arXiv subjects

Uri Stemmer

Publications and source records attributed to Uri Stemmer.

At least 19 recordsLinked to original sources

arXiv2026

Tight Bounds on the Cost of Adaptivity for the Meyerson Sketch

In online facility location, points arrive one at a time, and the algorithm must either open a facility at the arriving point or route the point to an existing facility. The Meyerson sketch opens a facility at each arriving point with probability proportional to the point's distance to the closest open facility, and requires no state beyond the set of open centers. Due to its simplicity, space efficiency, and strong guarantees against the offline optimum, the Meyerson sketch has become a workhorse of streaming and online clustering. In many such applications, however, the set of open facilities are visible to the process that generates the stream, which can adaptively select future points based on the algorithm's past random choices, voiding its classical guarantees. In this work, we quantify the effect of such adaptivity. We compare an adaptively generated run of the sketch against an \emph{oblivious replay}, an independent execution, with fresh coins, on the very same generated sequence, and study the \emph{adaptivity ratio} of expected adaptive cost to expected replay cost. We determine the worst-case ratio in both directions: adaptivity can neither inflate nor deflate the expected cost, or the number of open facilities, by more than an $O(\log\Delta/\log\log\Delta)$ factor, where $\Delta$ is the aspect ratio of the input points (the ratio of the largest to the smallest pairwise distance). This is asymptotically tight as there are deterministic generators on the real line that inflate or deflate the cost by an $\Omega(\log\Delta/\log\log\Delta)$ factor. We show that these robustness guarantees carry over to Meyerson-based sketches for approximate $k$ clustering with sketch size $O(k\,\mathrm{polylog}(n))$.

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arXiv2026

Machine Unlearning as Private Retroactive Algorithms

Machine unlearning typically aims to emulate retraining from scratch: upon a deletion request, the unlearning algorithm should produce an outcome that would have been obtained had the deleted point never been included. Recent work has shown that this emulation requirement carries no meaningful privacy semantics against an adversary who observes a sequence of releases. Machine unlearning is thus not a privacy question per se, but rather a data maintenance question, which is precisely the subject of retroactive algorithms. These are algorithms supporting modifications of past operations, guaranteeing that all subsequent answers reflect the revised history as if it had always been in force. We put forward a definition of private retroactive algorithms, combining the retroactivity requirement with differential privacy under continual observation. We present constructions achieving both privacy and retroactivity at no asymptotic cost over privacy alone for linear statistics, clustering, and histograms, alongside impossibility results.

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arXiv2026

Is Randomness Necessary for Adaptive Data Analysis?

The Adaptive Data Analysis (ADA) problem formalizes the challenge of preventing false discovery and overfitting when a dataset is repeatedly reused. Formally, our input is a dataset containing $n$ i.i.d.\ samples from an unknown distribution $P$ over a domain $X$, and our goal is to answer a sequence of $k$ adaptively chosen statistical queries with respect to $P$. The main question is how many queries we can support (i.e., how large $k$ can be), primarily as a function of the number of samples $n$. This question has been intensively studied and is relatively well-understood for randomized mechanisms: there are computationally efficient mechanisms that support $k \approx n^2$ queries, and no computationally efficient mechanism can answer $k \gg n^2$ queries. In this paper, we address a fundamental question: is randomness necessary for ADA? Despite a decade of work on ADA, this question remains open. A folklore observation dating back to the initial works on ADA is that randomness is {\em not} necessary when the analyst is computationally bounded. Yet, the necessity of randomness against computationally unbounded analysts has remained elusive. Our main contribution resolves this gap in the information-theoretic setting. Perhaps surprisingly, we show that randomness is strictly necessary to answer a non-trivial number of adaptive queries: when the analyst is unbounded, any deterministic mechanism can be forced to fail after just $k = \tilde{O}(n)$ queries.

