data privacy engineers

Abstract: Differential privacy (DP) has become the standard for privacy-preserving data analysis, yet its practical implementation in federated or distributed settings often faces a significant utility gap compared to the central model. While existing frameworks, including local, shuffle, and secure aggregation models, offer vetted primitives, they can incur high error for important tasks such as selection. Our first contribution is to show that this is inherent in the aggregation model: any private selection algorithm relying on the standard noisy aggregation primitive requires $Ω(\sqrt{d}/\varepsilon)$ samples. To address this limitation, we propose adding a new primitive that implements a version of the Sparse Vector Technique (SVT) and argue that it has simple implementations under various trust models. We demonstrate its power by developing an $\varepsilon$-differentially private algorithm for the selection problem. For selection in dimension $d$, our algorithm achieves an additive error of $O\left(\frac{\log(dn)}{\varepsilon}\right)$, matching that of the central model when $n$ is polynomially bounded in $d$. Furthermore, we show that this can be done using a near-optimal expected number $O(d\log^*d)$ of SVT queries. Together with existing lower bounds for the shuffle model, this result establishes an exponential separation between the SVT model and shuffle or aggregation-based models. We demonstrate the model's broad applicability to diverse tasks such as $F_p$ loss minimization, heavy-hitter identification, and sparse mean estimation.

Abstract: Disseminating synthetic data in place of original ones is a promising way to enforce privacy while complying with open science principles, especially in the healthcare domain. To keep pace with the rate at which researchers collect such data, there is a need for fast and flexible synthesis procedures. A popular class of such procedures is based on models of conditional distributions induced by decision trees. Such models can be combined into a synthetic distribution following two main approaches: sequential specification and fully conditional specification. However, there is currently no recommendation on which specification to use to optimize the risk-utility tradeoffs. In this work, we use both specifications to synthesize medical datasets by combining tree-based models of conditional distributions. We compare the quality of the resulting synthetic data using several metrics of risk and utility. Our results indicate no general superiority of either specification over the other. Sequential synthesis seems sensitive to the ordering of the variables, while the fully conditional specification involves more hyperparameters and incurs higher computational costs, which may limit its suitability for off-the-shelf synthesis procedures.

Abstract: Sparse linear regression is a fundamental problem in high-dimensional statistics, and its private counterparts leave a large gap between the central and the local model of differential privacy. Shuffled differential privacy (SDP) sits between the two, offering accuracy closer to the central model without the trust requirement of a central curator. This paper studies sparse linear regression under both non-interactive and interactive SDP protocols. In the non-interactive setting, any non-interactive $(ε,δ)$-SDP protocol is shown to incur an $\ell_2$-norm estimation error of $Ω( \frac{\sqrt{dk}}{nε} )$ with dimension $d$, sparsity $k$, and $n$ users, revealing an inherent dimensionality barrier. In addition, a non-interactive algorithm is proposed that achieves an $\ell_2$-norm upper bound of $\tilde{\mathcal{O}}( \sqrt{\frac{k}{n}} + \frac{d\sqrt{k}}{nε})$. To overcome this barrier, we turn to the interactive user-level setting, where each user holds $m$ samples. A two-round interactive algorithm is developed that first recovers the support through a heavy hitter step and then estimates the parameter, achieving an error of $\tilde{\mathcal{O}}( \sqrt{\frac{k}{nm}} + \frac{k}{n\sqrt{m}ε} )$ with no polynomial dependence on $d$. Furthermore, by extending the score attack framework to user-level data, a new lower bound $Ω( \sqrt{\frac{k\log(d/k)}{nm}} + \frac{k\log(d/k)}{n\sqrt{m}ε} )$ is established for any user-level $(ε,δ)$-DP, showing that the proposed algorithm is near-optimal with only a gap of the factor $\log(d/k)$.

Abstract: We study learning a discrete distribution under person-level differential privacy in the batched setting. Given $n$ users, each contributing $m$ i.i.d. samples from an unknown distribution $μ$ over $[k]$, we seek an estimate of $μ$ with total-variation error $α$. We give polynomial-time algorithms under both pure and approximate differential privacy. Under pure $(\varepsilon,0)$-DP, we achieve $n = \widetilde O(k/(α^2 m)+k/(α\sqrt{m}\varepsilon)+k/\varepsilon)$, the first polynomial-time pure-DP guarantee matching the information-theoretic optimum up to logarithmic factors. Under approximate $(\varepsilon,δ)$-DP, we achieve $n = \widetilde O(k/(α^2 m)+k/(α\sqrt{m}\varepsilon)+k+\log(1/δ)/\varepsilon)$. At $δ=2^{-Θ(k)}$, this is $\widetilde O(k)$ for fixed $α,\varepsilon,m$ and failure probability. Our algorithms use a new degree-6 sum-of-squares estimator for learning from untrusted batches. Its key ingredient is a trace-bounded diagonal majorizer for the difference between the empirical covariance of the repaired batch averages and the multinomial covariance predicted by their mean. We prove that clean data admit this certificate through semidefinite-programming duality and a new application of the stronger symmetric form of Grothendieck's inequality due to Friedland and Lim. The certificate preserves the mean-dependent variance of multinomial batch averages, yielding the near-optimal robust rate $O(η\sqrt{\log(1/η)/m})$ and providing the score required by the privacy reduction. We also prove a statistical query lower bound ruling out a uniformly smaller order of error under fixed polynomial SQ resource bounds.

Abstract: The rapid evolution of Large Language Models is fueled by massive datasets, yet this reliance poses severe privacy risks, as models can inadvertently memorize and even directly output sensitive training data. Synthetic text generation offers a promising solution to this challenge; however, existing methods struggle to reconcile rigorous privacy guarantees with high data utility. In this paper, we propose a new paradigm for private synthetic text generation: Guided Diffusion. Leveraging the unique steerability of Diffusion Language Models, we introduce novel sampling and re-masking procedures that actively guide the iterative denoising steps. These mechanisms steer the generative process to reconstruct fluent text that adheres to a target semantic distribution. We demonstrate that our framework is naturally compatible with Differential Privacy (DP): once the semantic embeddings of the private corpus are protected, the DP guarantee carries over to the generated text by post-processing. Empirically, we show that our approach generates high-quality synthetic text with precise semantic alignment. Furthermore, we validate its effectiveness in DP synthetic text generation: across two datasets and two diffusion backbones, it outperforms Private Evolution and DP-SGD-based fine-tuning in distributional fidelity and downstream utility, while generating significantly faster than Private Evolution. We further extend the framework to Data-Specific Indistinguishability (DSI), which adds a formal certificate against data poisoning and memorization at a small utility cost.

