# Basis Selection: Low-Rank Decomposition of Pretrained Large Language Models for Target Applications

arXiv: https://arxiv.org/abs/2405.15877 · HTML: https://mlsanity.com/paper/2405.15877/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 35 references that are in the map.
- First posted on arXiv 24 May 2024.

## Builds on (most cited first, 23 of 23)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [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)
- [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 Truth is in There: Improving Reasoning in Language Models with Layer-Selective Rank Reduction](https://mlsanity.com/paper/2312.13558/) (2023)
- [Fluctuation-based Adaptive Structured Pruning for Large Language Models](https://mlsanity.com/paper/2312.11983/) (2023)
- [Accelerating Very Deep Convolutional Networks for Classification and Detection](https://mlsanity.com/paper/1505.06798/) (2015)
- [Information Flow Routes: Automatically Interpreting Language Models at Scale](https://mlsanity.com/paper/2403.00824/) (2024)
- [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)
- [Folding Attention: Memory and Power Optimization for On-Device Transformer-based Streaming Speech Recognition](https://mlsanity.com/paper/2309.07988/) (2023)
- [Breaking Down Power Barriers in On-Device Streaming ASR: Insights and Solutions](https://mlsanity.com/paper/2402.13076/) (2024)

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

- [Importance-Guided Basis Selection for Low-Rank Decomposition of Large Language Models](https://mlsanity.com/paper/2605.01627/) (2026)

## Abstract (arXiv)

Large language models (LLMs) significantly enhance the performance of various applications, but they are computationally intensive and energy-demanding. This makes it challenging to deploy them on devices with limited resources, such as personal computers and mobile/wearable devices, and results in substantial inference costs in resource-rich environments like cloud servers. To extend the use of LLMs, we introduce a low-rank decomposition approach to effectively compress these models, tailored to the requirements of specific applications. We observe that LLMs pretrained on general datasets contain many redundant components not needed for particular applications. Our method focuses on identifying and removing these redundant parts, retaining only the necessary elements for the target applications. Specifically, we represent the weight matrices of LLMs as a linear combination of base components. We then prune the irrelevant bases and enhance the model with new bases beneficial for specific applications. Deep compression results on the Llama 2-7b and -13B models, conducted on target applications including mathematical reasoning and code generation, show that our method significantly reduces model size while maintaining comparable accuracy to state-of-the-art low-rank compression techniques.