# PMSS: Pretrained Matrices Skeleton Selection for LLM Fine-tuning

arXiv: https://arxiv.org/abs/2409.16722 · HTML: https://mlsanity.com/paper/2409.16722/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 57 references that are in the map.
- First posted on arXiv 25 Sep 2024.

## Builds on (most cited first, 30 of 33)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [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)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphs](https://mlsanity.com/paper/1903.00161/) (2019)
- [Towards a Unified View of Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2110.04366/) (2021)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [Measuring the Intrinsic Dimension of Objective Landscapes](https://mlsanity.com/paper/1804.08838/) (2018)
- [LoRA Learns Less and Forgets Less](https://mlsanity.com/paper/2405.09673/) (2024)
- [Gradient Descent Happens in a Tiny Subspace](https://mlsanity.com/paper/1812.04754/) (2018)
- [Semi-supervised Sequence Learning](https://mlsanity.com/paper/1511.01432/) (2015)
- [ReFT: Representation Finetuning for Language Models](https://mlsanity.com/paper/2404.03592/) (2024)
- [Yara Parser: A Fast and Accurate Dependency Parser](https://mlsanity.com/paper/1503.06733/) (2015)
- [Flora: Low-Rank Adapters Are Secretly Gradient Compressors](https://mlsanity.com/paper/2402.03293/) (2024)
- [MiLoRA: Harnessing Minor Singular Components for Parameter-Efficient LLM Finetuning](https://mlsanity.com/paper/2406.09044/) (2024)
- [LoRA-XS: Low-Rank Adaptation with Extremely Small Number of Parameters](https://mlsanity.com/paper/2405.17604/) (2024)
- [SVFT: Parameter-Efficient Fine-Tuning with Singular Vectors](https://mlsanity.com/paper/2405.19597/) (2024)
- [CorDA: Context-Oriented Decomposition Adaptation of Large Language Models for Task-Aware Parameter-Efficient Fine-tuning](https://mlsanity.com/paper/2406.05223/) (2024)
- [QuanTA: Efficient High-Rank Fine-Tuning of LLMs with Quantum-Informed Tensor Adaptation](https://mlsanity.com/paper/2406.00132/) (2024)

## Built on by (most cited first, 5 of 5)

- [LLM Bias Detection and Mitigation through the Lens of Desired Distributions](https://mlsanity.com/paper/2510.06354/) (2025)
- [tCURLoRA: Tensor CUR Decomposition Based Low-Rank Parameter Adaptation and Its Application in Medical Image Segmentation](https://mlsanity.com/paper/2501.02227/) (2025)
- [On the Duality between Gradient Transformations and Adapters](https://mlsanity.com/paper/2502.13811/) (2025)
- [Lotus: Efficient LLM Training by Randomized Low-Rank Gradient Projection with Adaptive Subspace Switching](https://mlsanity.com/paper/2602.01233/) (2026)
- [GLT-PEFT: Gated Lie-Tucker Parameter-Efficient Fine-Tuning for Alzheimer's Disease Diagnosis with Hippocampal Segmentation Pretraining](https://mlsanity.com/paper/2605.16769/) (2026)

## Abstract (arXiv)

Low-rank adaptation (LoRA) and its variants have recently gained much interest due to their ability to avoid excessive inference costs. However, LoRA still encounters the following challenges: (1) Limitation of low-rank assumption; and (2) Its initialization method may be suboptimal. To this end, we propose PMSS(Pre-trained Matrices Skeleton Selection), which enables high-rank updates with low costs while leveraging semantic and linguistic information inherent in pre-trained weight. It achieves this by selecting skeletons from the pre-trained weight matrix and only learning a small matrix instead. Experiments demonstrate that PMSS outperforms LoRA and other fine-tuning methods across tasks with much less trainable parameters. We demonstrate its effectiveness, especially in handling complex tasks such as DROP benchmark(+3.4%/+5.9% on LLaMA2-7B/13B) and math reasoning(+12.89%/+5.61%/+3.11% on LLaMA2-7B, Mistral-7B and Gemma-7B of GSM8K). The code and model will be released soon.