Hidden-State Privacy Has an Empty Middle

We introduce PACZero, a family of PAC-private zeroth-order mechanisms for fine-tuning large language models that delivers usable utility at $I(S^*; Y_{1:T})=0$. This privacy regime bounds the membership-inference attack (MIA) posterior success rate at the prior, an MIA-resistance level the DP framework matches only at $\varepsilon=0$ and infinite noise. All DP-ZO comparisons below are matched at the MIA posterior level. The key insight is that PAC Privacy charges mutual information only when the release depends on which candidate subset is the secret. Sign-quantizing subset-aggregated zeroth-order gradients creates frequent unanimity, steps at which every candidate subset agrees on the update direction; at these steps the released sign costs zero conditional mutual information. We propose two variants that span the privacy-utility trade-off: PACZero-MI (budgeted MI via exact calibration on the binary release) and PACZero-ZPL ($I=0$ via a uniform coin flip on disagreement steps). We evaluate on SST-2 and SQuAD with OPT-1.3B and OPT-6.7B in both LoRA and full-parameter tracks. On SST-2 OPT-1.3B full fine-tuning at $I=0$, PACZero-ZPL reaches ${88.99\pm0.91}$, within $2.1$pp of the non-private MeZO baseline ($91.1$ FT). No prior method produces usable utility in the high-privacy regime $\varepsilon<1$, and PACZero-ZPL obtains competitive SST-2 accuracy and nontrivial SQuAD F1 across OPT-1.3B and OPT-6.7B at $I=0$.

We propose PACE-GGM, a data-adaptive differentially private method for covariance estimation that concentrates its privacy budget on the most informative entries of the empirical covariance matrix, rather than perturbing all entries. This applies in the natural setting where the modeler supplies separate bounds for each variable, so that individual entries can be measured with less noise than the full matrix. In each round, our method selects a poorly approximated entry, measures it using the Gaussian mechanism, and then reconstructs a full covariance matrix using a maximum-entropy reconstruction objective, leading to a Gaussian graphical model structure. Experiments on diverse real-world datasets demonstrate consistent improvements in estimation error with respect to the Gaussian mechanism and other baselines, particularly in high-dimensional and low-to-moderate privacy regimes.

Federated fine-tuning of large language models (LLMs) enables collaborative training without exposing raw data. However, a recent attack, NeuroImprint, demonstrates that a malicious parameter server can corrupt a PEFT adapter into a privacy backdoor: by assigning a dedicated memorization neuron to each training sample and ensuring each neuron updates at most once, the server can analytically reconstruct 59%--79% of client training data with high semantic fidelity. Existing defenses---including local differential privacy (LDP) and gradient clipping---either fail against this attack or impose unacceptable utility degradation. We present \textbf{TriShield}, a three-layer deterministic defense that completely prevents NeuroImprint-style reconstruction with zero model utility loss and no additional communication rounds. TriShield consists of: (1) a Parameter Artifact Detector that identifies memory-neuron signatures in distributed model parameters before local training begins; (2) a Stateful Virtual Iteration} mechanism that forces Adam/AdamW's momentum state to irreversibly entangle gradients across virtual steps, invalidating NeuroImprint's closed-form inversion; and (3) a Zero-Utility Orthogonal Projection operator that projects all local gradient updates onto the main-task semantic subspace computed via SVD, physically eliminating any gradient components that carry private memorization. We prove theoretically that after Layers 2 and 3, the mutual information between the uploaded gradient and any individual training sample is zero. Experiments on GPT-2 (117M) and Llama-Guard-3-1B verify that TriShield reduces NeuroImprint reconstruction rate to 0% across all tested attack variants, while maintaining or improving training accuracy, with less than 5% additional GPU computation overhead.