Abstract: This paper derives an exact attenuation formula for multivariate cross-moments under differential privacy achieved through randomized response. From a proposed alternative formulation of randomization matrices compliant with differential privacy guarantees we show that, under attribute-level randomization and where the randomization of the whole distribution is characterized by Kronecker products, any cross-moment of the anonymized dataset involving distinct attributes is equal to the original cross-moment multiplied by attenuation parameters, themselves determined by the part of the overall privacy budget allocated to each attribute. This characterization enables explicit and transparent controls of multivariate relationships preservations in differential privacy through privacy budget allocation. A simple numerical illustration demonstrates that identical total budgets can yield substantially different covariance-preservation profiles. The results also make the multiplicative loss of higher-order interactions explicit and thus can support mechanism design guided by analytical priorities.

Abstract: Hidden randomized rounding couples the privacy loss of successive integer releases. We study a rational-feedback mechanism under predictable signed-unit participation and full observation of every physical output. A preparation's lifetime connects three results. First, preserving complete carries until an observed echo synchronizes the worlds gives exact finite-law point compilation, with support-width exponent $3C-2$ at every fixed budget $C\ge2$. Second, releasing commitments earlier gives a monotone hierarchy whose exact endpoint, strict gaps and numerical brackets quantify calibration loss. At one fixed discrete Gaussian, a loss allowance of 0.09 requires all four commitments. Third, legal regeneration yields an unrestricted KL rate with a square-root testing remainder and a complete asymptotic frontier under joint physical-time and participation constraints. At fixed rational parameters, finite-window occupation programs approximate that frontier to error $2^{-b}$ in polynomial bit time in $b$. Verified countable-transcript semantics and independently checked finite certificates support these analyses. A matched static workload illustrates the resulting design tradeoff: a structured finite integer matrix improves error and fresh randomness, while the scalar feedback instance retains fewer noise-state and source-table bits.

Abstract: An AI agent can reproduce the distribution of its messages and of the receiver's task outcomes while disclosing private information that the task never required. We ask what a passive audit can certify when the auditor knows the authorised sender and the exact observable law but has no trusted pairing of messages with the private states behind them. For a single round, compatible mutual-information leakage forms a sharp interval, and fixing the entire task-relevant message law, with every declared task utility, can still leave a full private bit undetermined; total leakage is determined if and only if, in every task state, the remaining private state or the authorised message is a deterministic function of that state. For a sender, such as an LLM, that selects among its own responses, we prove that in a balanced case its change to the message law within each task state equals $(1-2^{-k})$ times the honest messages' dependence on the attribute, which also sets, up to a constant, how many messages a monitor needs. With Qwen2.5-1.5B-Instruct on a synthetic routing task, selection among 16 responses lets a public decoder recover a private bit in all 8,192 held-out rounds at 98.60\% routing accuracy (honest sender 98.90\%). A monitor that knows the selection rule reaches AUC 0.645 on single messages, close to the ceiling of 0.671 that honest messages predict, and 0.972 over 16, while generic monitors stay near chance. A law-preserving sender built from the same samples recovers the bit in 97.7\% of rounds, and every monitor without the true bit stays near chance against it. A canonical task interface preserves every receiver decision and bounds the remaining information about a balanced attribute by twice the routing-error rate, even for a receiver that shares a key with the sender. These results distinguish what passive auditing can certify from what restricting communication can enforce.

Abstract: We study differentially private black-box evaluation of arbitrary high-dimensional functions. Given a dataset $S$ and query access to a function $f$---whose sensitivity may be unknown or unbounded---the goal is to privately output an approximation to $f(S)$. The black-box evaluator can only query the value of $f$ over a down neighborhood of $S$ (i.e., those subsets of $S$ that are obtained by removing a bounded number of elements from $S$). We design generic black-box evaluators for both pure and approximate differential privacy through a reduction to high-dimensional private quasi-concave optimization (QCO). Our black-box evaluator enjoys a geometric notion of utility. Consider the vectors obtained by applying $f$ on sets in a down neighborhood of $S$. With high probability, the evaluator's output is guaranteed to be in the convex hull of these vectors. Our work generalizes the result of Linder et al. [LRSS25] for real-valued function evaluation to high dimensions. It also recovers the private center-point guarantees of Beimel et al. [BMNS19], with an explicit additive approximation to maximum Tukey depth. We also apply our evaluators to user-level quasi-concave and convex optimization, showing how they can improve upon the sample-and-aggregate baseline of Nissim et al. [NRS07] by replacing the multiplicative data overhead with an additive overhead. Finally, we show that our formulation of high dimensional black-box evaluation and high dimensional private QCO are equivalent up to a factor of the dimension: the hardest private evaluation instances already arise from the cases that $f$ is a (non-private) quasi-concave optimizer.

Abstract: Differentially private learning aims to learn from data while protecting individual training examples. For binary classification, finite Littlestone dimension characterizes approximate private PAC learnability (Alon et al., JACM 2022). Understanding how this dimension controls private sample complexity remains a central question. For classes of Littlestone dimension $d$, the first general upper bound was doubly exponential in $d$ (Bun, Livni, and Moran, FOCS 2020). Subsequent work improved this to $\widetilde O(d^6)$ (Ghazi et al., STOC 2021) and then to $\widetilde O(d^5)$ (Lyu, STOC 2026). We prove a nearly linear upper bound of $O(d\log d)$. Our main algorithmic contribution is a structural exponential mechanism for data-dependent candidate sets equipped with a rank satisfying suitable stability conditions. For natural Littlestone classes such as subspace indicators, this rank has a simple geometric interpretation: it is the codimension. This yields a private PAC learner for subspaces of dimension at most $d$ over any field, with tight linear dependence on $d$ and no dependence on the ambient dimension, improving the quadratic dependence of Kaplan et al. (STOC 2025). Our second contribution is combinatorial: drawing on model-theoretic ideas, we construct a suitable rank for general Littlestone classes and establish the counting bounds required by the mechanism.

