The US Census Bureau Disclosure Avoidance System (DAS) balances confidentiality and utility requirements for the decennial US Census (Abowd et al., 2022). The DAS was used in the 2020 Census to produce demographic datasets critically used for legislative apportionment and redistricting, federal and state funding allocation, municipal and infrastructure planning, and scientific research. At the heart of DAS is TopDown, a heuristic post-processing method that combines billions of private noisy measurements across six geographic levels in order to produce new estimates that are consistent, more accurate, and satisfy certain structural constraints on the data. In this work, we introduce BlueDown, a new post-processing method that produces more accurate, consistent estimates while satisfying the same privacy guarantees and structural constraints. We obtain especially large accuracy improvements for aggregates at the county and tract levels on evaluation metrics proposed by the US Census Bureau. From a technical perspective, we develop a new algorithm for generalized least-squares regression that leverages the hierarchical structure of the measurements and that is statistically optimal among linear unbiased estimators. This reduces the computational dependence on the number of geographic regions measured from matrix multiplication time, which would be infeasible for census-scale data, to linear time. We incorporate the additional structural constraints by combining this regression algorithm with an optimization routine that extends TDA to support correlated measurements. We further improve the efficiency of our algorithm using succinct linear-algebraic operations that exploit symmetries in the structure of the measurements and constraints. We believe our hierarchical regression and succinct operations to be of independent interest.

We study the problem of generating synthetic data under differential privacy. We establish fixed-parameter tractability (FPT) for this problem where the parameter is the treewidth of the query family's incidence graph. Our algorithms attain optimal error rates across all regimes and are realized by two different approaches: the first is based on linear programming (LP) and the FPT of the separation problem for the LP dual; the second is based on a subsampled private multiplicative weights method, where we obtain FPT for sampling from Gibbs distributions. Both approaches are unified by a dynamic programming framework over a tree decomposition.

We study differentially private (DP) k-means and k-median clustering in the online streaming setting. In this model, points arrive sequentially, and at each time step, we need to output a set of k centers that optimizes the clustering objective for all points seen so far. We give a generic reduction that transforms the (sensitive) input stream into a private stream, which is a semi-coreset of the input stream. This implies that any (non-private) online clustering algorithm, run as a post-processing step, can achieve good utility for the original clustering objective. Our algorithm matches or improves upon the approximation ratio, space usage, and running time of existing algorithms [Epasto et al., 2026, Dupré la Tour et al., 2024]. A key aspect of our reduction is that it inherits desirable properties of the underlying non-private clustering algorithm, such as consistency [Lattanzi and Vassilvitskii, 2017]–a property not satisfied by previous DP algorithms.

We study the problem of differentially private (DP) computation of coreset for the k-means objective. For a given input set of points, a coreset is another set of points such that the k-means objective for any candidate solution is preserved up to a multiplicative (1 ± α) factor (and some additive factor). We prove the first computational lower bounds for this problem. Specifically, assuming the existence of one-way functions, we show that no polynomial-time (ε, 1/n^ω(1))-DP algorithm can compute a coreset for k-means in the ℓ_∞-metric for some constant α> 0 (and some constant additive factor), even for k=3. For k-means in the Euclidean metric, we show a similar result but only for α= Θ(1/d^2), where d is the dimension.

We study the problem of Stochastic Convex Optimization (SCO) under the constraint of local Label Differential Privacy (L-LDP). In this setting, the features are considered public, but the corresponding labels are sensitive and must be randomized by each user locally before being sent to an untrusted analyzer. Prior work for SCO under L-LDP (Ghazi et al., 2021) established an excess population risk bound with a linear dependence on the size of the label space, K: O(K/ε√(n)) in the high-privacy regime (ε≤ 1) and O(K/e^ε √(n)) in the medium-privacy regime (1 ≤ ε≤ln K). This left open whether this linear cost is fundamental to the L-LDP model. In this note, we resolve this question. First, we present a novel and efficient non-interactive L-LDP algorithm that achieves an excess risk of O(√(K/εn)) in the high-privacy regime (ε≤ 1) and O(√(K/e^ε n)) in the medium-privacy regime (1 ≤ ε≤ln K). This quadratically improves the dependency on the label space size from O(K) to O(√(K)). Second, we prove a matching information-theoretic lower bound across all privacy regimes for any sufficiently large n.

