# 1+1>2: A Synergistic Sparse and Low-Rank Compression Method for Large Language Models

arXiv: https://arxiv.org/abs/2510.26446 · HTML: https://mlsanity.com/paper/2510.26446/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 41 references that are in the map.
- First posted on arXiv 30 Oct 2025.

## Builds on (most cited first, 22 of 22)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [BLOOM: A 176B-Parameter Open-Access Multilingual Language Model](https://mlsanity.com/paper/2211.05100/) (2022)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [LLM.int8(): 8-bit Matrix Multiplication for Transformers at Scale](https://mlsanity.com/paper/2208.07339/) (2022)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [SpinQuant: LLM quantization with learned rotations](https://mlsanity.com/paper/2405.16406/) (2024)
- [SpQR: A Sparse-Quantized Representation for Near-Lossless LLM Weight Compression](https://mlsanity.com/paper/2306.03078/) (2023)
- [Optimal Brain Compression: A Framework for Accurate Post-Training Quantization and Pruning](https://mlsanity.com/paper/2208.11580/) (2022)
- [SVD-LLM: Truncation-aware Singular Value Decomposition for Large Language Model Compression](https://mlsanity.com/paper/2403.07378/) (2024)
- [Language model compression with weighted low-rank factorization](https://mlsanity.com/paper/2207.00112/) (2022)
- [LoSparse: Structured Compression of Large Language Models based on Low-Rank and Sparse Approximation](https://mlsanity.com/paper/2306.11222/) (2023)
- [Dynamic Sparse No Training: Training-Free Fine-tuning for Sparse LLMs](https://mlsanity.com/paper/2310.08915/) (2023)
- [Compressing Large Language Models using Low Rank and Low Precision Decomposition](https://mlsanity.com/paper/2405.18886/) (2024)
- [ViTCoD: Vision Transformer Acceleration via Dedicated Algorithm and Accelerator Co-Design](https://mlsanity.com/paper/2210.09573/) (2022)
- [LoRAShear: Efficient Large Language Model Structured Pruning and Knowledge Recovery](https://mlsanity.com/paper/2310.18356/) (2023)

## Abstract (arXiv)

Large Language Models (LLMs) have demonstrated remarkable proficiency in language comprehension and generation; however, their widespread adoption is constrained by substantial bandwidth and computational demands. While pruning and low-rank approximation have each demonstrated promising performance individually, their synergy for LLMs remains underexplored. We introduce underlineSynergistic underlineSparse and underlineLow-Rank underlineCompression (SSLC) methods for LLMs, which leverages the strengths of both techniques: low-rank approximation compresses the model by retaining its essential structure with minimal information loss, whereas sparse optimization eliminates non-essential weights, preserving those crucial for generalization. Based on theoretical analysis, we first formulate the low-rank approximation and sparse optimization as a unified problem and solve it by iterative optimization algorithm. Experiments on LLaMA and Qwen2.5 models (7B-70B) show that SSLC, without any additional training steps, consistently surpasses standalone methods, achieving state-of-the-arts results. Notably, SSLC compresses Qwen2.5 by 50% with no performance drop and achieves at least 1.63× speedup, offering a practical solution for efficient LLM deployment.