Content platforms typically engage with their users through small recommendation sets of items drawn from an extensive catalog. These sets are curated using machine-learned models optimized to present choices most likely to align with user preferences. We present surprising findings about such platforms. Even with complete information on user preferences within sets of up to k items, these models can only predict preferences within a "quadratic horizon" of k 2 items and might fail to identify the best items in larger sets. To illustrate, we present striking examples where a platform interacting with users through small item sets, despite knowing that one item is favored by millions of users, cannot identify this item with better than random chance. Through both theoretical analysis and studies across various datasets, we demonstrate that "hidden gems," items preferred by many users but invisible to platforms, exist in real-world datasets of moderate size, highlighting a significant gap in current recommendation platforms.

Recent advances in large language models (LLMs) have opened new avenues for accelerating scientific research. While models are increasingly capable of assisting with routine tasks, their ability to contribute to novel, expert-level mathematical discovery is less understood. We present a collection of case studies demonstrating how researchers have successfully collaborated with advanced AI models, specifically Google's Gemini-based models (in particular Gemini Deep Think and its advanced variants), to solve open problems, refute conjectures, and generate new proofs across diverse areas in theoretical computer science, as well as other areas such as economics, optimization, and physics. Based on these experiences, we extract common techniques for effective human-AI collaboration in theoretical research, such as iterative refinement, problem decomposition, and cross-disciplinary knowledge transfer. While the majority of our results stem from this interactive, conversational methodology, we also highlight specific instances that push beyond standard chat interfaces. These include deploying the model as a rigorous adversarial reviewer to detect subtle flaws in existing proofs, and embedding it within a "neuro-symbolic" loop that autonomously writes and executes code to verify complex derivations. Together, these examples highlight the potential of AI not just as a tool for automation, but as a versatile, genuine partner in the creative process of scientific discovery.

A classic approach to beyond worst-case algorithm design is to impose stochastic assumptions on the input. However, a limiting feature of stochastic analyses is that, by the min-max principle, performance on worst-case distributions mirrors that of randomized algorithms on worst-case inputs. In other words, the same shortcoming of worst-case analysis – its inability to distinguish "easy" and "hard" instances – reappears as an inability to distinguish "easy" and "hard" distributions. This raises a natural question: Can we characterize "easy" input distributions with useful beyond worst-case bounds? A canonical example is the stochastic caching problem (Aho et al. 1971). When the page requests are drawn i.i.d. from the uniform distribution, the best achievable competitive ratio is O(log k), matching the performance of the best randomized algorithm on worst-case instances (Fiat et al. 1991). However, when the input distribution has less entropy, intuition suggests that we should be able to do better by exploiting the information provided by the distribution. We formalize this by defining a new information-theoretic parameter called subset entropy which we use to give a fine-grained characterization of the competitive ratio of stochastic caching, including a new analysis for the well-known LRU algorithm on stochastic inputs. While our technical results are for the caching problem, we believe the broader principle – parameterizing algorithmic performance by an entropy measure of the input – is of independent interest and might apply to other online/stochastic optimization problems. Indeed, for problems such as (comparison-based) sorting, online matching, load balancing, etc., the hardest stochastic instances involve high-entropy distributions. We hope our work is a step toward a broader theory of fine-grained algorithmic performance for this class of problems.

A Multinomial Logit (MNL) model is composed of a finite universe of items [n]={1,..., n}, each assigned a positive weight. A query specifies an admissible subset – called a slate – and the model chooses one item from that slate with probability proportional to its weight. This query model is also known as the Plackett-Luce model or conditional sampling oracle in the literature. Although MNLs have been studied extensively, a basic computational question remains open: given query access to slates, how efficiently can we learn weights so that, for every slate, the induced choice distribution is within total variation distance ε of the ground truth? This question is central to MNL learning and has direct implications for modern recommender system interfaces. We provide two algorithms for this task, one with adaptive queries and one with non-adaptive queries. Each algorithm outputs an MNL M' that induces, for each slate S, a distribution M'_S on S that is within ε total variation distance of the true distribution. Our adaptive algorithm makes O(n/ε^3log n) queries, while our non-adaptive algorithm makes O(n^2/ε^3log n logn/ε) queries. Both algorithms query only slates of size two and run in time proportional to their query complexity. We complement these upper bounds with lower bounds of Ω(n/ε^2log n) for adaptive queries and Ω(n^2/ε^2log n) for non-adaptive queries, thus proving that our adaptive algorithm is optimal in its dependence on the support size n, while the non-adaptive one is tight within a log n factor.

We define the M-point query problem in data streams. Given a fixed matrix M, the goal is to maintain a vector x under turnstile updates and answer each query u with an estimate y_u satisfying |y_u-y_u| ≤εx_1, where y=Mx. We show that if M admits a factorization M=AB, where A and B have space-efficient representations, then there is a streaming algorithm using O(ε^-1A_2→∞B_1→ 1+(ε^-1A_∞→∞B_1→ 1)^2/3) words of memory. An important special case is the lower-triangular all-ones matrix, which corresponds to the quantiles problem with additive error ±ε n, where n is the database size. Our framework generalizes the dyadic approach of Cormode and Muthukrishnan (J. Algorithms, 2005) for turnstile quantiles, and simplifies and improves the analysis of the state-of-the-art dyadic CountSketch algorithms of Wang et al. (SIGMOD, 2013) and Luo et al. (VLDB, 2016). Our approach is also related to the matrix mechanism of Li et al. (VLDB J., 2015) in differential privacy: given a database x∈ℝ^U and a matrix M, the mechanism outputs a private approximation to Mx, with the privacy-error tradeoff governed by a matrix factorization norm of M. We also improve the prior lower bound for quantiles with deletions, showing a memory lower bound of Ω(ε^-1log U) words. We also show any factorization has A_2→∞B_1→ 1 = Ω((log^1.5 U) / loglog U). This lower bound is new, and shows that for quantiles, the dyadic CountSketch is nearly optimal amongst factorization-based approaches.

