# CoLA: Collaborative Low-Rank Adaptation

arXiv: https://arxiv.org/abs/2505.15471 · HTML: https://mlsanity.com/paper/2505.15471/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Mixture of LoRA experts, one of 12 directions in Mixture-of-experts.
- Builds on 33 of its 53 references that are in the map.
- First posted on arXiv 21 May 2025.

## Placed in

- Mixture-of-experts / [Mixture of LoRA experts](https://mlsanity.com/moe/mixture-of-lora-experts/)

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

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [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)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [Few-Shot Parameter-Efficient Fine-Tuning is Better and Cheaper than In-Context Learning](https://mlsanity.com/paper/2205.05638/) (2022)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [The Flan Collection: Designing Data and Methods for Effective Instruction Tuning](https://mlsanity.com/paper/2301.13688/) (2023)
- [GPT Understands, Too](https://mlsanity.com/paper/2103.10385/) (2021)
- [FinBERT: Financial Sentiment Analysis with Pre-trained Language Models](https://mlsanity.com/paper/1908.10063/) (2019)
- [Med-BERT: pre-trained contextualized embeddings on large-scale structured electronic health records for disease prediction](https://mlsanity.com/paper/2005.12833/) (2020)
- [ChatDoctor: A Medical Chat Model Fine-Tuned on a Large Language Model Meta-AI (LLaMA) Using Medical Domain Knowledge](https://mlsanity.com/paper/2303.14070/) (2023)
- [Scaling Laws for Transfer](https://mlsanity.com/paper/2102.01293/) (2021)
- [LoRA-GA: Low-Rank Adaptation with Gradient Approximation](https://mlsanity.com/paper/2407.05000/) (2024)
- [HydraLoRA: An Asymmetric LoRA Architecture for Efficient Fine-Tuning](https://mlsanity.com/paper/2404.19245/) (2024)
- [When MOE Meets LLMs: Parameter Efficient Fine-tuning for Multi-task Medical Applications](https://mlsanity.com/paper/2310.18339/) (2023)
- [Higher Layers Need More LoRA Experts](https://mlsanity.com/paper/2402.08562/) (2024)
- [Asymmetry in Low-Rank Adapters of Foundation Models](https://mlsanity.com/paper/2402.16842/) (2024)
- [LoRA-Pro: Are Low-Rank Adapters Properly Optimized?](https://mlsanity.com/paper/2407.18242/) (2024)
- [FinGPT: Instruction Tuning Benchmark for Open-Source Large Language Models in Financial Datasets](https://mlsanity.com/paper/2310.04793/) (2023)
- [MathBERT: A Pre-Trained Model for Mathematical Formula Understanding](https://mlsanity.com/paper/2105.00377/) (2021)
- [SVFT: Parameter-Efficient Fine-Tuning with Singular Vectors](https://mlsanity.com/paper/2405.19597/) (2024)
- [LeXFiles and LegalLAMA: Facilitating English Multinational Legal Language Model Development](https://mlsanity.com/paper/2305.07507/) (2023)
- [The Impact of Initialization on LoRA Finetuning Dynamics](https://mlsanity.com/paper/2406.08447/) (2024)
- [Overcoming Data Scarcity in Biomedical Imaging with a Foundational Multi-Task Model](https://mlsanity.com/paper/2311.09847/) (2023)
- [Exploring Universal Intrinsic Task Subspace via Prompt Tuning](https://mlsanity.com/paper/2110.07867/) (2021)

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

- [MASA: Rethinking the Representational Bottleneck in LoRA with Multi-A Shared Adaptation](https://mlsanity.com/paper/2510.06005/) (2025)
- [Beyond Student: An Asymmetric Network for Neural Network Inheritance](https://mlsanity.com/paper/2602.09509/) (2026)
- [Joint Information Extraction Across Classical and Modern Chinese with Tea-MOELoRA](https://mlsanity.com/paper/2509.01158/) (2025)
- [CeRA: Breaking the Linear Ceiling of Low-Rank Adaptation with Non-linearity Retained at Inference](https://mlsanity.com/paper/2602.22911/) (2026)
- [A3B2: Adaptive Asymmetric Adapter for Alleviating Branch Bias in Vision-Language Image Classification with Few-Shot Learning](https://mlsanity.com/paper/2605.13161/) (2026)

## Abstract (arXiv)

The scaling law of Large Language Models (LLMs) reveals a power-law relationship, showing diminishing return on performance as model scale increases. While training LLMs from scratch is resource-intensive, fine-tuning a pre-trained model for specific tasks has become a practical alternative. Full fine-tuning (FFT) achieves strong performance; however, it is computationally expensive and inefficient. Parameter-efficient fine-tuning (PEFT) methods, like LoRA, have been proposed to address these challenges by freezing the pre-trained model and adding lightweight task-specific modules. LoRA, in particular, has proven effective, but its application to multi-task scenarios is limited by interference between tasks. Recent approaches, such as Mixture-of-Experts (MOE) and asymmetric LoRA, have aimed to mitigate these issues but still struggle with sample scarcity and noise interference due to their fixed structure. In response, we propose CoLA, a more flexible LoRA architecture with an efficient initialization scheme, and introduces three collaborative strategies to enhance performance by better utilizing the quantitative relationships between matrices A and B. Our experiments demonstrate the effectiveness and robustness of CoLA, outperforming existing PEFT methods, especially in low-sample scenarios. Our data and code are fully publicly available at https://github.com/zyy-2001/CoLA.