arXiv subjects

Kunal Talwar

Publications and source records attributed to Kunal Talwar.

At least 19 recordsLinked to original sources

arXiv2026

Complexity of Differentially Private Selection via Federated APIs

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.

cs.CR↗

arXiv2026

Understanding Private Evolution as Learning-Augmented Clustering

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.

cs.LG↗

arXiv2026

Wally: Batched Private Nearest Neighbor Search at Scale

We present Wally, a batched private nearest-neighbor search protocol that uses differential privacy to break the linear computation barrier of fully-oblivious schemes. In Tiptoe, the server must process the entire database per query to hide the access pattern, resulting in low throughput (909 QPS) and high communication (17.4 MB) on a 3.2M-entry database. Sublinear alternatives like Pacmann require 614 MB of client storage and an offline streaming phase. Wally's key insight is that fully-oblivious schemes are prohibitively expensive at scale, but the same scale also provides an opportunity. Large-scale systems naturally have many concurrent clients. Wally batches queries from non-coordinating clients, each independently adding fake queries to hide which clusters it accesses. The fake query counts follow a negative binomial distribution, which is non-negative and infinitely divisible, allowing independent sampling without coordination. Clients send queries at random times through an existing anonymization service, avoiding a centralized shuffler. The server sees only an anonymized, noisy stream of cluster accesses that is provably (epsilon, delta)-differentially private, computing over only the relevant clusters. The client encrypts its query under SHE so the server returns only encrypted similarity scores. On a 3.2M-entry database with 500K-query batches, Wally achieves 7-29x higher throughput and 6.7-31x lower communication than Tiptoe, and 15,000x lower client storage than Pacmann, with strong (epsilon=0.1, delta=2^{-26})-DP and comparable accuracy. We also propose optimizations to SHE and keyword PIR yielding 2-3x improvements in PIR and 20-25% in BFV operations, and release an open-source BFV library in Swift.

cs.CR↗

arXiv2026

Cram Less to Fit More: Training Data Pruning Improves Memorization of Facts

Large language models (LLMs) can struggle to memorize factual knowledge in their parameters, often leading to hallucinations and poor performance on knowledge-intensive tasks. In this paper, we formalize fact memorization from an information-theoretic perspective and study how training data distributions affect fact accuracy. We show that fact accuracy is suboptimal (below the capacity limit) whenever the amount of information contained in the training data facts exceeds model capacity. This is further exacerbated when the fact frequency distribution is skewed (e.g. a power law). We propose data selection schemes based on the training loss alone that aim to limit the number of facts in the training data and flatten their frequency distribution. On semi-synthetic datasets containing high-entropy facts, our selection method effectively boosts fact accuracy to the capacity limit. When pretraining language models from scratch on an annotated Wikipedia corpus, our selection method enables a GPT2-Small model (110m parameters) to memorize 1.3X more entity facts compared to standard training, matching the performance of a 10X larger model (1.3B parameters) pretrained on the full dataset.

cs.CL↗

arXiv2026

The Importance of Being Smoothly Calibrated

Recent work has highlighted the centrality of smooth calibration [Kakade and Foster, 2008] as a robust measure of calibration error. We generalize, unify, and extend previous results on smooth calibration, both as a robust calibration measure, and as a step towards omniprediction, which enables predictions with low regret for downstream decision makers seeking to optimize some proper loss unknown to the predictor. We present a new omniprediction guarantee for smoothly calibrated predictors, for the class of all bounded proper losses. We smooth the predictor by adding some noise to it, and compete against smoothed versions of any benchmark predictor on the space, where we add some noise to the predictor and then post-process it arbitrarily. The omniprediction error is bounded by the smooth calibration error of the predictor and the earth mover's distance from the benchmark. We exhibit instances showing that this dependence cannot, in general, be improved. We show how this unifies and extends prior results [Foster and Vohra, 1998; Hartline, Wu, and Yang, 2025] on omniprediction from smooth calibration. We present a crisp new characterization of smooth calibration in terms of the earth mover's distance to the closest perfectly calibrated joint distribution of predictions and labels. This also yields a simpler proof of the relation to the lower distance to calibration from [Blasiok, Gopalan, Hu, and Nakkiran, 2023]. We use this to show that the upper distance to calibration cannot be estimated within a quadratic factor with sample complexity independent of the support size of the predictions. This is in contrast to the distance to calibration, where the corresponding problem was known to be information-theoretically impossible: no finite number of samples suffice [Blasiok, Gopalan, Hu, and Nakkiran, 2023].

cs.LG↗

arXiv2025

Enabling Differentially Private Federated Learning for Speech Recognition: Benchmarks, Adaptive Optimizers and Gradient Clipping

