Differentially Private Training and Long-Tailed Data: An In-Depth Analysis

A recent study published on arXiv (arXiv:2602.03872v1) analyzes the implications of differentially private training (DP-SGD) on the memorization of long-tailed data by deep learning models. This data is characterized by a non-uniform distribution, with a prevalence of rare or atypical samples.

The research highlights how the use of DP-SGD can compromise generalization performance, particularly on long-tailed data. The theoretical analysis presented in the paper focuses on feature learning and demonstrates that the error on long-tailed data is significantly greater than the overall error on the entire dataset.

The study also characterizes the training dynamics of DP-SGD, showing how gradient clipping and noise injection negatively affect the model's ability to memorize informative but underrepresented samples. The theoretical results were validated through experiments on synthetic and real-world datasets.