Pre-trained language models, trained on large-scale corpora, demonstrate strong generalizability across various NLP tasks. Fine-tuning these models for specific tasks typically involves updating all parameters, which is resource-intensive. Parameter-efficient fine-tuning (PEFT) methods, such as the popular LoRA family, introduce low-rank matrices to learn only a few parameters efficiently. However, during inference, the product of these matrices updates all pre-trained parameters, complicating tasks like knowledge editing that require selective updates. We propose a novel PEFT method, which conducts row and column-wise sparse low-rank adaptation (RoseLoRA), to address this challenge. RoseLoRA identifies and updates only the most important parameters for a specific task, maintaining efficiency while preserving other model knowledge. By adding a sparsity constraint on the product of low-rank matrices and converting it to row and column-wise sparsity, we ensure efficient and precise model updates. Our theoretical analysis guarantees the lower bound of the sparsity with respective to the matrix product. Extensive experiments on five benchmarks across twenty datasets demonstrate that RoseLoRA outperforms baselines in both general fine-tuning and knowledge editing tasks.

Pre-trained language models (LMs) have brought remarkable performance on numerous NLP tasks. However, they require significant resources and entail high computational costs for inference, making them challenging to deploy in real-world and real-time systems. Existing early exiting methods aim to reduce computational complexity by selecting the layer at which to exit, but suffer from the limitation that they have to sequentially traverse through all layers prior to the selected exit layer, which lacks flexibility and degrades their performance. To solve this problem, we propose a homotopic and adaptive layer skipping fine-tuning method named HadSkip. HadSkip adaptively selects the layers to skip based on a predefined budget. Specifically, we introduce a learnable gate before each layer of the LM to determine whether the current layer should be skipped. To tackle various challenges in training such as discrete gates and the budget constraint, we propose a fine-grained initialization strategy and homotopic optimization strategy. We conduct extensive experiments on the GLUE benchmark, and experimental results demonstrate the proposed HadSkip outperforms all state-of-the-art baselines significantly.