While federated learning (FL) and differential privacy (DP) have been extensively studied, their application to automatic speech recognition (ASR) remains largely unexplored due to the challenges in training large transformer models. Specifically, large models further exacerbate issues in FL as they are particularly susceptible to gradient heterogeneity across layers, unlike the relatively uniform gradient behavior observed in shallow models. As a result, prior works struggle to converge with standard optimization techniques, even in the absence of DP mechanisms. To the best of our knowledge, no existing work establishes a competitive, practical recipe for FL with DP in the context of ASR. To address this gap, we establish \textbf{the first benchmark for FL with DP in end-to-end ASR}. Our approach centers on per-layer clipping and layer-wise gradient normalization: theoretical analysis reveals that these techniques together mitigate clipping bias and gradient heterogeneity across layers in deeper models. Consistent with these theoretical insights, our empirical results show that FL with DP is viable under strong privacy guarantees, provided a population of at least several million users. Specifically, we achieve user-level (7.2, $10^{-9}$)-DP (resp. (4.5, $10^{-9}$)-DP) with only a 1.3% (resp. 4.6%) absolute drop in word error rate when extrapolating to high (resp. low) population scales for FL with DP in ASR. Although our experiments focus on ASR, the underlying principles we uncover - particularly those concerning gradient heterogeneity and layer-wise gradient normalization - offer broader guidance for designing scalable, privacy-preserving FL algorithms for large models across domains. Code of all experiments and benchmarks is available at https://github.com/apple/ml-pfl4asr.

cs.LG↗

arXiv2025

Efficient Calibration for Decision Making

A decision-theoretic characterization of perfect calibration is that an agent seeking to minimize a proper loss in expectation cannot improve their outcome by post-processing a perfectly calibrated predictor. Hu and Wu (FOCS'24) use this to define an approximate calibration measure called calibration decision loss ($\mathsf{CDL}$), which measures the maximal improvement achievable by any post-processing over any proper loss. Unfortunately, $\mathsf{CDL}$ turns out to be intractable to even weakly approximate in the offline setting, given black-box access to the predictions and labels. We suggest circumventing this by restricting attention to structured families of post-processing functions $K$. We define the calibration decision loss relative to $K$, denoted $\mathsf{CDL}_K$ where we consider all proper losses but restrict post-processings to a structured family $K$. We develop a comprehensive theory of when $\mathsf{CDL}_K$ is information-theoretically and computationally tractable, and use it to prove both upper and lower bounds for natural classes $K$. In addition to introducing new definitions and algorithmic techniques to the theory of calibration for decision making, our results give rigorous guarantees for some widely used recalibration procedures in machine learning.

cs.LG↗

arXiv2025

PREAMBLE: Private and Efficient Aggregation via Block Sparse Vectors

We revisit the problem of secure aggregation of high-dimensional vectors in a two-server system such as Prio. These systems are typically used to aggregate vectors such as gradients in private federated learning, where the aggregate itself is protected via noise addition to ensure differential privacy. Existing approaches require communication scaling with the dimensionality, and thus limit the dimensionality of vectors one can efficiently process in this setup. We propose PREAMBLE: {\bf Pr}ivate {\bf E}fficient {\bf A}ggregation {\bf M}echanism via {\bf BL}ock-sparse {\bf E}uclidean Vectors. PREAMBLE builds on an extension of distributed point functions that enables communication- and computation-efficient aggregation of {\em block-sparse vectors}, which are sparse vectors where the non-zero entries occur in a small number of clusters of consecutive coordinates. We show that these block-sparse DPFs can be combined with random sampling and privacy amplification by sampling results, to allow asymptotically optimal privacy-utility trade-offs for vector aggregation, at a fraction of the communication cost. When coupled with recent advances in numerical privacy accounting, our approach incurs a negligible overhead in noise variance, compared to the Gaussian mechanism used with Prio.

cs.CR↗

arXiv2025

Improved Sample Complexity for Private Nonsmooth Nonconvex Optimization

We study differentially private (DP) optimization algorithms for stochastic and empirical objectives which are neither smooth nor convex, and propose methods that return a Goldstein-stationary point with sample complexity bounds that improve on existing works. We start by providing a single-pass $(ε,δ)$-DP algorithm that returns an $(α,β)$-stationary point as long as the dataset is of size $\widetildeΩ(\sqrt{d}/αβ^{3}+d/εαβ^{2})$, which is $Ω(\sqrt{d})$ times smaller than the algorithm of Zhang et al. [2024] for this task, where $d$ is the dimension. We then provide a multi-pass polynomial time algorithm which further improves the sample complexity to $\widetildeΩ\left(d/β^2+d^{3/4}/εα^{1/2}β^{3/2}\right)$, by designing a sample efficient ERM algorithm, and proving that Goldstein-stationary points generalize from the empirical loss to the population loss.

