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Related papers: Noise-Tolerant Learning, the Parity Problem, and t…

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Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…

Quantum Physics · Physics 2008-02-03 Dorit Aharonov , Michael Ben-Or

In dictionary learning, also known as sparse coding, the algorithm is given samples of the form $y = Ax$ where $x\in \mathbb{R}^m$ is an unknown random sparse vector and $A$ is an unknown dictionary matrix in $\mathbb{R}^{n\times m}$…

Data Structures and Algorithms · Computer Science 2014-01-06 Sanjeev Arora , Aditya Bhaskara , Rong Ge , Tengyu Ma

Quantum noise constitutes a fundamental obstacle to realizing practical quantum technologies. To address the pivotal challenge of identifying quantum systems least affected by noise, we introduce the purest quantum state identification,…

Quantum Physics · Physics 2025-09-24 Yingqi Yu , Honglin Chen , Jun Wu , Wei Xie , Xiangyang Li

Departing from traditional communication theory where decoding algorithms are assumed to perform without error, a system where noise perturbs both computational devices and communication channels is considered here. This paper studies…

Information Theory · Computer Science 2010-05-31 Lav R. Varshney

A wide range of NLP tasks benefit from the fine-tuning of pretrained language models (PLMs). However, a number of redundant parameters which contribute less to the downstream task are observed in a directly fine-tuned model. We consider the…

Computation and Language · Computer Science 2022-10-26 Yupeng Zhang , Hongzhi Zhang , Sirui Wang , Wei Wu , Zhoujun Li

Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…

Data Structures and Algorithms · Computer Science 2023-05-29 Jonathan Kelner , Frederic Koehler , Raghu Meka , Dhruv Rohatgi

Motivated by applications in recommender systems, web search, social choice and crowdsourcing, we consider the problem of identifying the set of top $K$ items from noisy pairwise comparisons. In our setting, we are non-actively given $r$…

Data Structures and Algorithms · Computer Science 2016-05-13 Xi Chen , Sivakanth Gopi , Jieming Mao , Jon Schneider

We analyse the complexity of learning first-order queries in a model-theoretic framework for supervised learning introduced by (Grohe and Tur\'an, TOCS 2004). Previous research on the complexity of learning in this framework focussed on the…

Logic in Computer Science · Computer Science 2021-06-29 Steffen van Bergerem , Martin Grohe , Martin Ritzert

Monotone learning describes learning processes in which expected performance consistently improves as the amount of training data increases. However, recent studies challenge this conventional wisdom, revealing significant gaps in the…

Machine Learning · Computer Science 2025-05-22 Ming Li , Chenyi Zhang , Qin Li

The main promise of quantum computing is to efficiently solve certain problems that are prohibitively expensive for a classical computer. Most problems with a proven quantum advantage involve the repeated use of a black box, or oracle,…

Recent works explore deep learning's success by examining functions or data with hierarchical structure. To study the learning complexity of functions with hierarchical structure, we study the noise stability of functions with tree…

Probability · Mathematics 2025-09-30 Rupert Li , Elchanan Mossel

The authors recently gave an $n^{O(\log\log n)}$ time membership query algorithm for properly learning decision trees under the uniform distribution (Blanc et al., 2021). The previous fastest algorithm for this problem ran in $n^{O(\log…

Data Structures and Algorithms · Computer Science 2022-06-30 Guy Blanc , Jane Lange , Mingda Qiao , Li-Yang Tan

Tasks that model the relation between pairs of tokens in a string are a vital part of understanding natural language. Such tasks, in general, require exhaustive pair-wise comparisons of tokens, thus having a quadratic runtime complexity in…

Computation and Language · Computer Science 2023-12-13 Tianyu Liu , Afra Amini , Mrinmaya Sachan , Ryan Cotterell

While quantum computing can accomplish tasks that are classically intractable, the presence of noise may destroy this advantage in the absence of fault tolerance. In this work, we present a classical algorithm that runs in…

Quantum Physics · Physics 2025-10-09 Yifan F. Zhang , Su-un Lee , Liang Jiang , Sarang Gopalakrishnan

In this paper we revisit some classic problems on classification under misspecification. In particular, we study the problem of learning halfspaces under Massart noise with rate $\eta$. In a recent work, Diakonikolas, Goulekakis, and Tzamos…

Machine Learning · Computer Science 2023-09-21 Sitan Chen , Frederic Koehler , Ankur Moitra , Morris Yau

We consider the sorted top-$k$ problem whose goal is to recover the top-$k$ items with the correct order out of $n$ items using pairwise comparisons. In many applications, multiple rounds of interaction can be costly. We restrict our…

Data Structures and Algorithms · Computer Science 2019-06-13 Mark Braverman , Jieming Mao , Yuval Peres

We study the problem of learning halfspaces with Massart noise in the distribution-specific PAC model. We give the first computationally efficient algorithm for this problem with respect to a broad family of distributions, including…

Machine Learning · Computer Science 2020-02-14 Ilias Diakonikolas , Vasilis Kontonis , Christos Tzamos , Nikos Zarifis

In this paper, we analyze PAC learnability from labels produced by crowdsourcing. In our setting, unlabeled examples are drawn from a distribution and labels are crowdsourced from workers who operate under classification noise, each with…

Machine Learning · Computer Science 2019-02-14 Shelby Heinecke , Lev Reyzin

Hamiltonian learning protocols are essential tools to benchmark quantum computers and simulators. Yet rigorous methods for time-dependent Hamiltonians and Lindbladians remain scarce despite their wide use. We close this gap by learning the…

Quantum Physics · Physics 2025-10-10 Daniel Stilck França , Tim Möbus , Cambyse Rouzé , Albert H. Werner

Understanding what can be learned from experiments is central to scientific progress. In this work, we use a learning-theoretic perspective to study the task of learning physical operations in a quantum machine when all operations (state…

Quantum Physics · Physics 2022-04-29 Hsin-Yuan Huang , Steven T. Flammia , John Preskill