# DeCAF: Decentralized Consensus-And-Factorization for Low-Rank Adaptation of Foundation Models

arXiv: https://arxiv.org/abs/2505.21382 · HTML: https://mlsanity.com/paper/2505.21382/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Prompt learning and adaptation of CLIP, one of 16 directions in Multimodal LLMs / vision-language models.
- Builds on 51 of its 71 references that are in the map.
- First posted on arXiv 27 May 2025.

## Placed in

- Multimodal LLMs / vision-language models / [Prompt learning and adaptation of CLIP](https://mlsanity.com/mllm/prompt-learning-and-adaptation-of-clip/)

## Builds on (most cited first, 30 of 51)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Scaling Language Models: Methods, Analysis & Insights from Training Gopher](https://mlsanity.com/paper/2112.11446/) (2021)
- [Few-Shot Parameter-Efficient Fine-Tuning is Better and Cheaper than In-Context Learning](https://mlsanity.com/paper/2205.05638/) (2022)
- [Towards Federated Learning at Scale: System Design](https://mlsanity.com/paper/1902.01046/) (2019)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [Local SGD Converges Fast and Communicates Little](https://mlsanity.com/paper/1805.09767/) (2018)
- [Learning multiple visual domains with residual adapters](https://mlsanity.com/paper/1705.08045/) (2017)
- [Sparsified SGD with Memory](https://mlsanity.com/paper/1809.07599/) (2018)
- [WiC: the Word-in-Context Dataset for Evaluating Context-Sensitive Meaning Representations](https://mlsanity.com/paper/1808.09121/) (2018)
- [A Unified Theory of Decentralized SGD with Changing Topology and Local Updates](https://mlsanity.com/paper/2003.10422/) (2020)
- [Parallel Restarted SGD with Faster Convergence and Less Communication: Demystifying Why Model Averaging Works for Deep Learning](https://mlsanity.com/paper/1807.06629/) (2018)
- [Mix-of-Show: Decentralized Low-Rank Adaptation for Multi-Concept Customization of Diffusion Models](https://mlsanity.com/paper/2305.18292/) (2023)
- [LoftQ: LoRA-Fine-Tuning-Aware Quantization for Large Language Models](https://mlsanity.com/paper/2310.08659/) (2023)
- [Towards Building the Federated GPT: Federated Instruction Tuning](https://mlsanity.com/paper/2305.05644/) (2023)
- [On the Linear Speedup Analysis of Communication Efficient Momentum SGD for Distributed Non-Convex Optimization](https://mlsanity.com/paper/1905.03817/) (2019)
- [Improving LoRA in Privacy-preserving Federated Learning](https://mlsanity.com/paper/2403.12313/) (2024)
- [QA-LoRA: Quantization-Aware Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2309.14717/) (2023)
- [On the Convergence of Local Descent Methods in Federated Learning](https://mlsanity.com/paper/1910.14425/) (2019)
- [Stochastic Gradient Push for Distributed Deep Learning](https://mlsanity.com/paper/1811.10792/) (2018)
- [FLoRA: Federated Fine-Tuning Large Language Models with Heterogeneous Low-Rank Adaptations](https://mlsanity.com/paper/2409.05976/) (2024)
- [Decentralized Federated Learning: Fundamentals, State of the Art, Frameworks, Trends, and Challenges](https://mlsanity.com/paper/2211.08413/) (2022)
- [OpenFedLLM: Training Large Language Models on Decentralized Private Data via Federated Learning](https://mlsanity.com/paper/2402.06954/) (2024)

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

- [DeMuon: A Decentralized Muon for Matrix Optimization over Graphs](https://mlsanity.com/paper/2510.01377/) (2025)
- [DECA: Decentralizing Block-Wise Adam for Efficient LLM Full-Parameter Fine-Tuning on Non-IID Data](https://mlsanity.com/paper/2606.03209/) (2026)

## Abstract (arXiv)

Low-Rank Adaptation (LoRA) has emerged as one of the most effective, computationally tractable fine-tuning approaches for training Vision-Language Models (VLMs) and Large Language Models (LLMs). LoRA accomplishes this by freezing the pre-trained model weights and injecting trainable low-rank matrices, allowing for efficient learning of these foundation models even on edge devices. However, LoRA in decentralized settings still remains under explored, particularly for the theoretical underpinnings due to the lack of smoothness guarantee and model consensus interference (defined formally below). This work improves the convergence rate of decentralized LoRA (DLoRA) to match the rate of decentralized SGD by ensuring gradient smoothness. We also introduce DeCAF, a novel algorithm integrating DLoRA with truncated singular value decomposition (TSVD)-based matrix factorization to resolve consensus interference. Theoretical analysis shows TSVD's approximation error is bounded and consensus differences between DLoRA and DeCAF vanish as rank increases, yielding DeCAF's matching convergence rate. Extensive experiments across vision/language tasks demonstrate our algorithms outperform local training and rivals federated learning under both IID and non-IID data distributions.