3BASiL: An Algorithmic Framework for Sparse plus Low-Rank Compression of LLMs

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 impressive capabilities across various tasks, but the billion-scale parameters pose deployment challenges. Although existing methods attempt to reduce the scale of LLMs, they require either special hardware support or expensive post-training to maintain model quality. To facilitate efficient and affordable model slimming, we propose a novel training-free compression method for LLMs, named "SoLA", which leverages Soft activation sparsity and Low-rAnk decomposition. SoLA can identify and retain a minority of components significantly contributing to inference, while compressing the majority through low-rank decomposition, based on our analysis of the activation pattern in the feed-forward network (FFN) of modern LLMs. To alleviate the decomposition loss, SoLA is equipped with an adaptive component-wise low-rank allocation strategy to assign appropriate truncation positions for different weight matrices. We conduct extensive experiments on LLaMA-2-7B/13B/70B and Mistral-7B models across a variety of benchmarks. SoLA exhibits remarkable improvement in both language modeling and downstream task accuracy without post-training. For example, with a 30% compression rate on the LLaMA-2-70B model, SoLA surpasses the state-of-the-art method by reducing perplexity from 6.95 to 4.44 and enhancing downstream task accuracy by 10%.

Prohibitive computational and environmental costs impede the scalable deployment of Large Language Models (LLMs). Traditional compression techniques (sparsity, quantization, low-rank approximations) are typically applied in isolation, and each hits an accuracy-efficiency wall. This thesis proposes the "Compression Trinity," a unified framework that applies the three pillars jointly: sparsity to reduce computation, quantization to minimize memory bandwidth, and low-rank approximations to recover accuracy. To accelerate pretraining, we apply the Trinity to the optimizer and model architecture. MKOR approximates curvature via block-diagonal sparsity and low-rank inversion, maintaining numerical stability for quantized states; it reduces curvature update complexity from $O(d^3)$ to $O(d^2)$ and accelerates convergence by up to 1.85x over KFAC. SLoPe accelerates training by up to 1.25x via a double-pruned backward pass for N:M sparsity, using low-rank "lazy" adapters in the final 1% of training to recover accuracy. For post-training compression, OPTIMA stabilizes static masks in a zero-training regime by formulating weight reconstruction as globally optimal column-wise quadratic programs, improving zero-shot accuracy by up to 3.97%. Given a fine-tuning budget, PATCH breaks the ceiling of static masks by learning a dynamic hybrid sparsity ratio between 0% and 50%, yielding up to 1.38x speedups. Finally, SLiM realizes the full Compression Trinity in one shot, using mathematically derived low-rank adapters to recover information lost to quantization and sparsity, improving accuracy by up to 5.66% over state-of-the-art methods and outperforming uncompressed dense models at equal parameter budgets by 0.6%. Together, these results show that jointly applying the Compression Trinity is essential for efficient, scalable, high-performance LLMs.