arXiv Machine Learning

DP-MacAdam: Differentially Private Mechanism with Adaptive Clipping and Adaptive Momentum

arXiv:2606. 05435v1 Announce Type: new Abstract: Differentially private stochastic gradient descent (DP-SGD) has become the standard framework for privacy-preserving machine learning, yet its reliance on a fixed gradient clipping threshold to limit sensitivity remains a significant practical limitation.

arXiv Machine Learning
Sep 14

Almost Sure Convergence Analysis of Stochastic Gradient Methods with Clipping and Additive Noise

The paper proves that stochastic gradient descent with gradient clipping and additive Gaussian noise (SGD‑CN) converges almost surely under smoothness and bounded noise assumptions, given standard decaying step sizes. The analysis extends to momentum variants such as the stochastic heavy ball and Nesterov's accelerated gradient, showing that careful energy constructions yield similar guarantees. These results provide stronger theoretical foundations for understanding the pathwise behaviour of clipped stochastic gradient methods in both convex and nonconvex regimes.

By Amartya Mukherjee, Jun Liu
arXiv Machine Learning
4d ago

Optimization Risk Bounds for Kolmogorov-Arnold Networks Trained by DP-SGD with Correlated Noise

The paper provides the first optimization risk bounds for two‑layer Kolmogorov‑Arnold Networks (KANs) trained with clipped mini‑batch differentially private stochastic gradient descent (DP‑SGD) that uses temporally correlated noise. The bounds explicitly capture the effects of temporal correlation, clipping, mini‑batch sampling, and network width, and show that correlation can reduce leading noise terms while the clipping threshold influences an effective step size. Experiments on synthetic data and MNIST confirm the theoretical predictions, and the authors extend the results to population risk guarantees via algorithmic stability, recovering several known special cases.

By Puyu Wang, Jan Schuchardt, Nikita Kalinin, Marcio Monteiro, Junyu Zhou, Sophie Fellenz, Christoph Lampert, Marius Kloft