Parameter-Efficient Fine-Tuning (PEFT) has become a key strategy for adapting large language models, with recent advances in sparse tuning reducing overhead by selectively updating key parameters or subsets of data. Existing approaches generally focus on two distinct paradigms: layer-selective methods aiming to fine-tune critical layers to minimize computational load, and data-selective methods aiming to select effective training subsets to boost training. However, current methods typically overlook the fact that different data points contribute varying degrees to distinct model layers, and they often discard potentially valuable information from data perceived as of low quality. To address these limitations, we propose Gradient-aligned Sparse Tuning (GAST), an innovative method that simultaneously performs selective fine-tuning at both data and layer dimensions as integral components of a unified optimization strategy. GAST specifically targets redundancy in information by employing a layer-sparse strategy that adaptively selects the most impactful data points for each layer, providing a more comprehensive and sophisticated solution than approaches restricted to a single dimension. Experiments demonstrate that GAST consistently outperforms baseline methods, establishing a promising direction for future research in PEFT strategies.

The rapid growth of large language models (LLMs) with traditional centralized fine-tuning emerges as a key technique for adapting these models to domain-specific challenges, yielding privacy risks for both model and data owners. One promising solution, called offsite-tuning (OT), is proposed to address these challenges, where a weaker emulator is compressed from the original model and further fine-tuned with adapter to enhance privacy. However, the existing OT-based methods require high computational costs and lack theoretical analysis. This paper introduces a novel OT approach based on gradient-preserving compression. By analyzing the OT problem through the lens of optimization, we propose a method that selectively applies compression techniques such as rank compression and channel pruning, preserving the gradients of fine-tuned adapters while ensuring privacy. Extensive experiments demonstrate that our approach surpasses existing OT methods, both in terms of privacy protection and model performance. Our method provides a theoretical foundation for OT and offers a practical, training-free solution for offsite-tuning of large-scale LLMs.