LoRA-FA: Efficient and Effective Low Rank Representation Fine-tuning

Fine-tuning large language models (LLMs) is crucial for improving their performance on downstream tasks, but full-parameter fine-tuning (Full-FT) is computationally expensive and memory-intensive. Parameter-efficient fine-tuning (PEFT) methods, such as Low-Rank Adaptation (LoRA), address this by optimizing only a small subset of parameters. However, LoRA may underperform Full-FT in certain scenarios due to the intrinsic limitations of its low-rank gradients. In this work, we reveal an asymmetric, collapsible structure in LoRA's update: the low-rank modification to W can be reformulated as a single-layer linear regression, implying that one of the LoRA factors can be frozen without sacrificing expressivity. Leveraging this insight, we introduce LoRA-FA, which freezes the projection-down matrix A and trains only the projection-up matrix B. We further close the gap to Full-FT by deriving closed-form gradient corrections that minimize the discrepancy between the induced low-rank gradient and the full gradient. Through extensive experiments on diverse benchmarks, including GLUE, GSM8K, MT-Bench, and HumanEval, we demonstrate that LoRA-FA consistently achieves comparable performance to existing PEFT methods and Full-FT. Experiments on system efficiency show that LoRA-FA significantly reduces activation memory consumption and computational workload in fine-tuning. Our code is available at https://github.com/huggingface/peft.