Large Scale Private Learning via Low-rank Reparametrization
This addresses privacy leakage risks in large-scale machine learning models like BERT, offering a practical solution for deploying private AI systems.
The paper tackles the challenges of applying differentially private SGD to large neural networks by proposing a low-rank reparametrization scheme, which reduces memory costs and improves utility, enabling private training of BERT with an average accuracy of 83.9% on downstream tasks at ε=8, within 5% loss compared to non-private baselines.
We propose a reparametrization scheme to address the challenges of applying differentially private SGD on large neural networks, which are 1) the huge memory cost of storing individual gradients, 2) the added noise suffering notorious dimensional dependence. Specifically, we reparametrize each weight matrix with two \emph{gradient-carrier} matrices of small dimension and a \emph{residual weight} matrix. We argue that such reparametrization keeps the forward/backward process unchanged while enabling us to compute the projected gradient without computing the gradient itself. To learn with differential privacy, we design \emph{reparametrized gradient perturbation (RGP)} that perturbs the gradients on gradient-carrier matrices and reconstructs an update for the original weight from the noisy gradients. Importantly, we use historical updates to find the gradient-carrier matrices, whose optimality is rigorously justified under linear regression and empirically verified with deep learning tasks. RGP significantly reduces the memory cost and improves the utility. For example, we are the first able to apply differential privacy on the BERT model and achieve an average accuracy of $83.9\%$ on four downstream tasks with $ε=8$, which is within $5\%$ loss compared to the non-private baseline but enjoys much lower privacy leakage risk.