SoLA: Leveraging Soft Activation Sparsity and Low-Rank Decomposition for Large Language Model Compression

The rapid growth of large language models (LLMs) presents significant deployment challenges due to their massive computational and memory demands. While model compression, such as network pruning, offers potential solutions, most existing methods often fail to maintain good performance at high compression ratios. To address this, we propose SLaB, a novel framework that decomposes each linear layer weight into three complementary components: a sparse matrix, a low-rank matrix, and a binary matrix. SLaB eliminates the need for retraining and leverages activation-aware pruning scores to guide the decomposition process. Experiments on Llama-family models demonstrate that SLaB achieves state-of-the-art performance, reducing perplexity by up to 36% compared to existing methods at 50% compression and improving accuracy by up to 8.98% over the baseline on zero-shot tasks.

Large language models (LLMs) have demonstrated remarkable capabilities, yet prohibitive parameter complexity often hinders their deployment. Existing singular value decomposition (SVD) based compression methods simply deem singular values as importance scores of decomposed components. However, this importance ordered by singular values does not necessarily correlate with the performance of a downstream task. In this work, we introduce SoCo (Singular spectrum optimization for large language model Compression), a novel compression framework that learns to rescale the decomposed components of SVD in a data-driven manner. Concretely, we employ a learnable diagonal matrix to assign importance scores for singular spectrum and develop a three-stage training process that progressively refines these scores from initial coarse compression to fine-grained sparsification-thereby striking an effective balance between aggressive model compression and performance preservation. Thanks to the learnable singular spectrum, SoCo adaptively prunes components according to the sparsified importance scores, rather than relying on the fixed order of singular values. More importantly, the remaining components with amplified importance scores can compensate for the loss of the pruned ones. Experimental evaluations across multiple LLMs and benchmarks demonstrate that SoCo surpasses the state-of-the-art methods in model compression.

This study presents an ensemble technique, SPQ (SVD-Pruning-Quantization), for large language model (LLM) compression that combines variance-retained singular value decomposition (SVD), activation-based pruning, and post-training linear quantization. Each component targets a different source of inefficiency: i) pruning removes redundant neurons in MLP layers, ii) SVD reduces attention projections into compact low-rank factors, iii) and 8-bit quantization uniformly compresses all linear layers. At matched compression ratios, SPQ outperforms individual methods (SVD-only, pruning-only, or quantization-only) in perplexity, demonstrating the benefit of combining complementary techniques. Applied to LLaMA-2-7B, SPQ achieves up to 75% memory reduction while maintaining or improving perplexity (e.g., WikiText-2 5.47 to 4.91) and preserving accuracy on downstream benchmarks such as C4, TruthfulQA, and GSM8K. Compared to strong baselines like GPTQ and SparseGPT, SPQ offers competitive perplexity and accuracy while using less memory (6.86 GB vs. 7.16 GB for GPTQ). Moreover, SPQ improves inference throughput over GPTQ, achieving up to a 1.9x speedup, which further enhances its practicality for real-world deployment. The effectiveness of SPQ's robust compression through layer-aware and complementary compression techniques may provide practical deployment of LLMs in memory-constrained environments. Code is available at: https://github.com/JiaminYao/SPQ_LLM_Compression/