Abstract: Differential Privacy (DP) provides a rigorous framework for quantifying privacy guarantees. While most methods achieve DP by injecting calibrated random noise, the intrinsic randomness of certain procedures such as sampling can yield DP guarantees ``for free''. In this work, we develop a unified Rényi divergence framework to characterize the inherent DP guarantees of sampling from a Bayesian posterior distribution. We show that the privacy loss incurred by One-Posterior-Sampling (OPS) is governed by posterior exponential moments of the single-record log-likelihood ratio, and establish explicit DP guarantees under uniformly bounded, sub-Gaussian, or sub-exponential tail regimes. We apply the framework to representative Bayesian models, including categorical likelihoods with arbitrary priors, Gaussian-Gaussian conjugate pair, generalized linear models from the exponential family and linear regression with Gaussian likelihood, both with Gaussian priors on the regression coefficients. Our results elucidate sample size, model structure, neighboring relations in DP (bounded or unbounded), and how prior if applicable, jointly determine the inherent DP guarantees of OPS. Furthermore, our results recover the existing DP guarantees for OPS as special cases -- often with tighter privacy loss bounds -- and substantially broaden the class of Bayesian models for which the inherent DP guarantees of OPS can be rigorously characterized.

Abstract: Differentially private (DP) pipelines often combine heterogeneous mechanisms, yet their guarantees are best analyzed using different notions of privacy (e.g., bounded range, zCDP, ADP). When composing them, we have to analyze the guarantees through a reduced common representation that loses accounting precision. This issue is particularly relevant in DP synthetic data generation, where data preprocessing, generation algorithms, and DP-SGD could appear within the same pipeline. We develop novel tools for tight end-to-end accounting of such compositions using privacy loss distributions (PLD), $f$-DP, and Gaussian DP (GDP). In particular, we derive PLD and GDP analyses of bounded-range mechanisms such as the Exponential mechanism. Building on these theoretical results, we introduce AIM-GDP, a GDP-native variant of AIM (a state-of-the-art DP synthetic data mechanism) that enables easy composability with complex pipelines via PLD, attack-aware risk calibration, and tight end-to-end auditing while consistently achieving better utility; and MixCal, an algorithm for calibrating adaptive mixed compositions using PLD accounting. Overall, our tools enable tighter end-to-end accounting and thus less noise at the same privacy level in DP synthetic data pipelines.

Abstract: We study privacy-preserving algorithms that redact information from a correlated dataset. The goal is to reduce the information leakage about sensitive parts. We analytically characterize the optimal tradeoff between privacy (leakage through correlation) and utility (number of redactions) for local mechanisms and binary Markovian correlations. Our result shows how to decompose the mechanism design problem into a sequence of local mechanism design problems and reveals their sequential relation. The optimal mechanism is the solution to a Finite-Horizon Deterministic Markov Decision Process.

Abstract: Full-support local randomizers can incur unnecessary reporting distortion on ordered alphabets. We study randomized response whose output is restricted to a radius-$t$ neighborhood of the private input. Input-dependent supports create privacy leakage at their boundaries, so ordinary likelihood-ratio calibration is no longer sufficient. Under approximate local privacy restricted to input pairs at distance at most $H$, we derive the exact hockey-stick defect of the mechanism. We then solve the joint design of the truthful probability, off-truth probability, and support radius. The fixed-radius optimum is available in closed form, while the global optimum requires only a one-dimensional integer search. We characterize both the privacy floor and its inverse, namely the smallest defect attainable under a reporting-distortion budget. We further prove that stringent approximate privacy forces the support size to scale as $Ω(H/δ)$. Deterministic evaluations illustrate the resulting tradeoff.

Abstract: We study the design of a statistical privacy mechanism under a bounded $α$-lift leakage constraint. An agent observes useful data $Y$, which is arbitrarily correlated with private data $X$, and releases $U$. The goal is to maximize Pearson $χ^2$-information $χ^2(Y;U)$ while satisfying the point-wise privacy constraint. This utility is an $f$-information that is nonnegative, obeys data processing, and measures the aggregate normalized change from the prior $P_Y$ to the posteriors $P_{Y|U=u}$. The main benefit of this choice is that $χ^2(Y;U)$ is exactly quadratic in the posterior perturbations; hence, no local approximation of the utility is required. For the nonlinear $α$-lift constraint, we derive a uniform Taylor-remainder bound that remains valid for the optimizing, $ε$-dependent perturbation. When $P_{X|Y}$ is invertible, this yields a closed-form quadratic surrogate, an explicitly scaled binary mechanism that satisfies the original $α$-lift constraint, a computable sufficient range for $ε$, and an $O(ε^{3/2})$ bound on the utility gap. For $α=2$, the solution is exact over an explicit range. We transfer these results to point-wise Rényi-divergence privacy, including an exact-feasible mechanism, an explicit privacy-budget range, and matching gap bounds. We also give an exact formulation for arbitrary leakage matrices and evaluate exact-feasible mechanisms numerically.

Abstract: Selection is a task that chooses one element from a finite public candidate range to maximize a data-dependent score. In differential privacy (DP), the exponential mechanism (EM) samples a candidate at a temperature calibrated to the global sensitivity. In this paper, we study when dataset-dependent sensitivity can safely replace global sensitivity in private selection. We propose three valid approaches. First, a private, high-probability upper bound on local sensitivity yields approximate DP, and the method extends to finite higher-order sensitivity hierarchies. Second, our Propose-Test-Release (PTR) variant privately searches a finite public grid for a temperature scale rather than fixing it in advance. Third, smooth sensitivity supports several designs. A candidate-independent smooth geometric construction produces a sensitivity envelope that is admissible under the local dampening framework, which privacy is guaranteed for any admissible envelope. Additionally, a separate logarithmic transformation utilizes smooth sensitivity to produce a smoothed candidate score function with advantages: having controlled global sensitivity, and preserving the maximizers of the original utility score, i.e., candidates maximizing the utility. Both of the designs yield range-independent pure DP. Besides that, we also give two approximate DP private selectors using smooth sensitivity: a direct EM with smooth sensitivity calibrated to the candidate range and privacy parameters that matches a theoretical lower bound up to some constant factor, and one using a privatized smooth upper scale by analyzing the logarithmic transform of the smoothness. For every proposed mechanism, we derive a high-probability regret bound under its stated conditions.