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arXiv2026

Load Balancing under Adaptive Bin Deletions

We analyze a balls-and-bins game against an adaptive adversary that sequentially deletes bins. Starting with $n$ balls distributed across $n$ bins, the adversary deletes a bin in each step, forcing the algorithm to redistribute its balls to surviving bins. We prove that after $n/2$ rounds, uniform random redistribution yields optimal $O(n)$ recourse and $O(\frac{\log n}{\log \log n})$ maximum load. Furthermore, we show that applying the ``power of two choices'' reduces the maximum load to $O(\log \log n)$ while maintaining linear recourse. We also consider a variation of this game where the balls from the deleted bin are partitioned evenly among $d \ll n$ random bins rather than being redistributed independently. We demonstrate that keeping the balls together ($d=1$), which gives small maximum load and recourse against an oblivious adversary, fails against an adaptive adversary. Nevertheless, we show that splitting the balls into just two groups ($d=2$) is sufficient to recover linear recourse and efficient load balancing in the adaptive setting.

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arXiv2026

Protecting the Undeleted in Machine Unlearning

Machine unlearning aims to remove specific data points from a trained model, often striving to emulate "perfect retraining", i.e., producing the model that would have been obtained had the deleted data never been included. We demonstrate that this approach, and security definitions that enable it, carry significant privacy risks for the remaining (undeleted) data points. We present a reconstruction attack showing that for certain tasks, which can be computed securely without deletions, a mechanism adhering to perfect retraining allows an adversary controlling merely $\omega(1)$ data points to reconstruct almost the entire dataset merely by issuing deletion requests. We survey existing definitions for machine unlearning, showing they are either susceptible to such attacks or too restrictive to support basic functionalities like exact summation. To address this problem, we propose a new security definition that specifically safeguards undeleted data against leakage caused by the deletion of other points. We show that our definition permits several essential functionalities, such as bulletin boards, summations, and statistical learning.

cs.LG↗

arXiv2026

Adaptively Robust Resettable Streaming

We study algorithms in the resettable streaming model, where the value of each key can either be increased or reset to zero. The model is suitable for applications such as active resource monitoring with support for deletions and machine unlearning. We show that all existing sketches for this model are vulnerable to adaptive adversarial attacks that apply even when the sketch size is polynomial in the length of the stream. To overcome these vulnerabilities, we present the first adaptively robust sketches for resettable streams that maintain polylogarithmic space complexity in the stream length. Our framework supports (sub) linear statistics including $L_p$ moments for $p\in[0,1]$ (in particular, Cardinality and Sum) and Bernstein statistics. We bypass strong impossibility results known for linear and composable sketches by designing dedicated streaming sketches robustified via Differential Privacy. Unlike standard robustification techniques, which provide limited benefits in this setting and still require polynomial space in the stream length, we leverage the Binary Tree Mechanism for continual observation to protect the sketch's internal randomness. This enables accurate prefix-max error guarantees with polylogarithmic space.

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arXiv2025

A Simple and Robust Protocol for Distributed Counting

We revisit the distributed counting problem, where a server must continuously approximate the total number of events occurring across $k$ sites while minimizing communication. The communication complexity of this problem is known to be $\Theta(\frac{k}{\epsilon}\log N)$ for deterministic protocols. Huang, Yi, and Zhang (2012) showed that randomization can reduce this to $\Theta(\frac{\sqrt{k}}{\epsilon}\log N)$, but their analysis is restricted to the {\em oblivious setting}, where the stream of events is independent of the protocol's outputs. Xiong, Zhu, and Huang (2023) presented a robust protocol for distributed counting that removes the oblivious assumption. However, their communication complexity is suboptimal by a $polylog(k)$ factor and their protocol is substantially more complex than the oblivious protocol of Huang et al. (2012). This left open a natural question: could it be that the simple protocol of Huang et al. (2012) is already robust? We resolve this question with two main contributions. First, we show that the protocol of Huang et al. (2012) is itself not robust by constructing an explicit adaptive attack that forces it to lose its accuracy. Second, we present a new, surprisingly simple, robust protocol for distributed counting that achieves the optimal communication complexity of $O(\frac{\sqrt{k}}{\epsilon} \log N)$. Our protocol is simpler than that of Xiong et al. (2023), perhaps even simpler than that of Huang et al. (2012), and is the first to match the optimal oblivious complexity in the adaptive setting.

cs.DC↗

arXiv2025

The Cost of Compression: Tight Quadratic Black-Box Attacks on Sketches for $\ell_2$ Norm Estimation

