On the Stability of Spherical Hellinger-Kantorovich Flows and Their Implications for Differential Privacy
arXiv:2605.23879v1 Announce Type: cross Abstract: Gradient-flow sampling interprets a Gibbs distribution as the minimizer of an energy functional over probability measures and generates dynamics converging to this target. Under spherical Hellinger-Kantorovich (SHK) geometry, the flow couples transport and reaction and coincides with birth-death Langevin dynamics. In this work, we develop a perturbation theory for SHK gradient flows. For two potentials $V$ and $V^{\prime}$, we compare the associated flows from a common initialization and quantify how potential discrepancies propagate over time.
This is a theoretical mathematics publication from arXiv, continuing ongoing research in gradient flow and differential privacy. Its publication date is purely academic.
For a sophisticated reader, this theoretical work on mathematical stability and differential privacy is foundational but offers no immediate strategic implications.
This research refines existing mathematical frameworks for understanding gradient flows and their implications for privacy, but does not introduce any practical changes to technology or markets.
Refines the mathematical understanding of spherical Hellinger-Kantorovich flows and differential privacy.
Could contribute to more robust theoretical foundations for privacy-preserving AI algorithms in the very long term.
Potentially enables the development of AI systems with stronger, provable privacy guarantees decades from now.
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Read at arXiv cs.LG