Parameter-efficient finetuning (PEFT) aims to mitigate the substantial computational and memory overhead involved in adapting large-scale pretrained models to diverse downstream tasks. Among numerous PEFT strategies, Low-Rank Adaptation (LoRA) has emerged as one of the most widely adopted approaches due to its robust empirical performance and low implementation complexity. In practical deployment, LoRA is typically applied to the $W^Q$ and $W^V$ projection matrices of self-attention modules, enabling an effective trade-off between model performance and parameter efficiency. While LoRA has achieved considerable empirical success, it still encounters challenges such as suboptimal performance and slow convergence. To address these limitations, we introduce \textbf{AILoRA}, a novel parameter-efficient method that incorporates function-aware asymmetric low-rank priors. Our empirical analysis reveals that the projection matrices $W^Q$ and $W^V$ in the self-attention mechanism exhibit distinct parameter characteristics, stemming from their functional differences. Specifically, $W^Q$ captures task-specific semantic space knowledge essential for attention distributions computation, making its parameters highly sensitive to downstream task variations. In contrast, $W^V$ encodes token-level feature representations that tend to remain stable across tasks and layers. Leveraging these insights, AILoRA performs a function-aware initialization by injecting the principal components of $W^Q$ to retain task-adaptive capacity, and the minor components of $W^V$ to preserve generalizable feature representations. This asymmetric initialization strategy enables LoRA modules to better capture the specialized roles of attention parameters, thereby enhancing both finetuning performance and convergence efficiency.