Generation-Resistant Data Publishing with Force Field and Finsler Geometry

In the era of generative AI, modern data publishing faces a new privacy challenge: datasets released to preserve utility for downstream tasks can be exploited to train or fine-tune generative AI models, enabling training-example extraction, membership inference, and style copying. This paper proposes a unified framework for generation-resistant data publishing (GRDP) that simultaneously preserves classification utility while degrading generative capability, by leveraging force field, Finsler geometry, and generative statistics theory. To preserve classification utility, we characterize boundary-sensitive local discriminative geometry in the embedding space through a physics-inspired bubble expansion process and construct a distance-decaying force field with intra-class attraction and inter-class repulsion. Under the induced Finsler geometry, anisotropic bubble shells evolve according to a Hamilton–Jacobi formulation, and force invariance is enforced along shell trajectories so that local decision-boundary geometry remains stable even when global distributional statistics are distorted. To degrade generative capability while preserving local geometry, we derive a Gaussian target prior whose covariance shift increases the FID-based feature-distribution mismatch under a quadratic approximation of the force-invariance budget. We further demonstrate that this covariance shift has a closed-form rank-one structure aligned with the minimum-eigenvalue direction of the induced force matrix, i.e., the least force-constrained direction. The published data are then matched to this prior through covariance shaping, distorting global distributional statistics while maintaining classification performance.