Differentially private global release of the manifold

Develop a differentially private mechanism that defines and releases a global estimate of the latent C^2 manifold—such as an implicit function or a geometric mesh—with formal (ε, δ)-differential privacy guarantees for the reference dataset by quantifying and controlling the global sensitivity of the manifold estimator.

Background

The paper introduces a framework for differentially private manifold denoising in a private-reference/public-queries setting by privatizing local tangent projectors and weighted means. The algorithm returns corrected query points while protecting the reference data via calibrated Gaussian mechanisms and zCDP accounting.

While the method provides strong utility and privacy guarantees for pointwise query corrections, it does not produce a global manifold representation. The authors explicitly identify the challenge of defining and releasing the entire manifold under differential privacy, noting that such a global release (e.g., as an implicit function or mesh) requires new mechanisms due to difficulties in quantifying global sensitivity.