Randomized Asymmetric Chain of LoRA: The First Meaningful Theoretical Framework for Low-Rank Adaptation

• URL: http://arxiv.org/abs/2410.08305v1
• Date: Thu, 10 Oct 2024 18:51:53 GMT
• Title: Randomized Asymmetric Chain of LoRA: The First Meaningful Theoretical Framework for Low-Rank Adaptation
• Authors: Grigory Malinovsky, Umberto Michieli, Hasan Abed Al Kader Hammoud, Taha Ceritli, Hayder Elesedy, Mete Ozay, Peter Richtárik,
• Abstract summary: Low-Rank Adaptation (LoRA) is a popular technique for finetuning models. LoRA often under performs when compared to full- parameter fine-tuning. We present a framework that rigorously analyzes the adaptation rates of LoRA methods.
• Score: 58.288682735160585
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Fine-tuning has become a popular approach to adapting large foundational models to specific tasks. As the size of models and datasets grows, parameter-efficient fine-tuning techniques are increasingly important. One of the most widely used methods is Low-Rank Adaptation (LoRA), with adaptation update expressed as the product of two low-rank matrices. While LoRA was shown to possess strong performance in fine-tuning, it often under-performs when compared to full-parameter fine-tuning (FPFT). Although many variants of LoRA have been extensively studied empirically, their theoretical optimization analysis is heavily under-explored. The starting point of our work is a demonstration that LoRA and its two extensions, Asymmetric LoRA and Chain of LoRA, indeed encounter convergence issues. To address these issues, we propose Randomized Asymmetric Chain of LoRA (RAC-LoRA) -- a general optimization framework that rigorously analyzes the convergence rates of LoRA-based methods. Our approach inherits the empirical benefits of LoRA-style heuristics, but introduces several small but important algorithmic modifications which turn it into a provably convergent method. Our framework serves as a bridge between FPFT and low-rank adaptation. We provide provable guarantees of convergence to the same solution as FPFT, along with the rate of convergence. Additionally, we present a convergence analysis for smooth, non-convex loss functions, covering gradient descent, stochastic gradient descent, and federated learning settings. Our theoretical findings are supported by experimental results.

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