用随机投影替代梯度奇异值分解，大幅降低差分隐私训练内存开销。

Differential privacy (DP) protects sensitive data during neural network training, but standard methods like DP-Adam suffer from high memory overhead due to per-sample gradient clipping, limiting scalability. We introduce DP-GRAPE (Gradient RAndom ProjEction), a DP training method that significantly reduces memory usage while maintaining utility on par with first-order DP approaches. DP-GRAPE is motivated by our finding that privatization flattens the gradient singular value spectrum, making SVD-based projections (as in GaLore (Zhao et al., 2024)) unnecessary. Consequently, DP-GRAPE employs three key components: (1) random Gaussian matrices replace SVD-based subspaces, (2) gradients are privatized after projection, and (3) projection is applied during backpropagation. These contributions eliminate the need for costly SVD computations, enable substantial memory savings, and lead to improved utility. Despite operating in lower-dimensional subspaces, our theoretical analysis shows that DP-GRAPE achieves a privacy-utility tradeoff comparable to DP-SGD. Our extensive empirical experiments show that DP-GRAPE can significantly reduce the memory footprint of DP training without sacrificing accuracy or training time. In particular, DP-GRAPE reduces memory usage by over 63% when pre-training Vision Transformers and over 70% when fine-tuning RoBERTa-Large as compared to DP-Adam, while achieving similar performance. We further demonstrate that DP-GRAPE scales to fine-tuning large models such as OPT with up to 6.7 billion parameters, a scale at which DP-Adam fails due to memory constraints. Our code is available at https://github.com/alexmul1114/DP_GRAPE.