Dimensionality reduction via linear sketching is a powerful and widely used technique, but it is known to be vulnerable to adversarial inputs. We study the black-box adversarial setting, where a fixed, hidden sketching matrix $A \in R^{k \times n}$ maps high-dimensional vectors $v \in R^n$ to lower-dimensional sketches $A v \in R^k$, and an adversary can query the system to obtain approximate $\ell_2$-norm estimates that are computed from the sketch. We present a universal, nonadaptive attack that, using $\tilde{O}(k^2)$ queries, either causes a failure in norm estimation or constructs an adversarial input on which the optimal estimator for the query distribution (used by the attack) fails. The attack is completely agnostic to the sketching matrix and to the estimator: it applies to any linear sketch and any query responder, including those that are randomized, adaptive, or tailored to the query distribution. Our lower bound construction tightly matches the known upper bounds of $\tilde{\Omega}(k^2)$, achieved by specialized estimators for Johnson Lindenstrauss transforms and AMS sketches. Beyond sketching, our results uncover structural parallels to adversarial attacks in image classification, highlighting fundamental vulnerabilities of compressed representations.

cs.LG↗

arXiv2025

Tight Bounds for Answering Adaptively Chosen Concentrated Queries

Most work on adaptive data analysis assumes that samples in the dataset are independent. When correlations are allowed, even the non-adaptive setting can become intractable, unless some structural constraints are imposed. To address this, Bassily and Freund [2016] introduced the elegant framework of concentrated queries, which requires the analyst to restrict itself to queries that are concentrated around their expected value. While this assumption makes the problem trivial in the non-adaptive setting, in the adaptive setting it remains quite challenging. In fact, all known algorithms in this framework support significantly fewer queries than in the independent case: At most $O(n)$ queries for a sample of size $n$, compared to $O(n^2)$ in the independent setting. In this work, we prove that this utility gap is inherent under the current formulation of the concentrated queries framework, assuming some natural conditions on the algorithm. Additionally, we present a simplified version of the best-known algorithms that match our impossibility result.

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arXiv2025

Nearly Optimal Sample Complexity for Learning with Label Proportions

We investigate Learning from Label Proportions (LLP), a partial information setting where examples in a training set are grouped into bags, and only aggregate label values in each bag are available. Despite the partial observability, the goal is still to achieve small regret at the level of individual examples. We give results on the sample complexity of LLP under square loss, showing that our sample complexity is essentially optimal. From an algorithmic viewpoint, we rely on carefully designed variants of Empirical Risk Minimization, and Stochastic Gradient Descent algorithms, combined with ad hoc variance reduction techniques. On one hand, our theoretical results improve in important ways on the existing literature on LLP, specifically in the way the sample complexity depends on the bag size. On the other hand, we validate our algorithmic solutions on several datasets, demonstrating improved empirical performance (better accuracy for less samples) against recent baselines.

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arXiv2025

Bayesian Perspective on Memorization and Reconstruction

We introduce a new Bayesian perspective on the concept of data reconstruction, and leverage this viewpoint to propose a new security definition that, in certain settings, provably prevents reconstruction attacks. We use our paradigm to shed new light on one of the most notorious attacks in the privacy and memorization literature - fingerprinting code attacks (FPC). We argue that these attacks are really a form of membership inference attacks, rather than reconstruction attacks. Furthermore, we show that if the goal is solely to prevent reconstruction (but not membership inference), then in some cases the impossibility results derived from FPC no longer apply.

cs.CR↗

arXiv2025

One Attack to Rule Them All: Tight Quadratic Bounds for Adaptive Queries on Cardinality Sketches

