On the Stability of Spherical Hellinger-Kantorovich Flows and Their Implications for Differential Privacy
Researchers have developed a perturbation theory for spherical Hellinger-Kantorovich (SHK) gradient flows, allowing for precise comparison of flows based on differing potentials. This theory provides dimension-free bounds on log-likelihood ratios and divergences, which are then applied to approximate sampling for differential privacy mechanisms. The findings offer explicit Pure-DP guarantees for SHK-based samplers and Approximate-DP certificates. AI
IMPACT This research provides new theoretical tools for differential privacy in machine learning, potentially improving the security of data used in AI models.