Abstract: Machine unlearning updates a trained model after records are deleted, aiming to match exact retraining without repeating the full training procedure. We develop Gaussian mechanisms for Newton updates under sequential deletion requests. Using Gaussian differential privacy (GDP) and its adaptive composition rule, we show that the full sequence of released models is statistically difficult to distinguish from matched exact retraining. To calibrate these mechanisms for empirical risk minimization, we derive upper bounds on the error of the Newton approximation relative to exact retraining and on how this error changes after each deletion batch. Independent Gaussian noise is calibrated using bounds on the full residual at each release, whereas Gaussian random walk noise uses smaller bounds on residual increments. These bounds yield allocations minimizing the worst-case maximum noise variance across releases under the resulting GDP certification constraints. With count-based bounds, the random walk asymptotically matches the worst-case variance of a single release at deletion cap $M$, while independent noise incurs an additional factor of order $M$. Set-based bounds can reduce the noise variances by using gradients and Hessians of the deleted records. For singleton deletion, we further show that count-based independent noise, count-based random walk noise, and set-based independent noise are minimax among fixed Gaussian covariances under their respective residual or increment bounds. With set-based bounds, allowing variances to adapt to deleted records can improve on every fixed covariance by a factor of order $(\log M)^2$ on some data sequences. The residual and noise bounds also yield parameter and predictive consistency relative to exact retraining, uniformly over deletion policies. Simulations and a credit default data analysis evaluate bounds, noise variances, and estimation errors.

Abstract: Blowfish privacy relaxes differential privacy (DP) by protecting only the attribute-value substitutions a data owner specifies as edges of a policy graph. A sparser policy can reduce the noise required by a mechanism, but only when the released statistic changes less across protected substitutions than across arbitrary DP neighbors. We study this question for evolutionary, nearest-neighbor DP synthesizers such as Private Evolution (PE) and its tabular instantiation Tab-PE, which score private records against a candidate population and release a noisy vote histogram. Their hard vote is constant inside each candidate's decision region and jumps at its boundary. Its policy-specific sensitivity therefore equals the full worst-case value whenever at least one protected substitution crosses a boundary, regardless of how short that substitution is. Because every round we examined contained such a substitution, the policy graph gave no reduction in noise. We propose BF-Soft, a temperature-smoothed soft vote whose response changes gradually with distance. Its sensitivity has a tight closed-form bound in the policy graph's reach and the temperature, independent of the number of candidates, and the bound can be computed once before synthesis. It also predicts from the policy alone when policy-aware smoothing cannot substantially reduce noise: protecting a flat categorical or binary attribute drives the reach to its maximum. On real and synthetic datasets under narrow numeric policies, BF-Soft reduces error relative to hard voting at strong privacy budgets, while the advantage reverses at weaker budgets. A public-data pilot predicts when soft voting is beneficial without spending private budget.

Abstract: Dense associative memory (DAM) provides an energy-based framework for memory retrieval with close connections to attention mechanisms in modern artificial intelligence. Despite growing interest in differential privacy for AI, the privacy of DAM retrieval dynamics remains relatively unexplored. In this paper, we develop a differential privacy framework for log-sum-ReLU (LSR) dense associative memory, whose finite-support retrieval dynamics pose distinctive challenges for privacy-preserving computation. We propose the Boundary-Responsive Adaptive Correction Evolution (BRACE) algorithm, a differentially private retrieval mechanism for LSR-DAM that adaptively corrects boundary-sensitive perturbations to control their cumulative effect over the retrieval trajectory. In theory, we prove that our method is minimax optimal by deriving dimension-independent terminal and full-trajectory retrieval error rates, with optimal dependence on the inverse temperature and, in the growing-horizon regime, the retrieval horizon. We further establish central limit theorems that enable uncertainty quantification for private retrieval by characterizing its asymptotic distribution and the additional variability introduced by privacy. Numerical experiments compare our proposed method with baseline differential privacy approaches and evaluate its retrieval accuracy. Together, our results provide a theoretical foundation for optimal privacy-preserving retrieval and uncertainty quantification in energy-based associative memory systems.

Abstract: As multimodal large language models (MLLMs) become more capable and widely deployed, concerns about privacy and safety have become increasingly pressing. Machine unlearning offers one approach to addressing these concerns by removing designated information from trained models while preserving unrelated capabilities. However, fragmented implementations and evaluation protocols, incomplete robustness testing, and limited understanding of metric reliability make progress in MLLM unlearning difficult to assess systematically. We introduce Open-MMUnlearning, an open-source, extensible framework that integrates target-model preparation, multimodal data processing, unlearning, and evaluation through shared interfaces and structured configurations. The framework supports five benchmarks spanning privacy, safety, and copyright, eight MLLMs from four model families, and twelve unlearning methods. Its evaluation suite jointly assesses forgetting effectiveness, retained utility, and robustness to model interventions, adversarial inputs, and membership inference attacks. Using a common evaluation protocol, we compare ten representative unlearning methods. In this comparison, GD and MIP-Editor tie for the highest overall score: GD achieves the highest Forget Quality, while MIP-Editor preserves more Model Utility. We further introduce a metric meta-evaluation protocol that tests faithfulness using models with controlled exposure to target knowledge and robustness under quantization and relearning. Among the thirteen evaluated metrics, BLEU achieves the highest aggregate reliability score. KS-Test attains the highest faithfulness AUC but performs less well on robustness. Together, the framework and these findings support reproducible comparison of MLLM unlearning methods and systematic assessment of evaluation reliability.

