available to both experts throughout training, while only selected experts update their weights. For memory-constrained environments, we also introduce MoLF-Efficient, which freezes base weights and only routes updates among a pair of LoRA experts of potentially varying rank. Our evaluations show that MoLF either improves on or stays within $1.5$ percentage points of the better of FFT and LoRA across the nine tested settings, while MoLF-Efficient outperforms both AdaLoRA and AdaMix in eight of nine settings, with gains over the stronger baseline of up to $11.70$ percentage points on Fact, $3.13$ on Med, and $2.98$ on SQL.

We present an innovative multi-stage optimization strategy combining reinforcement learning (RL) and supervised fine-tuning (SFT) to enhance the pedagogical knowledge of large language models (LLMs), as illustrated by EduQwen 32B-RL1, EduQwen 32B-SFT, and an optional third-stage model EduQwen 32B-SFT-RL2: (1) RL optimization that implements progressive difficulty training, focuses on challenging examples, and employs extended reasoning rollouts; (2) a subsequent SFT phase that leverages the RL-trained model to synthesize high-quality training data with difficulty-weighted sampling; and (3) an optional second round of RL optimization. EduQwen 32B-RL1, EduQwen 32B-SFT, and EduQwen 32B-SFT-RL2 are an application-driven family of open-source pedagogical LLMs built on a dense Qwen3-32B backbone. These models remarkably achieve high enough accuracy on the Cross-Domain Pedagogical Knowledge (CDPK) Benchmark to establish new state-of-the-art (SOTA) results across the interactive Pedagogy Benchmark Leaderboard and surpass significantly larger proprietary systems such as the previous benchmark leader Gemini-3 Pro. These dense 32-billion-parameter models demonstrate that domain-specialized optimization can transform mid-sized open-source LLMs into true pedagogical domain experts that outperform much larger general-purpose systems, while preserving the transparency, customizability, and cost-efficiency required for responsible educational AI deployment.