# Assigning Distinct Roles to Quantized and Low-Rank Matrices Toward Optimal Weight Decomposition

arXiv: https://arxiv.org/abs/2506.02077 · HTML: https://mlsanity.com/paper/2506.02077/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 46 references that are in the map.
- First posted on arXiv 2 Jun 2025.

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

- [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)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [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)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [BRECQ: Pushing the Limit of Post-Training Quantization by Block Reconstruction](https://mlsanity.com/paper/2102.05426/) (2021)
- [A White Paper on Neural Network Quantization](https://mlsanity.com/paper/2106.08295/) (2021)
- [QuIP: 2-Bit Quantization of Large Language Models With Guarantees](https://mlsanity.com/paper/2307.13304/) (2023)
- [HAWQ: Hessian AWare Quantization of Neural Networks with Mixed-Precision](https://mlsanity.com/paper/1905.03696/) (2019)
- [QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebooks](https://mlsanity.com/paper/2402.04396/) (2024)
- [SpQR: A Sparse-Quantized Representation for Near-Lossless LLM Weight Compression](https://mlsanity.com/paper/2306.03078/) (2023)
- [Model compression via distillation and quantization](https://mlsanity.com/paper/1802.05668/) (2018)
- [SVD-LLM: Truncation-aware Singular Value Decomposition for Large Language Model Compression](https://mlsanity.com/paper/2403.07378/) (2024)
- [Integer Quantization for Deep Learning Inference: Principles and Empirical Evaluation](https://mlsanity.com/paper/2004.09602/) (2020)
- [RedPajama: an Open Dataset for Training Large Language Models](https://mlsanity.com/paper/2411.12372/) (2024)
- [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)
- [Compression of Generative Pre-trained Language Models via Quantization](https://mlsanity.com/paper/2203.10705/) (2022)
- [And the Bit Goes Down: Revisiting the Quantization of Neural Networks](https://mlsanity.com/paper/1907.05686/) (2019)
- [Compressing Large Language Models using Low Rank and Low Precision Decomposition](https://mlsanity.com/paper/2405.18886/) (2024)
- [With Shared Microexponents, A Little Shifting Goes a Long Way](https://mlsanity.com/paper/2302.08007/) (2023)
- [LQER: Low-Rank Quantization Error Reconstruction for LLMs](https://mlsanity.com/paper/2402.02446/) (2024)
- [Matrix Compression via Randomized Low Rank and Low Precision Factorization](https://mlsanity.com/paper/2310.11028/) (2023)
- [Mitigating Quantization Errors Due to Activation Spikes in GLU-Based LLMs](https://mlsanity.com/paper/2405.14428/) (2024)

## Built on by (most cited first, 1 of 1)

- [Preserve-Then-Quantize: Balancing Rank Budgets for Quantization Error Reconstruction in LLMs](https://mlsanity.com/paper/2602.02001/) (2026)

## Abstract (arXiv)

Decomposing weight matrices into quantization and low-rank components (W ≈ Q + LR) is a widely used technique for compressing large language models (LLMs). Existing joint optimization methods iteratively alternate between quantization and low-rank approximation. However, these methods tend to prioritize one component at the expense of the other, resulting in suboptimal decompositions that fail to leverage each component's unique strengths. In this work, we introduce Outlier-Driven Low-Rank Initialization (ODLRI), which assigns low-rank components the specific role of capturing activation-sensitive weights. This structured decomposition mitigates outliers' negative impact on quantization, enabling more effective balance between quantization and low-rank approximation. Experiments on Llama2 (7B, 13B, 70B), Llama3-8B, and Mistral-7B demonstrate that incorporating ODLRI into the joint optimization framework consistently reduces activation-aware error, minimizes quantization scale, and improves perplexity and zero-shot accuracy in low-bit settings.