Low-Rank Adaptation Secretly Imitates Differentially Private SGD

Abstract: As pre-trained LLMs grow in size, full fine-tuning their parameters on task adaptation data becomes increasingly impractical. To address this challenge, some methods for low-rank adaptation of LLMs have been proposed, e.g. LoRA, which incorporates trainable low-rank decomposition matrices into only some parameters of the pre-trained model, called adapters. This approach significantly reduces the number of trainable parameters compared to fine-tuning all parameters or adapters. In this work, we look at low-rank adaptation method from the lens of data privacy. We show theoretically that the low-rank adaptation used in LoRA is equivalent to fine-tuning adapters with noisy batch gradients - just like what DPSGD algorithm does. We also quantify the variance of the injected noise as a decreasing function of adaptation rank. By establishing a Berry-Esseen type bound on the total variation distance between the injected noise distribution and a Gaussian noise distribution with the same variance, we show that the dynamics of low-rank adaptation is very close to when DPSGD is performed w.r.t the adapters. Following our theoretical findings and approved by our experimental results, we show that low-rank adaptation provides robustness to membership inference attacks w.r.t the fine-tuning data.