[2605.24042] Hidden-State Privacy Has an Empty Middle
[Submitted on 21 May 2026]
Title:Hidden-State Privacy Has an Empty Middle
View a PDF of the paper titled Hidden-State Privacy Has an Empty Middle, by Alexander Okezue Bell
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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. A generalized-eigen mechanism reaching $13\times$ Pareto reduction under Euclidean retrieval collapses to $100\%$ top-1 under the adaptive Mahalanobis attacker, and a full-trajectory sequence inverter recovers $94\%$ of clean GPT-2 prefixes but $0\%$ under $\Sigma_{\mathrm{diag}}$. A split-memory transformer trained from scratch reaches $G_{\mathrm{Mah}} \in [20, 33]$ at 90M and maintains a $6$--$24\times$ advantage over same-budget GPT baselines from 30M to 1B at a fixed-token language-modeling loss penalty; pretrained models top out at 9.3. These results reframe hidden-state release from mechanism-design within the Gaussian class to architecture or release co-design.
Comments: 74 pages, 61 figures
Subjects:
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
Cite as: arXiv:2605.24042 [cs.LG]
(or arXiv:2605.24042v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2605.24042
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Okezue Bell [view email] [v1] Thu, 21 May 2026 20:12:09 UTC (811 KB)
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