Abstract: Differentially private time-series generators commonly produce fixed-length synthetic windows, whereas downstream forecasting models often require long continuous training sequences. How these windows are assembled after generation can therefore alter the effective synthetic data presented to a forecaster, even when the trained generator remains unchanged. We study this post-generation sequence assembly process by systematically varying overlap rates and window-weighting schemes and evaluating the resulting sequences in terms of boundary continuity, statistical and temporal fidelity, and Train-on-Synthetic-Test-on-Real (TSTR) forecasting utility. Across four types of public datasets (ETTh1, ETTm1, Weather, and Appliances) and five forecasting models, the results reveal a clear forecaster-dependent assembly principle: downstream TSTR utility is jointly shaped by the forecaster, overlap rate, and window-weighting scheme, leading to distinct assembly preferences across forecasting models. Increased overlap generally improves boundary continuity, but improvements in continuity or individual fidelity diagnostics do not consistently reduce forecasting error, indicating that these diagnostics alone are insufficient for selecting assembly configurations. Complete five-forecaster assembly grids, together with matched Train-on-Real-Test-on-Real (TRTR) references, further characterize these regularities and quantify assembly-dependent utility relative to real-data training. We then validate the identified principles through additional analyses of robustness and generator variability.

Abstract: Finding heavy nodes in a tree---those whose counts exceed a given threshold---is a building block for analysis and learning over structured data. Achieving record-level differential privacy (DP) without sacrificing accuracy is challenging because each record contributes to counts along an entire root-to-leaf path, allowing privacy costs to accumulate across levels. Existing methods account for the multiple threshold comparisons for each record incur additive error margins of $Ω_{\varepsilon,δ}(\log h)$ or $Ω_{\varepsilon,δ}(\sqrt{\log h})$ for tree height $h$. We introduce \textsc{BetweenCut}, an $(\varepsilon,δ)$-DP algorithm with an additive error margin of $O_{\varepsilon,δ}(\log\log h)$, improving the existing bounds for deep trees. This error holds simultaneously for all nodes and is independent of the input database size.

Abstract: A cryptographic secret is issued for a purpose but grants a capability, and the capability is usually larger: a decryption key meant for computing aggregates can read every record, and a token meant to pay one invoice can drain the account. Deployed systems state the purpose in policy and enforce only the capability. We make the purpose a property of the secret. A mechanism sees operations, not reasons, so a scheme enforces an admissible set $A(P)$ of operations that stands in for a declared intended use $I$; whether $I$ captures the human purpose is a modeling obligation that marks where policy takes over. Against the same $I$ we define three regimes: under confinement an operation outside the intended use is infeasible, under mediation a trusted component refuses it, and under accountability use beyond a stated bound is possible but attributed to the holder. The confinement games, for unpredictability and indistinguishability, coincide with the key-query forms of functional-signature unforgeability and constrained-PRF pseudorandomness and correspond to simulation-secure functional encryption within its feasibility boundary; stated against $I$, they also register a predicate that permits too much. A payment token uses all three regimes on one secret: it pays one capped charge at one merchant, can be narrowed but not widened, is checked by the merchant, and identifies the withdrawing account if spent twice. Attenuation unforgeability reduces to unforgeable signatures and a collision-resistant hash without random oracles; traceability and non-frameability hold under discrete log and unforgeable signatures in the random-oracle model. We claim no new primitive, hardness assumption, or general composition theorem; the framework is a common specification against which such primitives are stated and compared.

Abstract: The widespread application of graph data inevitably brings significant privacy risks, as its unprotected use can lead to the leakage of sensitive information. These risks are particularly acute in the setting with an untrusted curator, where the data remains decentralized and each user only holds the connections to their neighbors. To mitigate such privacy risks, we adopt local differential privacy (LDP) to collect users' private information and generate a synthetic graph. However, existing methods suffer from either excessive noise injection by perturbing the local adjacency lists or significant structural information loss due to the simplistic graph encoding process. To address these issues, we propose LDPGraph, an effective graph synthesis algorithm that takes one step further by exploiting neighborhood structures under LDP. To obtain neighborhood statistics beyond degrees, LDPGraph aggregates a noisy global view from perturbed adjacency lists and combines it with projected local connections to estimate node-level triangle counts. To correct the structural inconsistency caused by separately perturbing degree and triangle count, LDPGraph jointly refines them into feasible degree-triangle targets. To reconstruct a global graph from these estimated targets, LDPGraph adopts a triangle-first strategy that first preserves local clustering structures and then fulfills remaining degree requirements. Extensive experiments on four real-world datasets and multiple commonly used graph metrics validate the superiority of LDPGraph. Source code is available at https://github.com/ZJU-TrustAID/LDPGraph.

Abstract: We propose a simple framework for constructing differentially private confidence regions \textit{in one shot}, i.e., by adding noise only to the final resampling quantile instead of privatizing the estimator computed on each resample. The cost of privacy of our procedure is only logarithmic in the number of resamples $B$ under with-replacement ($m$-out-of-$n$) sampling and independent of $B$ under without replacement sampling (subsampling), avoiding the $\sqrt{B}$ factor that arises in previous works. We provide nonasymptotic Gaussian Differential Privacy (GDP) and utility guarantees for both subsampling and $m$-out-of-$n$ resampling, covering mean-like estimators with small global sensitivity as well as estimators admitting efficiently computable smooth sensitivity bounds, including quantiles and degenerate U-statistics. This allows us to also obtain private confidence regions for degenerate U-statistics where the private error is much smaller than the non-private error. In all, we provide a toolbox for widely applicable DP uncertainty quantification procedures under popular resampling strategies while avoiding the computational and privacy costs of privatizing many intermediate resample statistics.

Abstract: We study sparse locally private discrete mechanisms generated by a nonnegative kernel and an input-dependent admissible output support. The support set is intentionally small relative to the ambient alphabet and acts as a mechanism-design parameter. This formulation covers metric-ball supports, sparse exponential mechanisms, sparse staircase mechanisms, sparse randomized response, sparse additive kernels such as Skellam perturbations, and Poisson-binomial-inspired bounded-support channels. We give a general exact characterization of pure and approximate local differential privacy for this sparse-kernel class. Pure local differential privacy forces all supports to coincide, so genuinely input-dependent sparse supports are incompatible with pure privacy. In the approximate regime, the privacy defect decomposes exactly into support leakage and overlap excess loss. We instantiate the formula for several discrete mechanism families. For sparse staircase mechanisms, a shell-ratio condition eliminates overlap excess loss. For graph-metric supports, overlap of metric balls is necessary for nontrivial privacy. For sparse randomized response, the support-leakage term has a closed form in terms of support mismatch. For generic radius-truncated additive kernels and, in particular, sparse Skellam mechanisms, we obtain exact finite-support formulas in terms of the Skellam CDF and an exact Bessel-ratio overlap condition. Numerical evaluations illustrate how support radius and kernel shape separately affect support leakage and overlap excess loss.

