# CoRA: Optimizing Low-Rank Adaptation with Common Subspace of Large Language Models

arXiv: https://arxiv.org/abs/2409.02119 · HTML: https://mlsanity.com/paper/2409.02119/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 34 references that are in the map.
- First posted on arXiv 31 Aug 2024.

## Builds on (most cited first, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [A Call for Clarity in Reporting BLEU Scores](https://mlsanity.com/paper/1804.08771/) (2018)
- [DyLoRA: Parameter Efficient Tuning of Pre-trained Models using Dynamic Search-Free Low-Rank Adaptation](https://mlsanity.com/paper/2210.07558/) (2022)
- [Parameter-Efficient Fine-Tuning Methods for Pretrained Language Models: A Critical Review and Assessment](https://mlsanity.com/paper/2312.12148/) (2023)
- [KnowPrompt: Knowledge-aware Prompt-tuning with Synergistic Optimization for Relation Extraction](https://mlsanity.com/paper/2104.07650/) (2021)
- [QA-LoRA: Quantization-Aware Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2309.14717/) (2023)
- [LoRA ensembles for large language model fine-tuning](https://mlsanity.com/paper/2310.00035/) (2023)
- [Empirical Analysis of the Strengths and Weaknesses of PEFT Techniques for LLMs](https://mlsanity.com/paper/2304.14999/) (2023)
- [Make Pre-trained Model Reversible: From Parameter to Memory Efficient Fine-Tuning](https://mlsanity.com/paper/2306.00477/) (2023)
- [P-Adapters: Robustly Extracting Factual Information from Language Models with Diverse Prompts](https://mlsanity.com/paper/2110.07280/) (2021)
- [Improving the Efficiency of Transformers for Resource-Constrained Devices](https://mlsanity.com/paper/2106.16006/) (2021)
- [GPT-4 as Evaluator: Evaluating Large Language Models on Pest Management in Agriculture](https://mlsanity.com/paper/2403.11858/) (2024)

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

- [KnowsLM: A framework for evaluation of small language models for knowledge augmentation and humanised conversations](https://mlsanity.com/paper/2504.04569/) (2025)
- [DIVE: Unlocking Self-Improvement in Frozen Language Models Through Diversity-Driven Skill Evolution](https://mlsanity.com/paper/2608.12486/) (2026)

## Abstract (arXiv)

In fine-tuning large language models (LLMs), conserving computational resources while maintaining effectiveness and improving outcomes within the same computational constraints is crucial. The Low-Rank Adaptation (LoRA) strategy balances efficiency and performance in fine-tuning large models by reducing the number of trainable parameters and computational costs. However, current advancements in LoRA might be focused on its fine-tuning methodologies, with not as much exploration as might be expected into further compression of LoRA. Since most of LoRA's parameters might still be superfluous, this may lead to unnecessary wastage of computational resources. In this paper, we propose CoRA: leveraging shared knowledge to optimize LoRA training by substituting its matrix B with a common subspace from large models. Our two-fold method includes (1) Freezing the substitute matrix B to halve parameters while training matrix A for specific tasks and (2) Using the substitute matrix B as an enhanced initial state for the original matrix B, achieving improved results with the same parameters. Our experiments show that the first approach achieves the same efficacy as the original LoRA fine-tuning while being more efficient than halving parameters. At the same time, the second approach has some improvements compared to LoRA's original fine-tuning performance. They generally attest to the effectiveness of our work.