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).

Despite exceptional capabilities, Large Language Models (LLMs) still face deployment challenges due to their enormous size. Post-training structured pruning is a promising solution that prunes LLMs without the need for retraining, reducing computational overhead, and it is hardware-deployment friendly. However, the training-free nature of post-training structured pruning leads to significant performance degradation. We argue that the key to mitigating this issue lies in accurately determining the pruning rate for each layer. Meanwhile, we find that LLMs may have prior knowledge about their own redundancy. Based on this insight, we introduce $\textbf{Self-Pruner}$ an end-to-end automatic self-pruning framework for LLMs, which efficiently search layer-wise pruning rates. Specifically, $\textbf{Self-Pruner}$ leverages LLMs to autonomously execute the entire evolutionary search process to search for pruning rate configurations. In this process, LLMs are used to generate populations, select parent solutions from the current population, and perform crossover and mutation operations to produce offspring solutions. In this way, LLMs automatically generate and evaluate a large number of candidate solutions, effectively converging to find the pruning rate configurations with minimal human intervention. Extensive experiments demonstrate $\textbf{Self-Pruner}$'s better performance compared to existing state-of-the-art methods. Notably, $\textbf{Self-Pruner}$ prunes LLaMA-2-70B to 49B level with only 0.80$\%$ drop in accuracy across seven commonsense reasoning tasks, achieving a 1.39$\times$ speedup on NVIDIA A100 80GB GPU. Further pruning to 35B level resulted in only a 3.80$\%$ decrease in accuracy while obtaining a 1.70$\times$ speedup.

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.