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新论文 · v1arXiv:2504.19874Google Research

TurboQuant: Online Vector Quantization with Near-optimal Distortion Rate

Amir Zandieh, Majid Daliri, Majid Hadian, Vahab Mirrokni

原文摘要

Vector quantization, a problem rooted in Shannon's source coding theory, aims to quantize high-dimensional Euclidean vectors while minimizing distortion in their geometric structure. We propose TurboQuant to address both mean-squared error (MSE) and inner product distortion, overcoming limitations of existing methods that fail to achieve optimal distortion rates. Our data-oblivious algorithms, suitable for online applications, achieve near-optimal distortion rates (within a small constant factor) across all bit-widths and dimensions. TurboQuant achieves this by randomly rotating input vectors, inducing a concentrated Beta distribution on coordinates, and leveraging the near-independence property of distinct coordinates in high dimensions to simply apply optimal scalar quantizers per each coordinate. Recognizing that MSE-optimal quantizers introduce bias in inner product estimation, we propose a two-stage approach: applying an MSE quantizer followed by a 1-bit Quantized JL (QJL) transform on the residual, resulting in an unbiased inner product quantizer. We also provide a formal proof of the information-theoretic lower bounds on best achievable distortion rate by any vector quantizer, demonstrating that TurboQuant closely matches these bounds, differing only by a small constant ($\approx 2.7$) factor. Experimental results validate our theoretical findings, showing that for KV cache quantization, we achieve absolute quality neutrality with 3.5 bits per channel and marginal quality degradation with 2.5 bits per channel. Furthermore, in nearest neighbor search tasks, our method outperforms existing product quantization techniques in recall while reducing indexing time to virtually zero.

cs.LG · cs.AI · cs.DB · cs.DS

版本更新 · v3arXiv:2403.10444Google Research

Block Verification Accelerates Speculative Decoding

Ziteng Sun, Uri Mendlovic, Yaniv Leviathan, Asaf Aharoni, Jae Hun Ro, Ahmad Beirami, Ananda Theertha Suresh

原文摘要

Speculative decoding is an effective method for lossless acceleration of large language models during inference. It uses a fast model to draft a block of tokens which are then verified in parallel by the target model, and provides a guarantee that the output is distributed identically to a sample from the target model. In prior works, draft verification is performed independently token-by-token. Surprisingly, we show that this approach is not optimal. We propose Block Verification, a simple draft verification algorithm that verifies the entire block jointly and provides additional wall-clock speedup. We prove that the proposed mechanism is optimal in the expected number of tokens produced each iteration and specifically is never worse than the standard token-level verification. Empirically, block verification provides modest but consistent wall-clock speedups over the standard token verification algorithm of 5%-8% in a range of tasks and datasets. Given that block verification does not increase code complexity, maintains the strong lossless guarantee of the standard speculative decoding verification algorithm, cannot deteriorate performance, and, in fact, consistently improves it, it can be used as a good default in speculative decoding implementations.

cs.LG · cs.CL · cs.DS · cs.IT

版本更新 · v8arXiv:1904.07272Google Research

多臂老虎机导论

Introduction to Multi-Armed Bandits

Aleksandrs Slivkins

AI 速读 基于摘要

一本以教科书方式系统介绍多臂老虎机(multi-armed bandits)的入门著作,覆盖IID奖励、对抗性奖励、上下文老虎机及与经济学相关的扩展。

cs.LG · cs.AI · cs.DS · stat.ML

查看原文摘要

Multi-armed bandits a simple but very powerful framework for algorithms that make decisions over time under uncertainty. An enormous body of work has accumulated over the years, covered in several books and surveys. This book provides a more introductory, textbook-like treatment of the subject. Each chapter tackles a particular line of work, providing a self-contained, teachable technical introduction and a brief review of the further developments; many of the chapters conclude with exercises. The book is structured as follows. The first four chapters are on IID rewards, from the basic model to impossibility results to Bayesian priors to Lipschitz rewards. The next three chapters cover adversarial rewards, from the full-feedback version to adversarial bandits to extensions with linear rewards and combinatorially structured actions. Chapter 8 is on contextual bandits, a middle ground between IID and adversarial bandits in which the change in reward distributions is completely explained by observable contexts. The last three chapters cover connections to economics, from learning in repeated games to bandits with supply/budget constraints to exploration in the presence of incentives. The appendix provides sufficient background on concentration and KL-divergence. The chapters on "bandits with similarity information", "bandits with knapsacks" and "bandits and agents" can also be consumed as standalone surveys on the respective topics.

新论文 · v1arXiv:2309.14558Google Research

Bicriteria Approximation Algorithms for the Submodular Cover Problem

Wenjing Chen, Victoria G. Crawford

原文摘要

In this paper, we consider the optimization problem Submodular Cover (SCP), which is to find a minimum cardinality subset of a finite universe $U$ such that the value of a submodular function $f$ is above an input threshold $τ$. In particular, we consider several variants of SCP including the general case, the case where $f$ is additionally assumed to be monotone, and finally the case where $f$ is a regularized monotone submodular function. Our most significant contributions are that: (i) We propose a scalable algorithm for monotone SCP that achieves nearly the same approximation guarantees as the standard greedy algorithm in significantly faster time; (ii) We are the first to develop an algorithm for general SCP that achieves a solution arbitrarily close to being feasible; and finally (iii) we are the first to develop algorithms for regularized SCP. Our algorithms are then demonstrated to be effective in an extensive experimental section on data summarization and graph cut, two applications of SCP.

cs.DS

版本更新 · v4arXiv:2006.03684Google Research

Differentially private partition selection

Damien Desfontaines, James Voss, Bryant Gipson, Chinmoy Mandayam

原文摘要

Many data analysis operations can be expressed as a GROUP BY query on an unbounded set of partitions, followed by a per-partition aggregation. To make such a query differentially private, adding noise to each aggregation is not enough: we also need to make sure that the set of partitions released is also differentially private. This problem is not new, and it was recently formally introduced as differentially private set union. In this work, we continue this area of study, and focus on the common setting where each user is associated with a single partition. In this setting, we propose a simple, optimal differentially private mechanism that maximizes the number of released partitions. We discuss implementation considerations, as well as the possible extension of this approach to the setting where each user contributes to a fixed, small number of partitions.

cs.CR · cs.DS

新论文 · v1arXiv:2103.00564Google Research

An Introduction to Johnson-Lindenstrauss Transforms

Casper Benjamin Freksen

原文摘要

Johnson--Lindenstrauss Transforms are powerful tools for reducing the dimensionality of data while preserving key characteristics of that data, and they have found use in many fields from machine learning to differential privacy and more. This note explains what they are; it gives an overview of their use and their development since they were introduced in the 1980s; and it provides many references should the reader wish to explore these topics more deeply.

cs.DS · cs.LG