cs.LG↗

arXiv2025

Instance-Optimality for Private KL Distribution Estimation

We study the fundamental problem of estimating an unknown discrete distribution $p$ over $d$ symbols, given $n$ i.i.d. samples from the distribution. We are interested in minimizing the KL divergence between the true distribution and the algorithm's estimate. We first construct minimax optimal private estimators. Minimax optimality however fails to shed light on an algorithm's performance on individual (non-worst-case) instances $p$ and simple minimax-optimal DP estimators can have poor empirical performance on real distributions. We then study this problem from an instance-optimality viewpoint, where the algorithm's error on $p$ is compared to the minimum achievable estimation error over a small local neighborhood of $p$. Under natural notions of local neighborhood, we propose algorithms that achieve instance-optimality up to constant factors, with and without a differential privacy constraint. Our upper bounds rely on (private) variants of the Good-Turing estimator. Our lower bounds use additive local neighborhoods that more precisely captures the hardness of distribution estimation in KL divergence, compared to ones considered in prior works.

stat.ML↗

arXiv2025

Faster Rates for Private Adversarial Bandits

We design new differentially private algorithms for the problems of adversarial bandits and bandits with expert advice. For adversarial bandits, we give a simple and efficient conversion of any non-private bandit algorithm to a private bandit algorithm. Instantiating our conversion with existing non-private bandit algorithms gives a regret upper bound of $O\left(\frac{\sqrt{KT}}{\sqrtε}\right)$, improving upon the existing upper bound $O\left(\frac{\sqrt{KT \log(KT)}}ε\right)$ for all $ε\leq 1$. In particular, our algorithms allow for sublinear expected regret even when $ε\leq \frac{1}{\sqrt{T}}$, establishing the first known separation between central and local differential privacy for this problem. For bandits with expert advice, we give the first differentially private algorithms, with expected regret $O\left(\frac{\sqrt{NT}}{\sqrtε}\right), O\left(\frac{\sqrt{KT\log(N)}\log(KT)}ε\right)$, and $\tilde{O}\left(\frac{N^{1/6}K^{1/2}T^{2/3}\log(NT)}{ε^{1/3}} + \frac{N^{1/2}\log(NT)}ε\right)$, where $K$ and $N$ are the number of actions and experts respectively. These rates allow us to get sublinear regret for different combinations of small and large $K, N$ and $ε.$

cs.LG↗

arXiv2025

On Privately Estimating a Single Parameter

We investigate differentially private estimators for individual parameters within larger parametric models. While generic private estimators exist, the estimators we provide repose on new local notions of estimand stability, and these notions allow procedures that provide private certificates of their own stability. By leveraging these private certificates, we provide computationally and statistical efficient mechanisms that release private statistics that are, at least asymptotically in the sample size, essentially unimprovable: they achieve instance optimal bounds. Additionally, we investigate the practicality of the algorithms both in simulated data and in real-world data from the American Community Survey and US Census, highlighting scenarios in which the new procedures are successful and identifying areas for future work.

cs.LG↗

arXiv2025

Local Pan-Privacy for Federated Analytics

Pan-privacy was proposed by Dwork et al. as an approach to designing a private analytics system that retains its privacy properties in the face of intrusions that expose the system's internal state. Motivated by federated telemetry applications, we study local pan-privacy, where privacy should be retained under repeated unannounced intrusions on the local state. We consider the problem of monitoring the count of an event in a federated system, where event occurrences on a local device should be hidden even from an intruder on that device. We show that under reasonable constraints, the goal of providing information-theoretic differential privacy under intrusion is incompatible with collecting telemetry information. We then show that this problem can be solved in a scalable way using standard cryptographic primitives.

cs.CR↗

arXiv2025

Adaptive Batch Size for Privately Finding Second-Order Stationary Points

There is a gap between finding a first-order stationary point (FOSP) and a second-order stationary point (SOSP) under differential privacy constraints, and it remains unclear whether privately finding an SOSP is more challenging than finding an FOSP. Specifically, Ganesh et al. (2023) claimed that an $α$-SOSP can be found with $α=O(\frac{1}{n^{1/3}}+(\frac{\sqrt{d}}{nε})^{3/7})$, where $n$ is the dataset size, $d$ is the dimension, and $ε$ is the differential privacy parameter. However, a recent analysis revealed an issue in their saddle point escape procedure, leading to weaker guarantees. Building on the SpiderBoost algorithm framework, we propose a new approach that uses adaptive batch sizes and incorporates the binary tree mechanism. Our method not only corrects this issue but also improves the results for privately finding an SOSP, achieving $α=O(\frac{1}{n^{1/3}}+(\frac{\sqrt{d}}{nε})^{1/2})$. This improved bound matches the state-of-the-art for finding a FOSP, suggesting that privately finding an SOSP may be achievable at no additional cost.