Cardinality sketches are compact data structures for representing sets or vectors. These sketches are space-efficient, typically requiring only logarithmic storage in the input size, and enable approximation of cardinality (or the number of nonzero entries). A crucial property in applications is \emph{composability}, meaning that the sketch of a union of sets can be computed from individual sketches. Existing designs provide strong statistical guarantees, ensuring that a randomly sampled sketching map remains robust for an exponential number of queries in terms of the sketch size $k$. However, these guarantees degrade to quadratic in $k$ when queries are \emph{adaptive}, meaning they depend on previous responses. Prior works on statistical queries (Steinke and Ullman, 2015) and specific MinHash cardinality sketches (Ahmadian and Cohen, 2024) established that this is tight in that they can be compromised using a quadratic number of adaptive queries. In this work, we develop a universal attack framework that applies to broad classes of cardinality sketches. We show that any union-composable sketching map can be compromised with $\tilde{O}(k^4)$ adaptive queries and this improves to a tight bound of $\tilde{O}(k^2)$ for monotone maps (including MinHash, statistical queries, and Boolean linear maps). Similarly, any linear sketching map over the reals $\mathbb{R}$ and finite fields $\mathbb{F}_p$ can be compromised using $\tilde{O}(k^2)$ adaptive queries, which is optimal and strengthens some of the recent results by~\citet{GribelyukLWYZ:FOCS2024}, who established a weaker polynomial bound.

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arXiv2025

Breaking the Quadratic Barrier: Robust Cardinality Sketches for Adaptive Queries

Cardinality sketches are compact data structures that efficiently estimate the number of distinct elements across multiple queries while minimizing storage, communication, and computational costs. However, recent research has shown that these sketches can fail under {\em adaptively chosen queries}, breaking down after approximately $\tilde{O}(k^2)$ queries, where $k$ is the sketch size. In this work, we overcome this \emph{quadratic barrier} by designing robust estimators with fine-grained guarantees. Specifically, our constructions can handle an {\em exponential number of adaptive queries}, provided that each element participates in at most $\tilde{O}(k^2)$ queries. This effectively shifts the quadratic barrier from the total number of queries to the number of queries {\em sharing the same element}, which can be significantly smaller. Beyond cardinality sketches, our approach expands the toolkit for robust algorithm design.

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arXiv2024

Differentially Private Release and Learning of Threshold Functions

We prove new upper and lower bounds on the sample complexity of $(ε, δ)$ differentially private algorithms for releasing approximate answers to threshold functions. A threshold function $c_x$ over a totally ordered domain $X$ evaluates to $c_x(y) = 1$ if $y \le x$, and evaluates to $0$ otherwise. We give the first nontrivial lower bound for releasing thresholds with $(ε,δ)$ differential privacy, showing that the task is impossible over an infinite domain $X$, and moreover requires sample complexity $n \ge Ω(\log^*|X|)$, which grows with the size of the domain. Inspired by the techniques used to prove this lower bound, we give an algorithm for releasing thresholds with $n \le 2^{(1+ o(1))\log^*|X|}$ samples. This improves the previous best upper bound of $8^{(1 + o(1))\log^*|X|}$ (Beimel et al., RANDOM '13). Our sample complexity upper and lower bounds also apply to the tasks of learning distributions with respect to Kolmogorov distance and of properly PAC learning thresholds with differential privacy. The lower bound gives the first separation between the sample complexity of properly learning a concept class with $(ε,δ)$ differential privacy and learning without privacy. For properly learning thresholds in $\ell$ dimensions, this lower bound extends to $n \ge Ω(\ell \cdot \log^*|X|)$. To obtain our results, we give reductions in both directions from releasing and properly learning thresholds and the simpler interior point problem. Given a database $D$ of elements from $X$, the interior point problem asks for an element between the smallest and largest elements in $D$. We introduce new recursive constructions for bounding the sample complexity of the interior point problem, as well as further reductions and techniques for proving impossibility results for other basic problems in differential privacy.

cs.CR↗

arXiv2024

Data Reconstruction: When You See It and When You Don't

We revisit the fundamental question of formally defining what constitutes a reconstruction attack. While often clear from the context, our exploration reveals that a precise definition is much more nuanced than it appears, to the extent that a single all-encompassing definition may not exist. Thus, we employ a different strategy and aim to "sandwich" the concept of reconstruction attacks by addressing two complementing questions: (i) What conditions guarantee that a given system is protected against such attacks? (ii) Under what circumstances does a given attack clearly indicate that a system is not protected? More specifically, * We introduce a new definitional paradigm -- Narcissus Resiliency -- to formulate a security definition for protection against reconstruction attacks. This paradigm has a self-referential nature that enables it to circumvent shortcomings of previously studied notions of security. Furthermore, as a side-effect, we demonstrate that Narcissus resiliency captures as special cases multiple well-studied concepts including differential privacy and other security notions of one-way functions and encryption schemes. * We formulate a link between reconstruction attacks and Kolmogorov complexity. This allows us to put forward a criterion for evaluating when such attacks are convincingly successful.

