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Exploring Gradient Subspaces: Addressing and Overcoming LoRA's Limitations in Federated Fine-Tuning of Large Language Models

Large Language Models (LLMs) have demonstrated remarkable capabilities across various domains, particularly in task generalization for both text and vision data. While fine-tuning these models can significantly enhance their performance on specific downstream tasks, it often requires high-quality data that cannot be shared due to privacy concerns. Federated Learning (FL) offers a promising solution for collaborative training without direct data sharing. However, many parameter-efficient fine-tuning strategies for LLMs in FL, particularly those based on Low-Rank Adaptation (LoRA), face limitations. In this paper, we critically analyze the convergence and performance guarantees of popular FL frameworks utilizing LoRA, highlighting its suboptimal nature due to constrained subspace learning of low-rank matrices. This limitation hinders effective fine-tuning of LLMs in federated settings. Through rigorous analytical and empirical evaluations, we demonstrate that direct weight averaging outperforms LoRA-based strategies, leading to superior performance for fine-tuned models. Our comprehensive comparison unmasks inefficiencies in LoRA approaches and underscores the advantages of direct weight aggregation. We extend our analysis to low-rank gradient-based optimizers, such as GaLore, used during local training steps. Our findings show that GaLore along with direct-weight aggregation is a more effective approach, outperforming federated LoRA methods like FlexLoRA and FFA-LoRA across both text and image modalities. While privacy remains paramount in FL discourse, our focus is on assessing performance outcomes of federated fine-tuned models and evaluating various FL frameworks from both theoretical and empirical perspectives. Our findings advocate reassessing the reliance on LoRA within FL contexts, paving the way for more efficient training methodologies.

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