We introduce VaultGemma 1B, a 1 billion parameter model within the Gemma family, fully trained with differential privacy. Pretrained on the identical data mixture used for the Gemma 2 series, VaultGemma 1B represents a significant step forward in privacy-preserving large language models. We openly release this model to the community

Understanding what and how neural networks memorize during training is crucial, both from the perspective of unintentional memorization of potentially sensitive information and from the standpoint of effective knowledge acquisition for real-world, knowledge-intensive tasks. While previous studies primarily investigate memorization within a single modality, such as text memorization in large language models or image memorization in diffusion models, unified multimodal models are becoming increasingly prevalent in practical applications. In this work, we focus on the unique characteristics of cross-modality memorization and conduct a systematic study centered on vision-language models. To facilitate controlled experiments, we first introduce a synthetic persona dataset comprising diverse synthetic person images and textual descriptions. We quantify factual knowledge memorization and cross-modal transferability by training models on a single modality and evaluating their performance in the other. Our results reveal that facts learned in one modality transfer to the other, but a significant gap exists between recalling information in the source and target modalities. Furthermore, we observe that this gap exists across various scenarios, including more capable models, machine unlearning, and the multi-hop case. At the end, we propose a baseline method to mitigate this challenge. We hope our study can inspire future research on developing more robust multimodal learning techniques to enhance cross-modal transferability.

Machine unlearning algorithms, designed for selective removal of training data from models, have emerged as a promising approach to growing privacy concerns. In this work, we expose a critical yet underexplored vulnerability in the deployment of unlearning systems: the assumption that the data requested for removal is always part of the original training set. We present a threat model where an attacker can degrade model accuracy by submitting adversarial unlearning requests for data \textit{not} present in the training set. We propose white-box and black-box attack algorithms and evaluate them through a case study on image classification tasks using the CIFAR-10 and ImageNet datasets, targeting a family of widely used unlearning methods. Our results show extremely poor test accuracy following the attack—3.6% on CIFAR-10 and 0.4% on ImageNet for white-box attacks, and 8.5% on CIFAR-10 and 1.3% on ImageNet for black-box attacks. Additionally, we evaluate various verification mechanisms to detect the legitimacy of unlearning requests and reveal the challenges in verification, as most of the mechanisms fail to detect stealthy attacks without severely impairing their ability to process valid requests. These findings underscore the urgent need for research on more robust request verification methods and unlearning protocols, should the deployment of machine unlearning systems become more prevalent in the future.

The Privacy Sandbox initiative from Google includes APIs for enabling privacy-preserving advertising functionalities as part of the effort around limiting third-party cookies. In particular, the Private Aggregation API (PAA) and the Attribution Reporting API (ARA) can be used for ad measurement while providing different guardrails for safeguarding user privacy, including a framework for satisfying differential privacy (DP). In this work, we provide an abstract model for analyzing the privacy of these APIs and show that they satisfy a formal DP guarantee under certain assumptions. Our analysis handles the case where both the queries and database can change interactively based on previous responses from the API.

We introduce Urania, a novel framework for generating insights about LLM chatbot interactions with rigorous differential privacy (DP) guarantees. The framework employs a private clustering mechanism and innovative keyword extraction methods, including frequency-based, TF-IDF-based, and LLM-guided approaches. By leveraging DP tools such as clustering, partition selection, and histogram-based summarization, Urania provides end-to-end privacy protection. Our evaluation assesses lexical and semantic content preservation, pair similarity, and LLM-based metrics, benchmarking against a non-private Clio-inspired pipeline (Tamkin et al., 2024). Moreover, we develop a simple empirical privacy evaluation that demonstrates the enhanced robustness of our DP pipeline. The results show the framework's ability to extract meaningful conversational insights while maintaining stringent user privacy, effectively balancing data utility with privacy preservation.

