Hidden-State Privacy Has an Empty Middle 文章

arXiv:2605.24042v1 Announce Type: cross Abstract: Of $1{,}536$ Gaussian release covariances we tested for single-layer hidden-state privacy, zero achieve both moderate utility and moderate privacy against an adaptive retrieval attacker. We prove a complementary Fisher-ball lower bound: every full-rank Gaussian release at $O(1)$ Fisher utility admits a direction whose Mahalanobis signal grows linearly in hidden width, ruling out uniform Gaussian safety in the class and matching the empirical empty middle. The diagonal inverse-Fisher release $\Sigma^\star_{\mathrm{diag}}(\mathcal{K}) = (2\mathcal{K}/d)\,\mathrm{diag}(1/F_{ii})$ is the unique minimax-optimal diagonal mechanism at first-order KL budget $\mathcal{K}$ and the only release with worst-attacker top-1 $\le 0.001$ at every point of a 32 model-layer grid, but it sits on a privacy/utility edge rather than filling the middle.