Large language models (LLMs) have revolutionized artificial intelligence, but their performance on specific tasks is often limited by knowledge boundaries. While fine-tuning techniques like low-rank adaptation (LoRA) aim to address this, they can suffer from overfitting. We propose flexible low-rank adaptation (Flexora), a novel method that automatically selects the most critical layers for fine-tuning to optimize performance across diverse downstream tasks. Flexora formulates layer selection as a hyperparameter optimization problem, employs unrolled differentiation for efficient solving, and identifies the most impactful layers based on optimized hyperparameters. Extensive experiments across various pre-trained models and natural language tasks demonstrate that Flexora consistently outperforms existing baselines. We provide theoretical insights and comprehensive ablation studies to elucidate the effectiveness of Flexora. Therefore, Flexora offers a robust solution to enhance LoRA fine-tuning for LLMs, potentially advancing the field of adaptive language model optimization.

Fine-tuning large language models (LLMs) often causes overfitting to specific prompt wording, where minor phrasing variations drastically reduce performance. To address this, we propose Prompt-Agnostic Fine-Tuning (PAFT), a method that enhances robustness through dynamic prompt variation during training. PAFT first generates diverse synthetic prompts, then continuously samples from this set to construct training instances, forcing models to learn fundamental task principles rather than surface-level patterns. Across systematic evaluations using both supervised fine-tuning (SFT) and reinforcement learning fine-tuning (RLFT), PAFT consistently demonstrates improved performance on benchmarks for question answering, mathematical reasoning, and tool use. It achieves 7% higher generalization accuracy on unseen prompts than standard methods with similar training efficiency. Notably, models trained with PAFT attain 3.2× faster inference speeds due to reduced prompt sensitivity. Ablation studies further validate effectiveness of PAFT, while theoretical analysis reveals that PAFT can effectively enhance the cross-domain generalization ability of LLM.