# Language model compression with weighted low-rank factorization

arXiv: https://arxiv.org/abs/2207.00112 · HTML: https://mlsanity.com/paper/2207.00112/

## Key facts

- Cited by 195 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 36 references that are in the map.
- First posted on arXiv 30 Jun 2022.

## Builds on (most cited first, 25 of 25)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [ALBERT: A Lite BERT for Self-supervised Learning of Language Representations](https://mlsanity.com/paper/1909.11942/) (2019)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [MiniLM: Deep Self-Attention Distillation for Task-Agnostic Compression of Pre-Trained Transformers](https://mlsanity.com/paper/2002.10957/) (2020)
- [TinyBERT: Distilling BERT for Natural Language Understanding](https://mlsanity.com/paper/1909.10351/) (2019)
- [SemEval-2017 Task 1: Semantic Textual Similarity - Multilingual and Cross-lingual Focused Evaluation](https://mlsanity.com/paper/1708.00055/) (2017)
- [Neural Network Acceptability Judgments](https://mlsanity.com/paper/1805.12471/) (2018)
- [Importance Estimation for Neural Network Pruning](https://mlsanity.com/paper/1906.10771/) (2019)
- [Patient Knowledge Distillation for BERT Model Compression](https://mlsanity.com/paper/1908.09355/) (2019)
- [MobileBERT: a Compact Task-Agnostic BERT for Resource-Limited Devices](https://mlsanity.com/paper/2004.02984/) (2020)
- [SWAG: A Large-Scale Adversarial Dataset for Grounded Commonsense Inference](https://mlsanity.com/paper/1808.05326/) (2018)
- [Exploiting Linear Structure Within Convolutional Networks for Efficient Evaluation](https://mlsanity.com/paper/1404.0736/) (2014)
- [Speeding up Convolutional Neural Networks with Low Rank Expansions](https://mlsanity.com/paper/1405.3866/) (2014)
- [MiniLMv2: Multi-Head Self-Attention Relation Distillation for Compressing Pretrained Transformers](https://mlsanity.com/paper/2012.15828/) (2020)
- [Revisiting Natural Gradient for Deep Networks](https://mlsanity.com/paper/1301.3584/) (2013)
- [Group Fisher Pruning for Practical Network Compression](https://mlsanity.com/paper/2108.00708/) (2021)
- [Fine-tune BERT for Extractive Summarization](https://mlsanity.com/paper/1903.10318/) (2019)
- [Accelerating Very Deep Convolutional Networks for Classification and Detection](https://mlsanity.com/paper/1505.06798/) (2015)
- [GroupReduce: Block-Wise Low-Rank Approximation for Neural Language Model Shrinking](https://mlsanity.com/paper/1806.06950/) (2018)
- [Online Embedding Compression for Text Classification using Low Rank Matrix Factorization](https://mlsanity.com/paper/1811.00641/) (2018)
- [Hyperparameter-free Continuous Learning for Domain Classification in Natural Language Understanding](https://mlsanity.com/paper/2201.01420/) (2022)

