改进隐私保护训练，让小梯度也能发挥作用

In the domain of deep learning, the challenge of protecting sensitive data while maintaining model utility is significant. Traditional Differential Privacy (DP) techniques such as Differentially Private Stochastic Gradient Descent (DP-SGD) typically employ strategies like direct or per-sample adaptive gradient clipping. These methods, however, compromise model accuracy due to their critical influence on gradient handling, particularly neglecting the significant contribution of small gradients during later training stages. In this paper, we introduce an enhanced version of DP-SGD, named Differentially Private Per-sample Adaptive Scaling Clipping (DP-PSASC). This approach replaces traditional clipping with non-monotonous adaptive gradient scaling, which alleviates the need for intensive threshold setting and rectifies the disproportionate weighting of smaller gradients. Our contribution is twofold. First, we develop a novel gradient scaling technique that effectively assigns proper weights to gradients, particularly small ones, thus improving learning under differential privacy. Second, we integrate a momentum-based method into DP-PSASC to reduce bias from stochastic sampling, enhancing convergence rates. Our theoretical and empirical analyses confirm that DP-PSASC preserves privacy and delivers superior performance across diverse datasets, setting new standards for privacy-sensitive applications.