Abstract: Multi-attribute user records are inherently heterogeneous, often combining continuous, categorical, and binary attributes, and they frequently exhibit strong cross-attribute dependencies. Designing high-utility metric differential privacy (mDP) mechanisms for such records is challenging. Simple predefined mechanisms, such as distance-based noise, may be poorly aligned with task-specific utility loss, whereas fully optimization-based mechanisms can be computationally prohibitive for multi-attribute records. We propose Dependency-aware Heterogeneous Data Perturbation (DepHDP)}, a framework for multi-attribute mDP that combines dependency-aware attribute grouping with heterogeneous perturbation design. Rather than applying a one-size-fits-all mechanism, DepHDP selects an appropriate perturbation strategy for each attribute or attribute group, choosing between efficient predefined mechanisms, such as Laplace or Exponential mechanisms, and optimization-based designs. This selection is guided by both domain size and a predefined-noise adequacy criterion, which quantifies whether task-induced utility loss can be well explained by perturbation magnitude. To support scalable end-to-end optimization, DepHDP estimates group-level utility loss through sampling and lightweight surrogate modeling, and jointly optimizes privacy-budget allocation and group-wise mechanism design under a global $\ell_p$-metric mDP constraint. Across three case studies, DepHDP improves privacy--utility trade-offs over uniform baselines at lower computational cost than full-record OPT on evaluated domains.

Abstract: Differential privacy (DP) admits several notions, but the choice among them may affect both privacy analysis and utility. In this paper, we consider four mainstream curve-based privacy notions within a unified information-theoretic framework. For a fixed ordered pair of output distributions, we establish information equivalence among the two directional privacy profiles of $(\varepsilon,δ)$-DP, the pair of hypothesis-testing trade-off functions, and the extended privacy-loss distribution. The exact Rényi differential privacy (RDP) curve joins this equivalence class whenever it is finite at some order greater than one. Under this mild condition, choosing among these notions changes only their semantic interpretation and computational requirements. In contrast, taking the maximum of the directional privacy profiles or compressing the RDP curve into a single zero-concentrated differential privacy (zCDP) parameter can lose information. We quantify the information loss between the exact RDP curve and its zCDP bound for standard noise mechanisms. This gap is zero for Gaussian noise but generally positive for Gaussian-mixture, Laplace, discrete Gaussian, and Poisson-subsampled Gaussian mechanisms. Moreover, this gap grows linearly with the number of independently composed mechanisms. Our information-theoretic perspective has practical consequences. At the same certified privacy level, retaining the full RDP curve rather than using zCDP reduces the required noise variance by up to $45\%$ for Gaussian-mixture noise in workloads comparable in size to the American Community Survey. For DP-SGD on Fashion-MNIST under Poisson subsampling, an RDP-based privacy accountant improves test accuracy by up to $8.73$ percentage points compared to a zCDP-based accountant when both are calibrated to the same $(\varepsilon,δ)$ guarantee.

Abstract: Generative models for tabular data are typically trained separately for each dataset, limiting knowledge transfer and requiring the storage of many specialized models. In this paper, we introduce CDMD, a tabular diffusion model trained jointly across heterogeneous datasets with different schemas and variable numbers of numerical and categorical features. Unlike existing cross-dataset tabular diffusion models that operate in continuous representation spaces, CDMD defines diffusion directly over the mixed-type feature space and is trained end-to-end. To accommodate heterogeneous categorical domains, we introduce a schema-restricted reverse-process parameterization for masked diffusion models, in which the output space dynamically adapts to each feature's vocabulary. We then compose numerical and categorical feature-level diffusion processes into a schema-dependent row-level process. A shared schema-aware Transformer denoiser captures dependencies between features and parameterizes the reverse process across varying schemas. On seven real-world datasets, a single jointly trained CDMD achieves the highest average generation quality among strong single-dataset and cross-dataset baselines, while using substantially fewer total parameters than the collection of separately trained models. Furthermore, pre-training on a corpus of 337 datasets improves generation on previously unseen datasets under both limited target data and limited adaptation epochs. These results demonstrate the potential of direct mixed-type diffusion for shared and transferable tabular data generation. Our code is available at https://github.com/ketatam/cdmd.

Abstract: Clinical research in psychiatry increasingly relies on large scale collection of spoken language data to identify acoustic and linguistic biomarkers. Yet evolving consent and protocol requirements can oblige investigators to remove a designated speaker from multi-speaker recordings and to verify said removal at a scale infeasible for manual review of entire corpora. We study this verification problem for role-driven dyadic clinical dialogue in psychiatry and investigate it with two parallel, symmetric pipelines: confirming that clinician speech has been removed from psychiatric interview recordings, and confirming that patient speech has been removed from the same recordings. Each pipeline redacts the raw audio for its target role and then scans the surviving output with audio-language and large-language models to identify missed deletions. We evaluate this approach on a corpus of 48 dyadic recordings drawn from psychiatry settings, testing four open-weight models in an inference-only setting: Gemma-4-12B, Gemma-4-31B, Nemotron-3-Nano, and Nemotron-3-Nano-Omni. A disjunctive OR ensemble over fourteen model-view configurations had a combined F1 of 0.478 (precision 0.330, recall 0.870), an improvement over individual model estimates driven by recall gains that point to substantial complementarity across models and context views.

Abstract: Private Evolution (PE) is a differentially private algorithm for synthetic data generation. While it can be viewed as a Wasserstein learning algorithm, it performs much better in practice than worst-case Wasserstein analyses would predict. We recast PE as generative model-augmented Wasserstein learning. We show theoretically that when we take into account the use of a generative model that is able to capture something about the true distribution, then we can obtain much better performance bounds. For example, if the generator gives samples in the same low-dimensional space as the distribution, then sample complexity depends on intrinsic, not ambient, dimension. We also show that standard variants of PE can fail to converge on simple well-clustered instances, and propose a new geometry-aware version of PE with provable convergence on such instances. Experimentally, we show that our new algorithm is competitive with standard baselines and can improve recall.