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arXiv2024

On Differentially Private Linear Algebra

We introduce efficient differentially private (DP) algorithms for several linear algebraic tasks, including solving linear equalities over arbitrary fields, linear inequalities over the reals, and computing affine spans and convex hulls. As an application, we obtain efficient DP algorithms for learning halfspaces and affine subspaces. Our algorithms addressing equalities are strongly polynomial, whereas those addressing inequalities are weakly polynomial. Furthermore, this distinction is inevitable: no DP algorithm for linear programming can be strongly polynomial-time efficient.

cs.DS↗

arXiv2024

Lower Bounds for Differential Privacy Under Continual Observation and Online Threshold Queries

One of the most basic problems for studying the "price of privacy over time" is the so called private counter problem, introduced by Dwork et al. (2010) and Chan et al. (2010). In this problem, we aim to track the number of events that occur over time, while hiding the existence of every single event. More specifically, in every time step $t\in[T]$ we learn (in an online fashion) that $Δ_t\geq 0$ new events have occurred, and must respond with an estimate $n_t\approx\sum_{j=1}^t Δ_j$. The privacy requirement is that all of the outputs together, across all time steps, satisfy event level differential privacy. The main question here is how our error needs to depend on the total number of time steps $T$ and the total number of events $n$. Dwork et al. (2015) showed an upper bound of $O\left(\log(T)+\log^2(n)\right)$, and Henzinger et al. (2023) showed a lower bound of $Ω\left(\min\{\log n, \log T\}\right)$. We show a new lower bound of $Ω\left(\min\{n,\log T\}\right)$, which is tight w.r.t. the dependence on $T$, and is tight in the sparse case where $\log^2 n=O(\log T)$. Our lower bound has the following implications: $\bullet$ We show that our lower bound extends to the "online thresholds problem", where the goal is to privately answer many "quantile queries" when these queries are presented one-by-one. This resolves an open question of Bun et al. (2017). $\bullet$ Our lower bound implies, for the first time, a separation between the number of mistakes obtainable by a private online learner and a non-private online learner. This partially resolves a COLT'22 open question published by Sanyal and Ramponi. $\bullet$ Our lower bound also yields the first separation between the standard model of private online learning and a recently proposed relaxed variant of it, called private online prediction.

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arXiv2024

Private Truly-Everlasting Robust-Prediction

Private Everlasting Prediction (PEP), recently introduced by Naor et al. [2023], is a model for differentially private learning in which the learner never publicly releases a hypothesis. Instead, it provides black-box access to a "prediction oracle" that can predict the labels of an endless stream of unlabeled examples drawn from the underlying distribution. Importantly, PEP provides privacy both for the initial training set and for the endless stream of classification queries. We present two conceptual modifications to the definition of PEP, as well as new constructions exhibiting significant improvements over prior work. Specifically, (1) Robustness: PEP only guarantees accuracy provided that all the classification queries are drawn from the correct underlying distribution. A few out-of-distribution queries might break the validity of the prediction oracle for future queries, even for future queries which are sampled from the correct distribution. We incorporate robustness against such poisoning attacks into the definition of PEP, and show how to obtain it. (2) Dependence of the privacy parameter $δ$ in the time horizon: We present a relaxed privacy definition, suitable for PEP, that allows us to disconnect the privacy parameter $δ$ from the number of total time steps $T$. This allows us to obtain algorithms for PEP whose sample complexity is independent from $T$, thereby making them "truly everlasting". This is in contrast to prior work where the sample complexity grows with $polylog(T)$. (3) New constructions: Prior constructions for PEP exhibit sample complexity that is quadratic in the VC dimension of the target class. We present new constructions of PEP for axis-aligned rectangles and for decision-stumps that exhibit sample complexity linear in the dimension (instead of quadratic). We show that our constructions satisfy very strong robustness properties.

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