# An Empirical Investigation of Matrix Factorization Methods for Pre-trained Transformers

arXiv: https://arxiv.org/abs/2406.11307 · HTML: https://mlsanity.com/paper/2406.11307/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 29 references that are in the map.
- First posted on arXiv 17 Jun 2024.

## Builds on (most cited first, 20 of 20)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [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)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [DeBERTa: Decoding-enhanced BERT with Disentangled Attention](https://mlsanity.com/paper/2006.03654/) (2020)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [TinyBERT: Distilling BERT for Natural Language Understanding](https://mlsanity.com/paper/1909.10351/) (2019)
- [Are Sixteen Heads Really Better than One?](https://mlsanity.com/paper/1905.10650/) (2019)
- [Reducing Transformer Depth on Demand with Structured Dropout](https://mlsanity.com/paper/1909.11556/) (2019)
- [Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations](https://mlsanity.com/paper/1609.07061/) (2016)
- [Fine-Tuning Pretrained Language Models: Weight Initializations, Data Orders, and Early Stopping](https://mlsanity.com/paper/2002.06305/) (2020)
- [Quantized Convolutional Neural Networks for Mobile Devices](https://mlsanity.com/paper/1512.06473/) (2015)
- [Monarch: Expressive Structured Matrices for Efficient and Accurate Training](https://mlsanity.com/paper/2204.00595/) (2022)
- [And the Bit Goes Down: Revisiting the Quantization of Neural Networks](https://mlsanity.com/paper/1907.05686/) (2019)

## Built on by (most cited first, 2 of 2)

- [Beyond Perplexity: Multi-dimensional Safety Evaluation of LLM Compression](https://mlsanity.com/paper/2407.04965/) (2024)
- [State Space Models are Strong Text Rerankers](https://mlsanity.com/paper/2412.14354/) (2024)

## Abstract (arXiv)

The increasing size of transformer-based models in NLP makes the question of compressing them important. In this work, we present a comprehensive analysis of factorization based model compression techniques. Specifically, we focus on comparing straightforward low-rank factorization against the recently introduced Monarch factorization, which exhibits impressive performance preservation on the GLUE benchmark. To mitigate stability issues associated with low-rank factorization of the matrices in pre-trained transformers, we introduce a staged factorization approach wherein layers are factorized one by one instead of being factorized simultaneously. Through this strategy we significantly enhance the stability and reliability of the compression process. Further, we introduce a simple block-wise low-rank factorization method, which has a close relationship to Monarch factorization. Our experiments lead to the surprising conclusion that straightforward low-rank factorization consistently outperforms Monarch factorization across both different compression ratios and six different text classification tasks.