# HASSLE-free: A unified Framework for Sparse plus Low-Rank Matrix Decomposition for LLMs

arXiv: https://arxiv.org/abs/2502.00899 · HTML: https://mlsanity.com/paper/2502.00899/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 59 references that are in the map.
- First posted on arXiv 2 Feb 2025.

## Builds on (most cited first, 30 of 39)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [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)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [Analyzing Multi-Head Self-Attention: Specialized Heads Do the Heavy Lifting, the Rest Can Be Pruned](https://mlsanity.com/paper/1905.09418/) (2019)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [Learning Structured Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1608.03665/) (2016)
- [Dynamic Network Surgery for Efficient DNNs](https://mlsanity.com/paper/1608.04493/) (2016)
- [LoftQ: LoRA-Fine-Tuning-Aware Quantization for Large Language Models](https://mlsanity.com/paper/2310.08659/) (2023)
- [Learning N:M Fine-grained Structured Sparse Neural Networks From Scratch](https://mlsanity.com/paper/2102.04010/) (2021)
- [The Optimal BERT Surgeon: Scalable and Accurate Second-Order Pruning for Large Language Models](https://mlsanity.com/paper/2203.07259/) (2022)
- [Interactive Supercomputing on 40,000 Cores for Machine Learning and Data Analysis](https://mlsanity.com/paper/1807.07814/) (2018)
- [LoSparse: Structured Compression of Large Language Models based on Low-Rank and Sparse Approximation](https://mlsanity.com/paper/2306.11222/) (2023)
- [LQ-LoRA: Low-rank Plus Quantized Matrix Decomposition for Efficient Language Model Finetuning](https://mlsanity.com/paper/2311.12023/) (2023)
- [Fast ConvNets Using Group-wise Brain Damage](https://mlsanity.com/paper/1506.02515/) (2015)
- [Dynamic Sparse No Training: Training-Free Fine-tuning for Sparse LLMs](https://mlsanity.com/paper/2310.08915/) (2023)
- [How Well Do Sparse Imagenet Models Transfer?](https://mlsanity.com/paper/2111.13445/) (2021)
- [Non-convex Robust PCA](https://mlsanity.com/paper/1410.7660/) (2014)
- [CATS: Contextually-Aware Thresholding for Sparsity in Large Language Models](https://mlsanity.com/paper/2404.08763/) (2024)
- [Fast as CHITA: Neural Network Pruning with Combinatorial Optimization](https://mlsanity.com/paper/2302.14623/) (2023)

## Built on by (most cited first, 3 of 3)

- [LOST: Low-rank and Sparse Pre-training for Large Language Models](https://mlsanity.com/paper/2508.02668/) (2025)
- [Rethinking the Role of Tensor Decompositions in Post-Training LLM Compression](https://mlsanity.com/paper/2606.03465/) (2026)
- [ELAS: Efficient Pre-Training of Low-Rank Large Language Models via 2:4 Activation Sparsity](https://mlsanity.com/paper/2605.03667/) (2026)

## Abstract (arXiv)

The impressive capabilities of large foundation models come at a cost of substantial computing resources to serve them. Compressing these pre-trained models is of practical interest as it can democratize deploying them to the machine learning community at large by lowering the costs associated with inference. A promising compression scheme is to decompose foundation models' dense weights into a sum of sparse plus low-rank matrices. In this paper, we design a unified framework coined HASSLE-free for (semi-structured) sparse plus low-rank matrix decomposition of foundation models. Our framework introduces the local layer-wise reconstruction error objective for this decomposition, we demonstrate that prior work solves a relaxation of this optimization problem; and we provide efficient and scalable methods to minimize the exact introduced optimization problem. HASSLE-free substantially outperforms state-of-the-art methods in terms of the introduced objective and a wide range of LLM evaluation benchmarks. For the Llama3-8B model with a 2:4 sparsity component plus a 64-rank component decomposition, a compression scheme for which recent work shows important inference acceleration on GPUs, HASSLE-free reduces the test perplexity by 12% for the WikiText-2 dataset and reduces the gap (compared to the dense model) of the average of eight popular zero-shot tasks by 15% compared to existing methods.