Large language models (LLMs) have achieved remarkable success across various tasks but face deployment challenges due to their massive computational demands. While post-training pruning methods like SparseGPT and Wanda can effectively reduce the model size, but struggle to maintain model performance at high sparsity levels, limiting their utility for downstream tasks. Existing fine-tuning methods, such as full fine-tuning and LoRA, fail to preserve sparsity as they require updating the whole dense metrics, not well-suited for sparse LLMs. In this paper, we propose Sparsity Evolution Fine-Tuning (SEFT), a novel method designed specifically for sparse LLMs. SEFT dynamically evolves the sparse topology of pruned models during fine-tuning, while preserving the overall sparsity throughout the process. The strengths of SEFT lie in its ability to perform task-specific adaptation through a weight drop-and-grow strategy, enabling the pruned model to self-adapt its sparse connectivity pattern based on the target dataset. Furthermore, a sensitivity-driven pruning criterion is employed to ensure that the desired sparsity level is consistently maintained throughout fine-tuning. Our experiments on various LLMs, including LLaMA families, DeepSeek, and Mistral, across a diverse set of benchmarks demonstrate that SEFT achieves stronger performance while offering superior memory and time efficiency compared to existing baselines. Our code is publicly available at: https://github.com/QiaoXiao7282/SEFT.

Applying Low-Rank Adaptation (LoRA) to fine-tune the sparse LLMs offers an intuitive approach to counter this predicament, while it holds shortcomings include: 1) The inability to integrate LoRA weights into sparse LLMs post-training, and 2) Insufficient performance recovery at high sparsity ratios. In this paper, we introduce dynamic Low-rank Sparse A daptation (LoSA), a novel method that seamlessly integrates low-rank adaptation into LLM sparsity within a unified framework, thereby enhancing the performance of sparse LLMs without increasing the inference latency. In particular, LoSA dynamically sparsifies the LoRA outcomes based on the corresponding sparse weights during fine-tuning, thus guaranteeing that the LoRA module can be integrated into the sparse LLMs post-training. Besides, LoSA leverages Representation Mutual Information (RMI) as an indicator to determine the importance of layers, thereby efficiently determining the layer-wise sparsity rates during fine-tuning. Predicated on this, LoSA adjusts the rank of the LoRA module based on the variability in layer-wise reconstruction errors, allocating an appropriate fine-tuning for each layer to reduce the output discrepancies between dense and sparse LLMs. Extensive experiments tell that LoSA can efficiently boost the efficacy of sparse LLMs within a few hours, without introducing any additional inferential burden. For example, LoSA reduced the perplexity of sparse LLaMA-2-7B by 68.73 and increased zero-shot accuracy by 16.32%, achieving a 2.60 speedup on CPU and 2.23 speedup on GPU, requiring only 45 minutes of fine-tuning on a single NVIDIA A100 80GB GPU. The development of large language models (LLMs) (Zhang et al., 2022; Touvron et al., 2023a;b) has marked substantial advancements in the field of natural language processing (Achiam et al., 2023). As the scale of these models increases, they demonstrate enhanced capabilities in understanding and generating across diverse contexts (Kaplan et al., 2020; Brown et al., 2020). Nevertheless, the exponential growth in model size presents formidable challenges for deployment and inference, primarily due to escalated computational demands and latency (Zhu et al., 2023). To mitigate these issues, a variety of model compression strategies have been developed. Additionally, LoRA weights cannot be merged into the sparse LLM weights. Moreover, LoSA dynamically determines the layer-wise sparsity rates based on representation mutual information and allocates the ranks of the low-rank adaptation according to the reconstruction errors of the sparse LLM. Among the diverse array of model compression techniques, sparsity emerges as a prominent method for diminishing both the size and computational demands of LLMs (Li et al., 2023b; Lu et al., 2024; Frantar & Alistarh, 2023; Sun et al., 2023).