User-level differentially private stochastic convex optimization (DP-SCO) has garnered significant attention due to the paramount importance of safeguarding user privacy in modern large-scale machine learning applications. Current methods, such as those based on differentially private stochastic gradient descent (DP-SGD), often struggle with high noise accumulation and suboptimal utility due to the need to privatize every intermediate iterate. In this work, we introduce a novel linear-time algorithm that leverages robust statistics, specifically the median and trimmed mean, to overcome these challenges. Our approach uniquely bounds the sensitivity of all intermediate iterates of SGD with gradient estimation based on robust statistics, thereby significantly reducing the gradient estimation noise for privacy purposes and enhancing the privacy-utility trade-off. By sidestepping the repeated privatization required by previous methods, our algorithm not only achieves an improved theoretical privacy-utility trade-off but also maintains computational efficiency. We complement our algorithm with an information-theoretic lower bound, showing that our upper bound is optimal up to logarithmic factors and the dependence on ϵ. This work sets the stage for more robust and efficient privacy-preserving techniques in machine learning, with implications for future research and application in the field.

The conventional approach in differential privacy (DP) literature formulates the privacy-utility tradeoff with a "privacy-first" perspective: for a predetermined level of privacy, a certain utility is achievable. However, practitioners often operate under a "utility-first" paradigm, prioritizing a desired level of utility and then determining the corresponding privacy cost. Wu et al. [2019] initiated a formal study of this ``utility-first'' perspective by introducing ex-post DP. They demonstrated that by adding correlated Laplace noise and progressively reducing it on demand, a sequence of increasingly accurate estimates of a private parameter can be generated, with the privacy cost attributed only to the least noisy iterate released. This led to a Laplace mechanism variant that achieves a specified utility with minimal privacy loss. However, their work, and similar findings by Whitehouse et al. [2023], are primarily limited to simple mechanisms based on Laplace or Gaussian noise. In this paper, we significantly generalize these results. In particular, we extend the findings of Wu et al. [2019] and Liu and Talwar [2019] to support any sequence of private estimators, incurring at most a doubling of the original privacy budget. Furthermore, we demonstrate that hyperparameter tuning for these estimators, including the selection of an optimal privacy budget, can be performed without additional privacy cost. Finally, we extend our results to ex-post Rényi DP, further broadening the applicability of utility-first privacy mechanisms.

Large language models (LLMs) achieve good performance on challenging reasoning benchmarks, yet could also make basic reasoning mistakes. This contrasting behavior is puzzling when it comes to understanding the mechanisms behind LLMs' reasoning capabilities. One hypothesis is that the increasingly high and nearly saturated performance on common reasoning benchmarks could be due to the memorization of similar problems. In this paper, we systematically investigate this hypothesis with a quantitative measurement of memorization in reasoning tasks, using a dynamically generated logical reasoning benchmark based on Knights and Knaves (K&K) puzzles. We found that LLMs could interpolate the training puzzles (achieving near-perfect accuracy) after fine-tuning, yet fail when those puzzles are slightly perturbed, suggesting that the models heavily rely on memorization to solve those training puzzles. On the other hand, we show that while fine-tuning leads to heavy memorization, it also consistently improves generalization performance. In-depth analyses with perturbation tests, cross difficulty-level transferability, probing model internals, and fine-tuning with wrong answers suggest that the LLMs learn to reason on K&K puzzles despite training data memorization. This phenomenon indicates that LLMs exhibit a complex interplay between memorization and genuine reasoning abilities. Finally, our analysis with per-sample memorization score sheds light on how LLMs switch between reasoning and memorization in solving logical puzzles. Our code and data are available at https://memkklogic.github.io.

Scaling laws have emerged as important components of large language model (LLM) training as they can predict performance gains through scale, and provide guidance on important hyper-parameter choices that would otherwise be expensive. LLMs also rely on large, high-quality training datasets, like those sourced from (sometimes sensitive) user data. Training models on this sensitive user data requires careful privacy protections like differential privacy (DP). However, the dynamics of DP training are significantly different, and consequently their scaling laws are not yet fully understood. In this work, we establish scaling laws that accurately model the intricacies of DP LLM training, providing a complete picture of the compute-privacy-utility tradeoffs and the optimal training configurations in many settings.

