Parameter-efficient fine-tuning (PEFT) has become a prevalent approach for adapting large language models (LLMs). However, low-rank adaptation methods face an inherent trade-off: improving target task performance can compromise pre-trained world knowledge, while aggressively constraining updates to preserve world knowledge may hinder improvements in the target task. Furthermore, most current methods fail to account for layer-wise differences in adaptation sensitivity, resulting in suboptimal preservation of world knowledge and task adaptation. To address these challenge, we propose Fisher-Optimized Adaptive Low Rank and Singular-VectorSelection (FARSS), an effective framework for knowledge-preserving fine-tuning. This framework introduces two key innovations. First, we propose a Fisher-guided adaptive rank allocation strategy, which assigns smaller ranks to shallow layers that are critical for preserving world knowledge, and larger ranks to deep layers that are essential for task adaptation. Second, we introduce a task-aware initialization method that integrates singular value information with layer-specific second-order statistics estimated from activation and gradient covariances, enabling efficient and task-sensitive low-rank updates. We evaluated several models across various tasks, and the experimental results show that our approach outperforms existing PEFT methods, including LoRA, Corda, and KaSA, achieving a balance between preserving world knowledge and enhancing target task performance. The code is available at https://github.com/chenyehuang/FARSS.

The deployment of large language models (LLMs) is largely hindered by their large number of parameters. Structural pruning has emerged as a promising solution. Prior structured pruning methods directly remove unimportant parameters based on certain metrics, which often causes knowledge loss and necessitates extensive retraining. To overcome this, we introduce a novel pruning method **TRSP**: **T**wo-Stage **R**egularization-Based **S**tructured **P**runing for LLMs. Specifically, we multiply the output of each transformer layer by an initial learnable weight and iteratively learn these weights by adding their ℓ₁-norm as a regularization term to the loss function, serving as the first-stage regularization. Subsequently, we apply additional regularization to the difference between the output and input of layers with smaller weights, encouraging the shift of knowledge to the preserved layers. This serves as the second-stage regularization. TRSP retains more knowledge and better preserves model performance than direct parameter elimination. Through extensive experimentation we show that TRSP outperforms strong layer-wise structured pruning methods without requiring retraining. As a layer-wise pruning method, it delivers notable end-to-end acceleration, making it a promising solution for efficient LLM deployment.