## Built on by (most cited first, 30 of 195)

- [SVD-LLM: Truncation-aware Singular Value Decomposition for Large Language Model Compression](https://mlsanity.com/paper/2403.07378/) (2024)
- [Assessing the Brittleness of Safety Alignment via Pruning and Low-Rank Modifications](https://mlsanity.com/paper/2402.05162/) (2024)
- [SVDQuant: Absorbing Outliers by Low-Rank Components for 4-Bit Diffusion Models](https://mlsanity.com/paper/2411.05007/) (2024)
- [ASVD: Activation-aware Singular Value Decomposition for Compressing Large Language Models](https://mlsanity.com/paper/2312.05821/) (2023)
- [Does Circuit Analysis Interpretability Scale? Evidence from Multiple Choice Capabilities in Chinchilla](https://mlsanity.com/paper/2307.09458/) (2023)
- [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 Inference of Mixture-of-Experts Language Models with Offloading](https://mlsanity.com/paper/2312.17238/) (2023)
- [Eigen Attention: Attention in Low-Rank Space for KV Cache Compression](https://mlsanity.com/paper/2408.05646/) (2024)
- [SVD-LLM V2: Optimizing Singular Value Truncation for Large Language Model Compression](https://mlsanity.com/paper/2503.12340/) (2025)
- [Palu: Compressing KV-Cache with Low-Rank Projection](https://mlsanity.com/paper/2407.21118/) (2024)
- [Compressing Large Language Models using Low Rank and Low Precision Decomposition](https://mlsanity.com/paper/2405.18886/) (2024)
- [MoE-I2: Compressing Mixture of Experts Models through Inter-Expert Pruning and Intra-Expert Low-Rank Decomposition](https://mlsanity.com/paper/2411.01016/) (2024)
- [MoDeGPT: Modular Decomposition for Large Language Model Compression](https://mlsanity.com/paper/2408.09632/) (2024)
- [Unlearning Isn't Deletion: Investigating Reversibility of Machine Unlearning in LLMs](https://mlsanity.com/paper/2505.16831/) (2025)
- [Towards Robust and Parameter-Efficient Knowledge Unlearning for LLMs](https://mlsanity.com/paper/2408.06621/) (2024)
- [Basis Sharing: Cross-Layer Parameter Sharing for Large Language Model Compression](https://mlsanity.com/paper/2410.03765/) (2024)
- [Tensor Networks Meet Neural Networks: A Survey and Future Perspectives](https://mlsanity.com/paper/2302.09019/) (2023)
- [TrojViT: Trojan Insertion in Vision Transformers](https://mlsanity.com/paper/2208.13049/) (2022)
- [RL Fine-Tuning Heals OOD Forgetting in SFT](https://mlsanity.com/paper/2509.12235/) (2025)
- [A phase transition between positional and semantic learning in a solvable model of dot-product attention](https://mlsanity.com/paper/2402.03902/) (2024)
- [TrojText: Test-time Invisible Textual Trojan Insertion](https://mlsanity.com/paper/2303.02242/) (2023)
- [LORD: Low Rank Decomposition Of Monolingual Code LLMs For One-Shot Compression](https://mlsanity.com/paper/2309.14021/) (2023)
- [Wanda++: Pruning Large Language Models via Regional Gradients](https://mlsanity.com/paper/2503.04992/) (2025)
- [From Low Rank Gradient Subspace Stabilization to Low-Rank Weights: Observations, Theories, and Applications](https://mlsanity.com/paper/2407.11239/) (2024)
- [Small Singular Values Matter: A Random Matrix Analysis of Transformer Models](https://mlsanity.com/paper/2410.17770/) (2024)
- [SlimLLM: Accurate Structured Pruning for Large Language Models](https://mlsanity.com/paper/2505.22689/) (2025)
- [TensorGPT: Efficient Compression of Large Language Models based on Tensor-Train Decomposition](https://mlsanity.com/paper/2307.00526/) (2023)
- [You Only Prune Once: Designing Calibration-Free Model Compression With Policy Learning](https://mlsanity.com/paper/2501.15296/) (2025)
- [ReCalKV: Low-Rank KV Cache Compression via Head Reordering and Offline Calibration](https://mlsanity.com/paper/2505.24357/) (2025)

## Abstract (arXiv)

Factorizing a large matrix into small matrices is a popular strategy for model compression. Singular value decomposition (SVD) plays a vital role in this compression strategy, approximating a learned matrix with fewer parameters. However, SVD minimizes the squared error toward reconstructing the original matrix without gauging the importance of the parameters, potentially giving a larger reconstruction error for those who affect the task accuracy more. In other words, the optimization objective of SVD is not aligned with the trained model's task accuracy. We analyze this previously unexplored problem, make observations, and address it by introducing Fisher information to weigh the importance of parameters affecting the model prediction. This idea leads to our method: Fisher-Weighted SVD (FWSVD). Although the factorized matrices from our approach do not result in smaller reconstruction errors, we find that our resulting task accuracy is much closer to the original model's performance. We perform analysis with the transformer-based language models, showing our weighted SVD largely alleviates the mismatched optimization objectives and can maintain model performance with a higher compression rate. Our method can directly compress a task-specific model while achieving better performance than other compact model strategies requiring expensive model pre-training. Moreover, the evaluation of compressing an already compact model shows our method can further reduce 9% to 30% parameters with an insignificant impact on task accuracy.