# MGAA: Multi-Granular Adaptive Allocation fof Low-Rank Compression of LLMs

arXiv: https://arxiv.org/abs/2507.03294 · HTML: https://mlsanity.com/paper/2507.03294/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 52 references that are in the map.
- First posted on arXiv 4 Jul 2025.

## Builds on (most cited first, 30 of 37)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Improved Baselines with Visual Instruction Tuning](https://mlsanity.com/paper/2310.03744/) (2023)
- [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)
- [Making the V in VQA Matter: Elevating the Role of Image Understanding in Visual Question Answering](https://mlsanity.com/paper/1612.00837/) (2016)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [MMMU: A Massive Multi-discipline Multimodal Understanding and Reasoning Benchmark for Expert AGI](https://mlsanity.com/paper/2311.16502/) (2023)
- [Learn to Explain: Multimodal Reasoning via Thought Chains for Science Question Answering](https://mlsanity.com/paper/2209.09513/) (2022)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [Towards VQA Models That Can Read](https://mlsanity.com/paper/1904.08920/) (2019)
- [MME: A Comprehensive Evaluation Benchmark for Multimodal Large Language Models](https://mlsanity.com/paper/2306.13394/) (2023)
- [ChartQA: A Benchmark for Question Answering about Charts with Visual and Logical Reasoning](https://mlsanity.com/paper/2203.10244/) (2022)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [VizWiz Grand Challenge: Answering Visual Questions from Blind People](https://mlsanity.com/paper/1802.08218/) (2018)
- [LLM-Pruner: On the Structural Pruning of Large Language Models](https://mlsanity.com/paper/2305.11627/) (2023)
- [InfographicVQA](https://mlsanity.com/paper/2104.12756/) (2021)
- [SliceGPT: Compress Large Language Models by Deleting Rows and Columns](https://mlsanity.com/paper/2401.15024/) (2024)
- [ShortGPT: Layers in Large Language Models are More Redundant Than You Expect](https://mlsanity.com/paper/2403.03853/) (2024)
- [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)
- [ASVD: Activation-aware Singular Value Decomposition for Compressing Large Language Models](https://mlsanity.com/paper/2312.05821/) (2023)
- [The Optimal BERT Surgeon: Scalable and Accurate Second-Order Pruning for Large Language Models](https://mlsanity.com/paper/2203.07259/) (2022)
- [Fluctuation-based Adaptive Structured Pruning for Large Language Models](https://mlsanity.com/paper/2312.11983/) (2023)

## Abstract (arXiv)

The enormous parameter scale of large language models (LLMs) has made model compression a research hotspot, which aims to alleviate computational resource demands during deployment and inference. As a promising direction, low-rank approximation technique has made remarkable achievements. Nevertheless, unfortunately, the vast majority of studies to low-rank approximation compression generally apply uniform compression ratios across all weight matrices, while disregarding their inherently differentiated impacts on the model's performance. Although a few recent work attempts to employ heuristic search strategies to achieve the optimal parameter allocation, such strategies are computationally inefficient and lose the generalization ability in the era of LLMs. In this study, we propose a novel parameter Multi-Granular Adaptive Allocation (MGAA) method, which can adaptively allocate parameters between and within sublayers without task-specific evaluations in the compression process. MGAA consists of two components: 1) Among different sublayers, it assigns compression ratios based on their cosine similarity between inputs and outputs, allowing for a more tailored compression in sublayers with varying degrees of importance, and 2) Within each sublayer, it allocates different compression ratios to weight matrices based on their energy distribution characteristics, ensuring a consistent energy retention ratio while optimizing compression efficiency. Comprehensive evaluations of MGAA across multiple LLMs backbone models and benchmark datasets demonstrate its superior performance. Additionally, we apply our MGAA to multimodal model LLaVA, exhibiting remarkable performance improvements.