Abstract: We study the problem of approximating the John ellipsoid (JE) of a given (centrally symmetric) polytope of $n$ constraints in a Euclidean space under differential privacy (DP). We give the first differentially private algorithm for this problem under the standard model, where neighboring datasets may differ arbitrarily in one a single constraint. Our work also extends to the complimentary problem of Minimum Enclosing Ellipsoid of $n$ points in the Euclidean space. Our approach is based on the recent non-private multiplicative-weights algorithm of~\cite{pmlr-v99-cohen19a}. First we introduce a non-private generalization of the Cohen et al algorithm, yielding a $(1+γ)$-approximation of the JE problem while violating at most $κn$ constraints in $O(\log(1/κ)/γ)$ iterations. This variant works by projecting the intermediate weights assigned to the constraints onto the set of $κ$-dense distributions, similarly to~\cite{bun2020efficientnoisetolerantprivatelearning}. We then design a $ρ$-zCDP variant of this algorithm by adding Gaussian noise to the weighted covariance matrix aggregated in each step of the algorithm. Under a mild goodness assumption on the data we can assert that the resulting noisy matrix is close to the true matrix, thereby achieving essentially the same guarantee as the non-private algorithm provided sufficiently many input points. Thus our method achieves an efficient DP poly-time algorithm under concrete sample complexity bounds.

Abstract: We give a gap-free differentially private algorithm for the principal component analysis (PCA) problem with Gaussian data.

Abstract: We study asymmetric simple binary hypothesis testing between $H_0:P_0^{n}$ and $H_1:P_1^{n}$, based on $n$ independent and identically distributed observations. Leveraging a variational representation of Rényi divergence of order $α$, we derive our main result: a finite-sample converse with $α>1$. The bound uses both directions of the divergence $D_α(P_1\|P_0)$ and $D_α(P_0\|P_1)$, tensorises under product measures, and contains familiar data-processing converses as boundary cases. For comparison, we apply the same variational approach to general $f$-divergences and specialise it to total variation, $E_γ$, Hellinger, and Kullback Leibler divergences, thereby recovering familiar converses within a unified framework. Together with an achievability bound involving Rényi divergence with $α\in (0,1)$, the main converse recovers the phase transition of the optimal Type II error under the exponentially decaying Type I error constraint $\varepsilon_n=e^{-nr}$. Under regularity conditions, the optimal Type II error vanishes exponentially when $r<D(P_1\|P_0)$ and converges exponentially fast to one when $r>D(P_1\|P_0)$. We also derive sample-complexity bounds and extend both the converse and achievability analyses to locally differentially private observations, quantifying the cost of privacy and recovering the non-private achievability bound as the privacy constraint vanishes.

Abstract: Deploying large language models (LLMs) on sensitive data via Retrieval-Augmented Generation (RAG) introduces severe privacy risks. Recent studies apply Differential Privacy (DP) to LLMs with RAG for formal privacy guarantees. However, existing DP-RAG frameworks rapidly exhaust the privacy budget. Although recent efforts attempt to save the budget by narrowing the retrieval scope or sparsifying private generation, these methods themselves cumulatively consume the budget, whereas they could actually rely merely on public information or at a negligible one-time privacy cost. This mismatch fails to align budget expenditure with the model's actual reliance on private data, causing substantial waste on operations that require no private access. To address this, we propose SparsePay-RAG, adopting "only pay what you must spend" as its core principle. Using public information as a zero-privacy prior, it charges the privacy budget only for the private increment. Specifically, SparsePay-RAG narrows the retrieval scope via public topic-guided clustering, adaptively controls private access frequency without privacy cost through isotonic cross-layer trajectory fitting, and compresses per-access budget via DP contrastive decoding. Under strong privacy constraints, experiments show SparsePay-RAG achieves superior privacy-utility trade-offs over baselines.

Abstract: Streaming principal component analysis (PCA) seeks to recover a leading spectral subspace in a single pass over a data stream. We give a new analysis of the ubiquitous Oja's algorithm [Oja82] for the most general, gap-free variant of this problem, where no eigengap assumptions are made on the underlying mean matrix, complemented by a nearly-matching lower bound. Prior works achieving near-optimal rates for streaming PCA either required gap assumptions [JJK+16, HNWW21], or were limited to rank-one updates [AZL17, Lia23]. Our proof only uses a second moment bound on the individual stochastic updates, bypassing the almost sure bounds needed by prior near-optimal analyses, and the analogous offline matrix Bernstein bound. We also extend our result to a Rayleigh quotient notion of approximate PCA, addressing an open question of [JJK+16]. As our main application, we give gap-free differentially private PCA guarantees for sub-Gaussian data, settling Conjecture 1.1 of [Bro26] up to logarithmic factors.

Abstract: We study differentially private covariance estimation in operator norm for mean-zero sub-Gaussian distributions with unknown covariance support and at most $k$ nonzero entries per row. We develop a multiscale random-threshold algorithm with sample complexity $\ot(k^2/α^2+k\sqrt d/(α\varepsilon))$ for $(\varepsilon,δ)$-differential privacy and error at most $ασ^2$, where $d$ is the dimension and $σ$ is a known sub-Gaussian scale. The bound improves the privacy-dependent term of the existing $\ot(k^2/α^2+k^{3/2}\sqrt d/(α\varepsilon))$ \citep{kumar2026curse} upper bound by a factor of $\sqrt k$, and matches the lower bound of $\widetildeΩ(k^2/α^2 + k\sqrt{d}/(α\varepsilon))$ in its applicable parameter regime. Our key technical ingredient is a direct operator-norm bound on the centered fluctuations of an ideal reconstruction, exploiting conditional independence rather than accumulating entrywise errors across each row. A multiscale allocation of threshold tests balances reconstruction variance against query sensitivity. Together, these ingredients sharpen the trade-off between approximation error and privacy protection, removing the additional $\sqrt{k}$ factor from the privacy-dependent sample complexity.

