arXiv cs.AI· Alexander Okezue Bell·· 13 小时前AI 评分15
高斯隐藏状态发布为何不存在隐私与效用的中间地带
Hidden-State Privacy Has an Empty Middle
AI 导读
在测试的 1,536 个高斯发布协方差中，没有一个能同时对抗自适应检索攻击者实现中等效用与中等隐私。作者证明 Fisher-ball 下界：任何 O(1) Fisher 效用的满秩高斯发布都存在一个方向，其 Mahalanobis 信号随隐藏宽度线性增长。
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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: | Results are incomplete throughout and need to be rerun for a future paper |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2605.24042 [cs.LG] |
| (or arXiv:2605.24042v4 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24042 arXiv-issued DOI via DataCite |
Submission history
From: Alexander Okezue Bell [view email]
[v1]
Thu, 21 May 2026 20:12:09 UTC (811 KB)
[v2]
Tue, 26 May 2026 03:25:09 UTC (811 KB)
[v3]
Mon, 6 Jul 2026 17:37:14 UTC (810 KB)
[v4]
Mon, 26 Oct 2026 11:12:49 UTC (1 KB) (withdrawn)
来源：arXiv cs.AI · arxiv.org