In this work we settle the complexity of three sketching problems. (i) We show that sketching vertex neighborhood sizes in graphs requires Ω(n^2) bits, standing in sharp contrast to the Õ(n) complexity of sketching edge cuts. (ii) We obtain tight lower and upper bounds of (n^2) for sketching coverage functions with additive and multiplicative errors. (iii) We prove an Ω(n^2) lower bound for sketching Random Utility Models under the ℓ_∞-norm, improving upon the previous Ω(n log n) bound and matching a known upper bound to within logarithmic factors. These bounds are obtained through a connection with the problem of sketching the intersection profile of a distribution D on 2^[n]. Specifically, we seek a succinct data structure that, for any query set S ⊆ [n], approximates the quantity _T ∼ D[T ∩ S ≠∅] to within a small constant additive error. One can obtain lower bounds for this latter problem directly from known results about the itemset frequency estimation problem in databases for which tight bounds are known. As an additional contribution, we also provide an alternative proof for the intersection profile sketching lower bound, in the setting in which the accuracy parameter is constant. This proof relies solely on elementary probability avoiding the heavier machinery used in previous proofs.

Locality-sensitive hashing (LSH) has found widespread use as a fundamental primitive, particularly to accelerate nearest neighbor search. An LSH scheme for a similarity function S:𝒳×𝒳→ [0,1] is a distribution over hash functions on 𝒳 with the property that the probability of collision of any two elements x,y∈𝒳 is exactly equal to S(x,y). However, not all similarity functions admit exact LSH schemes. The notion of LSH distortion measures how multiplicatively close a similarity function is to having an LSH scheme. In this work, we study the LSH distortion of the Ulam and Cayley similarities, which are popular similarity measures on permutations of n elements. We show that the Ulam similarity admits a sublinear LSH distortion of O(n / √(log n)); we also prove a lower bound of Ω(n^0.12) on the best LSH distortion achievable. On the other hand, we show that the LSH distortion of the Cayley similarity is Θ(n).

We present a new online algorithm for the well-known Multi-Level Aggregation Problem (MLAP) with arbitrary delay functions, achieving a 2D-competitive ratio, where D is the depth of the underlying tree. This result improves the current best-known competitive ratio of O(D^2) and asymptotically matches the D-competitive bound previously known only for the deadline variant, thereby closing the asymptotic gap between the two settings. Our key technical contribution is a novel dual fitting framework that provides a unified analysis for both settings; in particular, it also establishes a D-competitive ratio for MLAP with deadlines. Our analysis is built upon two new ideas: a hindsight dual construction, which resolves the infeasibility issues in traditional online primal-dual methods, and a time-dependent dual packing that maintains feasibility over dynamic request sets.

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 selecting the largest among n unknown values x_1,…,x_n given only a single unbiased estimate y_i for each x_i. We design strategies that are simultaneously admissible (not uniformly dominated by any other strategy) and also never worse than a given baseline such as uniform random selection. We provide an application to stochastic optimization, where we obtain online-to-batch conversion bounds with a desirable "no-compromise" guarantee: they are never worse than standard random iterate selection, and yet can be significantly better in benign settings.

Discrete choice models are used to describe, explain, and predict choices made by people among a finite set of alternatives. However, standard discrete choice models come with an unrealistic assumption: that users are able to provide an unequivocal clear winner from any slate of alternatives. Often the user knows the winner but cannot report it, as when a UI does not allow a user to specify which of two movies they rated five stars is better. And often, among the myriad options available, the user is able to identify some good candidates, but finds it difficult to distinguish between the top contenders. In this paper, we study the problem of interacting with user choice data in which, sometimes, the user is unable to settle on a single compelling winner. To address this issue, we introduce an extension to the well-known random utility models (RUMs), which we call RUMs-with-Ties, where comparisons can result in a tie. We begin with an axiomatic formulation of Luce dating to the 1950s, and provide algorithms and matching lower bounds for operating on data with ties. We also provide a comprehensive comparison of RUMs versus RUMs-with-Ties from different angles. We present theoretical results indicating that simple ways of incorporating ties into existing approaches are unlikely to perform well. We also prove in our setting that the presence of additional items, even if lower in quality, allows an algorithm to learn the highest ranked element with far fewer trials. Finally, we provide experimental evaluations of different approaches to handling indistinguishable items in choice settings and demonstrate the advantages of direct modeling of ties via our approach.

We consider the problem of minimizing a convex objective given access to an oracle that outputs "misaligned" stochastic gradients, where the expected value of the output is guaranteed to be correlated with, but not necessarily equal to the true gradient of the objective. In the case where the misalignment (or bias) of the oracle changes slowly, we obtain an optimization algorithm that achieves the optimum iteration complexity of $\tilde O(\epsilon^{-2})$; for the more general case where the changes need not be slow, we obtain an algorithm with $\tilde O(\epsilon^{-3})$ iteration complexity. As an application of our framework, we consider optimization problems with a "hidden convexity" property, and obtain an algorithm with $O(\epsilon^{-3})$ iteration complexity.

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.

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.

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.

The ACM Web Conference 2024 was held from May 13 to 17, 2024 at Resorts World Convention Centre, Singapore. The first two days featured workshops, tutorials, special days, and symposia. The last three days were the main conference days dedicated to keynote speeches, parallel presentation sessions of research, industry and special tracks, as well as multiple poster and demo sessions. This report provides a summary of organization and program. Date: 13--17 May 2024. Website: https://www2024.thewebconf.org/.