In this paper, we address the challenge of determining the layer-wise sparsity rates of large language models (LLMs) through a theoretical perspective. Specifically, we identify a critical issue of "reconstruction error explosion" in existing LLMs sparsification methods. This refers to the cumulative effect of reconstruction errors throughout the sparsification process, where errors from earlier layers propagate and amplify in subsequent layers. Through theoretical analysis, we derive a simple yet effective approach to layer-wise sparsity allocation that mitigates this issue. Our method uses a monotonically increasing arithmetic progression, reducing the process of determining sparsity rates for multiple layers to the determination of a single common difference hyperparameter. Remarkably, this allows for the optimal layer-wise sparsity rates to be identified with just a few trials. Both our theoretical analysis and experimental results demonstrate that this sparsity allocation scheme is near optimal. Extensive experiments show that our method significantly improves the performance of sparse LLMs across various architectures, outperforming existing layer-wise sparsity methods. Furthermore, it enhances the performance of various compression techniques and is applicable to vision and multimodal models. Notably, our method achieves a reduction of 52.10 in perplexity for the 70 % sparse LLaMA2-7B model obtained via Wanda, improves average zero-shot accuracy by 10.50 %, and delivers speedups of 2.63 and 2.23 on CPU and GPU, respectively. All methods face the problem of "reconstruction error explosion"; however, our method achieves lower reconstruction error compared to other methods. The metric-based method calculates the importance of each layer to obtain the sparsity rate. However, this method is heuris-tically designed by human experts and is not optimal. And the search-based method requires a large number of iterative searches, which is time-consuming.

Existing low-rank adaptation (LoRA) methods face challenges on sparse large language models (LLMs) due to the inability to maintain sparsity. Recent works introduced methods that maintain sparsity by augmenting LoRA techniques with additional masking mechanisms. Despite these successes, such approaches suffer from an increased memory and computation overhead, which affects efficiency of LoRA methods. In response to this limitation, we introduce LoRS, an innovative method designed to achieve both memory and computation efficiency when fine-tuning sparse LLMs. To mitigate the substantial memory and computation demands associated with preserving sparsity, our approach incorporates strategies of weight recompute and computational graph rearrangement. In addition, we also improve the effectiveness of LoRS through better adapter initialization. These innovations lead to a notable reduction in memory and computation consumption during the fine-tuning phase, all while achieving performance levels that outperform existing LoRA approaches.

The ever-increasing large language models (LLMs), though opening a potential path for the upcoming artificial general intelligence, sadly drops a daunting obstacle on the way towards their on-device deployment. As one of the most well-established pre-LLMs approaches in reducing model complexity, network pruning appears to lag behind in the era of LLMs, due mostly to its costly fine-tuning (or re-training) necessity under the massive volumes of model parameter and training data. To close this industry-academia gap, we introduce Dynamic Sparse No Training (DSnoT), a training-free fine-tuning approach that slightly updates sparse LLMs without the expensive backpropagation and any weight updates. Inspired by the Dynamic Sparse Training, DSnoT minimizes the reconstruction error between the dense and sparse LLMs, in the fashion of performing iterative weight pruning-and-growing on top of sparse LLMs. To accomplish this purpose, DSnoT particularly takes into account the anticipated reduction in reconstruction error for pruning and growing, as well as the variance w.r.t. different input data for growing each weight. This practice can be executed efficiently in linear time since its obviates the need of backpropagation for fine-tuning LLMs. Extensive experiments on LLaMA-V1/V2, Vicuna, and OPT across various benchmarks demonstrate the effectiveness of DSnoT in enhancing the performance of sparse LLMs, especially at high sparsity levels. For instance, DSnoT is able to outperform the state-of-the-art Wanda by 26.79 perplexity at 70% sparsity with LLaMA-7B. Our paper offers fresh insights into how to fine-tune sparse LLMs in an efficient training-free manner and open new venues to scale the great potential of sparsity to LLMs. Codes are available at https://github.com/zyxxmu/DSnoT.