cs.LG↗

arXiv2025

Private Online Learning via Lazy Algorithms

We study the problem of private online learning, specifically, online prediction from experts (OPE) and online convex optimization (OCO). We propose a new transformation that transforms lazy online learning algorithms into private algorithms. We apply our transformation for differentially private OPE and OCO using existing lazy algorithms for these problems. Our final algorithms obtain regret, which significantly improves the regret in the high privacy regime $\varepsilon \ll 1$, obtaining $\sqrt{T \log d} + T^{1/3} \log(d)/\varepsilon^{2/3}$ for DP-OPE and $\sqrt{T} + T^{1/3} \sqrt{d}/\varepsilon^{2/3}$ for DP-OCO. We also complement our results with a lower bound for DP-OPE, showing that these rates are optimal for a natural family of low-switching private algorithms.

cs.LG↗

arXiv2024

Fingerprinting Codes Meet Geometry: Improved Lower Bounds for Private Query Release and Adaptive Data Analysis

Fingerprinting codes are a crucial tool for proving lower bounds in differential privacy. They have been used to prove tight lower bounds for several fundamental questions, especially in the ``low accuracy'' regime. Unlike reconstruction/discrepancy approaches however, they are more suited for query sets that arise naturally from the fingerprinting codes construction. In this work, we propose a general framework for proving fingerprinting type lower bounds, that allows us to tailor the technique to the geometry of the query set. Our approach allows us to prove several new results, including the following. First, we show that any (sample- and population-)accurate algorithm for answering $Q$ arbitrary adaptive counting queries over a universe $\mathcal{X}$ to accuracy $α$ needs $Ω(\frac{\sqrt{\log |\mathcal{X}|}\cdot \log Q}{α^3})$ samples, matching known upper bounds. This shows that the approaches based on differential privacy are optimal for this question, and improves significantly on the previously known lower bounds of $\frac{\log Q}{α^2}$ and $\min(\sqrt{Q}, \sqrt{\log |\mathcal{X}|})/α^2$. Second, we show that any $(\varepsilon,δ)$-DP algorithm for answering $Q$ counting queries to accuracy $α$ needs $Ω(\frac{\sqrt{ \log|\mathcal{X}| \log(1/δ)} \log Q}{\varepsilonα^2})$ samples, matching known upper bounds up to constants. Our framework allows for proving this bound via a direct correlation analysis and improves the prior bound of [BUV'14] by $\sqrt{\log(1/δ)}$. Third, we characterize the sample complexity of answering a set of random $0$-$1$ queries under approximate differential privacy. We give new upper and lower bounds in different regimes. By combining them with known results, we can complete the whole picture.

cs.DS↗

arXiv2024

Privacy-Computation trade-offs in Private Repetition and Metaselection

A Private Repetition algorithm takes as input a differentially private algorithm with constant success probability and boosts it to one that succeeds with high probability. These algorithms are closely related to private metaselection algorithms that compete with the best of many private algorithms, and private hyperparameter tuning algorithms that compete with the best hyperparameter settings for a private learning algorithm. Existing algorithms for these tasks pay either a large overhead in privacy cost, or a large overhead in computational cost. In this work, we show strong lower bounds for problems of this kind, showing in particular that for any algorithm that preserves the privacy cost up to a constant factor, the failure probability can only fall polynomially in the computational overhead. This is in stark contrast with the non-private setting, where the failure probability falls exponentially in the computational overhead. By carefully combining existing algorithms for metaselection, we prove computation-privacy tradeoffs that nearly match our lower bounds.

cs.CR↗

arXiv2024

Concentration of the Langevin Algorithm's Stationary Distribution

A canonical algorithm for log-concave sampling is the Langevin Algorithm, aka the Langevin Diffusion run with some discretization stepsize $η> 0$. This discretization leads the Langevin Algorithm to have a stationary distribution $π_η$ which differs from the stationary distribution $π$ of the Langevin Diffusion, and it is an important challenge to understand whether the well-known properties of $π$ extend to $π_η$. In particular, while concentration properties such as isoperimetry and rapidly decaying tails are classically known for $π$, the analogous properties for $π_η$ are open questions with algorithmic implications. This note provides a first step in this direction by establishing concentration results for $π_η$ that mirror classical results for $π$. Specifically, we show that for any nontrivial stepsize $η> 0$, $π_η$ is sub-exponential (respectively, sub-Gaussian) when the potential is convex (respectively, strongly convex). Moreover, the concentration bounds we show are essentially tight. We also show that these concentration bounds extend to all iterates along the trajectory of the Langevin Algorithm, and to inexact implementations which use sub-Gaussian estimates of the gradient. Key to our analysis is the use of a rotation-invariant moment generating function (aka Bessel function) to study the stationary dynamics of the Langevin Algorithm. This technique may be of independent interest because it enables directly analyzing the discrete-time stationary distribution $π_η$ without going through the continuous-time stationary distribution $π$ as an intermediary.

stat.ML↗