Abstract: We study the statistical privacy of outsourcing matrix multiplication over a finite field ${\mathbb F_q}$ to a single server using additive masks of rank at most $r$. For independent uniform $n\times n$ inputs, we show that uniform \emph{rank-ball masks} and products of independent uniform factors give maximal-correlation secrecy of at most $q^{-r}$ against the complete server view, with $O(n^2r)$ field operations for encoding and decoding. This secrecy captures how effectively the server is prevented from estimating functions of the inputs. We prove an asymptotically matching lower bound of this secrecy measure for $r=o(n)$, showing that both sampling methods are asymptotically optimal among input-independent additive masks of rank at most $r$, even when secret invertible transformations are allowed. We also characterize the posterior distribution for uniform rank-ball masks under arbitrary joint input distributions and prove approximate individual security for rows and columns under independent uniform inputs. Finally, we show that every input-independent additive mask of rank at most $r=o(n)$ requires $δ\to1$ in entry-level $(\varepsilon,δ)$-differential privacy for fixed field size $q$ and bounded $\varepsilon$.

Abstract: Degree-sequence realizability is the combinatorial basis of configuration models, but degree constraints alone do not ensure the preservation of graph dynamics. Hence, configuration models are unable to recover centrality measures, unless these are strongly correlated with the degree sequence. To address this matter, we introduce EP-realizability, the analogue problem induced by an equitable partition (EP): given the EP of a graph, decide whether the partition is realized by a simple undirected loopless graph and therefore construct such a graph. After defining the problem, we solve it by reducing it to sub-problems related to Havel--Hakimi and the Gale--Ryser theorem. We also face the challenge of solving the problem with an Approximate Equitable Partition ($\varepsilon$-EP), so that it is possible to reconstruct a network starting from partial and more privacy-preserving information. We evaluate privacy with edge overlap, deriving also, for our proposed $\varepsilon$-EP-realizability solution, a predictor for this metric. Experiments on Karate, Cora, CiteSeer and PubMed datasets show that our algorithm achieves a favourable and tunable privacy--utility trade-off, comparing the results with Havel--Hakimi algorithm, Newman's configuration model and a stochastic block model. Finally, both with real data and random graphs, we show that our algorithm has approximately linear time complexity with respect to the number of edges.

Abstract: We study the fair division of indivisible goods under pure differential privacy, continuing the line of work initiated by Manurangsi and Suksompong. For $n$ agents with nonnegative additive utilities over $m$ goods and a fixed privacy parameter, we give an entry-private algorithm that, with high probability, achieves consensus envy-freeness up to $O(\sqrt n+\log^3 m)$ goods. This substantially improves the dependence on $n$ over the previous $O(n\log m)$ guarantee for ordinary envy-freeness, while providing the stronger consensus guarantee. A key ingredient is a private algorithm for multicolor discrepancy, which may be of independent interest. Our algorithm may require exponential time. We also obtain substantially stronger guarantees under additional structure: when all item values belong to a public alphabet of size $D$, we give a polynomial-time entry-private algorithm achieving ordinary envy-freeness up to $O(\operatorname{polylog}(mD))$ goods with high probability. Finally, we prove an $Ω(\log n)$ lower bound on the number of goods that must be removed to achieve ordinary envy-freeness under entry privacy, for sufficiently many goods, even with binary utilities.

Abstract: Graph property testing asks whether a massive graph satisfies a given property, or is far from doing so, using only a sublinear number of queries to the graph. Since property testers typically inspect only a small, randomly sampled portion of the input, they appear naturally compatible with differential privacy and privacy amplification by subsampling. Despite this, few results link these two fields. We initiate a systematic study of differentially private graph property testing with the goal of designing efficient testers with formal privacy guarantees in the dense and bounded-degree graph models. We develop new privacy amplification theorems for several widely used graph-sampling procedures such as induced subgraph sampling, random walks and k-disc sampling. We then leverage these privacy amplification techniques to design a private canonical tester in the dense graph model, as well as private bipartiteness testers and subgraph freeness testers in the dense and bounded-degree graph models. Finally, using the new privacy amplification theorem for k-disc sampling, we prove that every property of hyperfinite graphs is privately testable. The resulting query complexities of our private testers are comparable to those of their non-private counterparts.

Abstract: We study combinatorial optimization problems under the constraint of $ε$-differential privacy ($ε$-DP). Given the strong lower bounds for explicitly outputting solutions, we work within the implicit representation framework of Gupta et al. (SODA 2010), where a private polynomial-time randomized "encoder" generates a representation of a solution, and a "decoder" uses this representation along with the input to extract a valid final solution. In this work, we generalize this framework by allowing the encoder to run in fixed-parameter tractable time. This circumvents approximation barriers inherent to polynomial-time algorithms and obtains improved guarantees for many fundamental combinatorial optimization problems. Finally, we establish the first representation-independent lower bounds for our framework. Assuming a non-uniform variant of the Gap Exponential Time Hypothesis, for sufficiently small $ε> 0$, we prove that no $ε$-DP encoder-decoder pair can achieve certain approximation guarantees, if the decoder runs in subexponential time. We further provide representation-dependent lower bounds that hold even for larger $ε$.

Abstract: We revisit differentially private (DP) text synthesis in the realistic setting of distributed users, where privacy concerns preclude a trusted curator with access to raw user texts. Existing DP text synthesis pipelines are designed for a trusted, centralized curator and often cannot be deployed in distributed settings due to unrealistic trust and access assumptions; when adapted naively, they require repeated, tightly synchronized user participation and incur significant overhead. To address this gap, we propose a DP--cryptography co-design for textual data synthesis that requires no trusted curator and requires only lightweight user participation. Our approach has two optimized components. First, we design a distributed-friendly DP synthesis algorithm that releases a one-time DP summary in an embedding space: it identifies frequent semantic regions and releases their DP centroids, enabling training-free, non-iterative offline text synthesis. We further introduce semantic support protection, which ensures the released summary avoids semantic neighborhoods of infrequent texts, reducing the risk of exposing rare user data. Second, we develop a custom secure protocol that implements this algorithm over distributed user data, enforcing end-to-end DP guarantees without requiring a trusted curator. On four benchmarks, we achieve utility comparable to the state-of-the-art centralized DP synthesis method.