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

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.

DIMAT: Decentralized Iterative Merging-And-Training for Deep Learning Models

Recent advances in decentralized deep learning algorithms have demonstrated cutting-edge performance on various tasks with large pre-trained models. However, a pivotal prerequisite for achieving this level of competitiveness is the significant communication and computation overheads when updating these models, which prohibits the applications of them to real-world scenarios. To address this issue, drawing inspiration from advanced model merging techniques without requiring additional training, we introduce the Decentralized Iterative Merging-And-Training (DIMAT) paradigm--a novel decentralized deep learning framework. Within DIMAT, each agent is trained on their local data and periodically merged with their neighboring agents using advanced model merging techniques like activation matching until convergence is achieved. DIMAT provably converges with the best available rate for nonconvex functions with various first-order methods, while yielding tighter error bounds compared to the popular existing approaches. We conduct a comprehensive empirical analysis to validate DIMAT's superiority over baselines across diverse computer vision tasks sourced from multiple datasets. Empirical results validate our theoretical claims by showing that DIMAT attains faster and higher initial gain in accuracy with independent and identically distributed (IID) and non-IID data, incurring lower communication overhead. This DIMAT paradigm presents a new opportunity for the future decentralized learning, enhancing its adaptability to real-world with sparse and light-weight communication and computation.