3BASiL: An Algorithmic Framework for Sparse plus Low-Rank Compression of LLMs
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| Format: | Preprint |
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2026
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| _version_ | 1866917305259130880 |
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| author | Makni, Mehdi Meng, Xiang Mazumder, Rahul |
| author_facet | Makni, Mehdi Meng, Xiang Mazumder, Rahul |
| contents | Sparse plus Low-Rank $(\mathbf{S} + \mathbf{LR})$ decomposition of Large Language Models (LLMs) has emerged as a promising direction in model compression, aiming to decompose pre-trained model weights into a sum of sparse and low-rank matrices $(\mathbf{W} \approx \mathbf{S} + \mathbf{LR})$. Despite recent progress, existing methods often suffer from substantial performance degradation compared to dense models. In this work, we introduce 3BASiL-TM, an efficient one-shot post-training method for $(\mathbf{S} + \mathbf{LR})$ decomposition of LLMs that addresses this gap. Our approach first introduces a novel 3-Block Alternating Direction Method of Multipliers (ADMM) method, termed 3BASiL, to minimize the layer-wise reconstruction error with convergence guarantees. We then design an efficient transformer-matching (TM) refinement step that jointly optimizes the sparse and low-rank components across transformer layers. This step minimizes a novel memory-efficient loss that aligns outputs at the transformer level. Notably, the TM procedure is universal as it can enhance any $(\mathbf{S} + \mathbf{LR})$ decomposition, including pure sparsity. Our numerical experiments show that 3BASiL-TM reduces the WikiText2 perplexity gap relative to dense LLaMA-8B model by over 30% under a (2:4 Sparse + 64 LR) configuration, compared to prior methods. Moreover, our method achieves over 2.5x faster compression runtime on an A100 GPU compared to SOTA $(\mathbf{S} + \mathbf{LR})$ method. Our code is available at https://github.com/mazumder-lab/3BASiL. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_01376 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | 3BASiL: An Algorithmic Framework for Sparse plus Low-Rank Compression of LLMs Makni, Mehdi Meng, Xiang Mazumder, Rahul Machine Learning Sparse plus Low-Rank $(\mathbf{S} + \mathbf{LR})$ decomposition of Large Language Models (LLMs) has emerged as a promising direction in model compression, aiming to decompose pre-trained model weights into a sum of sparse and low-rank matrices $(\mathbf{W} \approx \mathbf{S} + \mathbf{LR})$. Despite recent progress, existing methods often suffer from substantial performance degradation compared to dense models. In this work, we introduce 3BASiL-TM, an efficient one-shot post-training method for $(\mathbf{S} + \mathbf{LR})$ decomposition of LLMs that addresses this gap. Our approach first introduces a novel 3-Block Alternating Direction Method of Multipliers (ADMM) method, termed 3BASiL, to minimize the layer-wise reconstruction error with convergence guarantees. We then design an efficient transformer-matching (TM) refinement step that jointly optimizes the sparse and low-rank components across transformer layers. This step minimizes a novel memory-efficient loss that aligns outputs at the transformer level. Notably, the TM procedure is universal as it can enhance any $(\mathbf{S} + \mathbf{LR})$ decomposition, including pure sparsity. Our numerical experiments show that 3BASiL-TM reduces the WikiText2 perplexity gap relative to dense LLaMA-8B model by over 30% under a (2:4 Sparse + 64 LR) configuration, compared to prior methods. Moreover, our method achieves over 2.5x faster compression runtime on an A100 GPU compared to SOTA $(\mathbf{S} + \mathbf{LR})$ method. Our code is available at https://github.com/mazumder-lab/3BASiL. |
| title | 3BASiL: An Algorithmic Framework for Sparse plus Low-Rank Compression of LLMs |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2603.01376 |