The recent advancements in parameter-efficient fine-tuning (PEFT) methods for large language models (LLMs) have significantly enhanced the adaptability and performance of these models across various tasks. A notable trend is the development of innovative PEFT techniques that leverage low-rank adaptations (LoRA) to efficiently update model weights while minimizing computational overhead. These methods, such as Knowledge-aware Singular-value Adaptation (KaSA) and Bi-dimensional Weight-Decomposed Low-Rank Adaptation (BoRA), have demonstrated superior performance by dynamically activating relevant knowledge and optimizing weight matrices symmetrically. Additionally, multi-task learning has seen improvements with the introduction of Mixture of Domain-Specific and Universal LoRA (MoDULA), which enhances parameter efficiency and generalization capability through a mixture-of-experts paradigm. Other approaches, like Geometric Adaptive Ranks for Efficient LoRA Fine-tuning (GeLoRA), provide a theoretical basis for optimizing the trade-off between model performance and efficiency by adapting LoRA ranks based on intrinsic dimensionality. These developments collectively indicate a shift towards more sophisticated, adaptive, and efficient fine-tuning strategies that promise to further advance the capabilities of LLMs in diverse applications.