We propose SCONE ($S$calable, $C$ontextualized, $O$ffloaded, $N$-gram $E$mbedding), a new method for extending input embedding layers to enhance language model performance. To avoid increased decoding costs, SCONE retains the original vocabulary while introducing embeddings for a set of frequent $n$-grams. These embeddings provide contextualized representation for each input token and are learned with a separate model during training. After training, embeddings are precomputed and stored in off-accelerator memory; during inference, querying them has minimal impact on latency due to the low complexity of embedding lookups. SCONE enables two new scaling strategies: increasing the number of $n$-gram embeddings and scaling the model used to learn them, both while maintaining fixed accelerator usage during inference (in terms of FLOPS and memory). We show that scaling both aspects enables a model with 1B accelerator-resident parameters to outperform a 1.9B-parameter baseline across diverse corpora, while using only about half the FLOPS and accelerator memory during inference.

We study differential privacy (DP) in a multi-party setting where each party only trusts a (known) subset of the other parties with its data. Specifically, given a trust graph where vertices correspond to parties and neighbors are mutually trusting, we give a DP algorithm for aggregation with a much better privacy-utility trade-off than in the well-studied local model of DP (where each party trusts no other party). We further study a robust variant where each party trusts all but an unknown subset of at most $t$ of its neighbors (where $t$ is a given parameter), and give an algorithm for this setting. We complement our algorithms with lower bounds, and discuss implications of our work to other tasks in private learning and analytics.

Differentially Private Stochastic Gradient Descent (DP-SGD) is one of the most widely used algorithms for private machine learning. Due to its efficiency, most practical implementations of DP-SGD shuffle the training examples and divide them into fixed-size mini-batches during training. However, the privacy accounting typically assumes that Poisson subsampling was used, wherein each example is included in each mini-batch independently with some probability. Our first contribution is to show that there can be a substantial gap between these two versions of DP-SGD; specifically, the privacy accounting implies much stronger privacy guarantees than the implementations actually provide. As our second contribution, we propose two approaches to address this gap: (i) an implementation of Poisson subsampling using the Map-Reduce framework that can scale to large datasets that do not fit in memory and (ii) a novel Balls-and-Bins sampling that achieves the “best of both” sampling approaches. Namely, its implementation is similar to shuffling, and it leads to similar utility for DP-SGD training with similar-or-better privacy compared to Poisson subsampling in practical regimes of parameters.

We introduce the Balls-and-Bins sampling for differentially private (DP) optimization methods such as DP-SGD. While it has been common practice to use some form of shuffling in DP-SGD implementations, privacy accounting algorithms have typically assumed that Poisson subsampling is used instead. Recent work by Chua et al. (2024a), however, pointed out that shuffling based DP-SGD can have a much larger privacy cost in practical regimes of parameters. In this work we show that the Balls-and-Bins sampling achieves the "best-of-both" samplers, namely, the implementation of Ballsand-Bins sampling is similar to that of Shuffling and models trained using DP-SGD with Balls-and-Bins sampling achieve utility comparable to those trained using DP-SGD with Shuffling at the same noise multiplier, and yet, Balls-and-Bins sampling enjoys similaror-better privacy amplification as compared to Poisson subsampling in practical regimes.

We introduce PREM (Private Relative Error Multiplicative weight update), a new framework for generating synthetic data that achieves a relative error guarantee for statistical queries under (epsilon, delta)differential privacy (DP). Namely, for a domain X, a family F of queries f : X -> {0, 1}, and zeta > 0, our framework yields a mechanism that on input dataset D is an element of X-n outputs a synthetic dataset (D) over cap is an element of X-n such that all statistical queries in F on D, namely Sigma(x is an element of D) f(x) for f is an element of F, are within a 1 +/- zeta multiplicative factor of the corresponding value on (D) over cap up to an additive error that is polynomial in log |F|, log |X |, log n, log(1/delta), 1/epsilon, and 1/zeta. In contrast, any (epsilon, delta)-DP mechanism is known to require worst-case additive error that is polynomial in at least one of n, |F|, or |X |. We complement our algorithm with nearly matching lower bounds.