[2603.01376] 3BASiL: An Algorithmic Framework for Sparse plus Low-Rank Compression of LLMs

Computer Science > Machine Learning arXiv:2603.01376 (cs) [Submitted on 2 Mar 2026] Title:3BASiL: An Algorithmic Framework for Sparse plus Low-Rank Compression of LLMs Authors:Mehdi Makni, Xiang Meng, Rahul Mazumder View a PDF of the paper titled 3BASiL: An Algorithmic Framework for Sparse plus Low-Rank Compression of LLMs, by Mehdi Makni and 2 other authors View PDF HTML (experimental) Abstract: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} ...