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Simple function classes have emerged as toy problems to better understand in-context-learning in transformer-based architectures used for large language models. But previously proposed simple function classes like linear regression or…

Machine Learning · Computer Science 2024-07-30 Max Wilcoxson , Morten Svendgård , Ria Doshi , Dylan Davis , Reya Vir , Anant Sahai

Since its introduction by Valiant in 1984, PAC learning of DNF expressions remains one of the central problems in learning theory. We consider this problem in the setting where the underlying distribution is uniform, or more generally, a…

Machine Learning · Computer Science 2015-03-20 Vitaly Feldman

The degree-$d$ Chow parameters of a Boolean function $f: \{-1,1\}^n \to \mathbb{R}$ are its degree at most $d$ Fourier coefficients. It is well-known that degree-$d$ Chow parameters uniquely characterize degree-$d$ polynomial threshold…

Machine Learning · Computer Science 2018-11-09 Ilias Diakonikolas , Daniel M. Kane

A simple way to generate a Boolean function is to take the sign of a real polynomial in $n$ variables. Such Boolean functions are called polynomial threshold functions. How many low-degree polynomial threshold functions are there? The…

Probability · Mathematics 2019-07-25 Pierre Baldi , Roman Vershynin

The scope of research in the domain of activation functions remains limited and centered around improving the ease of optimization or generalization quality of neural networks (NNs). However, to develop a deeper understanding of deep…

Machine Learning · Computer Science 2020-12-10 Mohit Goyal , Rajan Goyal , Brejesh Lall

Data generation and labeling are usually an expensive part of learning for robotics. While active learning methods are commonly used to tackle the former problem, preference-based learning is a concept that attempts to solve the latter by…

Machine Learning · Computer Science 2018-10-11 Erdem Bıyık , Dorsa Sadigh

We make progress on two important problems regarding attribute efficient learnability. First, we give an algorithm for learning decision lists of length $k$ over $n$ variables using $2^{\tilde{O}(k^{1/3})} \log n$ examples and time…

Machine Learning · Computer Science 2007-05-23 Adam R. Klivans , Rocco A. Servedio

Active learning is a branch of machine learning that deals with problems where unlabeled data is abundant yet obtaining labels is expensive. The learning algorithm has the possibility of querying a limited number of samples to obtain the…

Disordered Systems and Neural Networks · Physics 2020-09-04 Hugo Cui , Luca Saglietti , Lenka Zdeborová

In a recent breakthrough, [Bshouty et al., 2005] obtained the first passive-learning algorithm for DNFs under the uniform distribution. They showed that DNFs are learnable in the Random Walk and Noise Sensitivity models. We extend their…

Machine Learning · Computer Science 2011-09-07 S. Roch

We show how to obtain improved active learning methods in the agnostic (adversarial noise) setting by combining marginal leverage score sampling with non-independent sampling strategies that promote spatial coverage. In particular, we…

Machine Learning · Computer Science 2024-05-07 Atsushi Shimizu , Xiaoou Cheng , Christopher Musco , Jonathan Weare

The deep-learning-based least squares method has shown successful results in solving high-dimensional non-linear partial differential equations (PDEs). However, this method usually converges slowly. To speed up the convergence of this…

Numerical Analysis · Mathematics 2025-07-10 Wenhan Gao , Chunmei Wang

Recent work due to Goel et al. gave the first efficient algorithms for learning with distribution shift in the challenging PQ framework. In this setting, a learner receives labeled training examples, unlabeled test examples, and must make…

Data Structures and Algorithms · Computer Science 2026-05-19 Gautam Chandrasekaran , Georgios Gkrinias , Adam R. Klivans , Konstantinos Stavropoulos , Arsen Vasilyan

We show that there is a randomized algorithm that, when given a small constant-depth Boolean circuit $C$ made up of gates that compute constant-degree Polynomial Threshold functions or PTFs (i.e., Boolean functions that compute signs of…

Computational Complexity · Computer Science 2018-09-18 Swapnam Bajpai , Vaibhav Krishan , Deepanshu Kush , Nutan Limaye , Srikanth Srinivasan

We study the problem of actively learning a classifier with a low calibration error. One of the most popular Acquisition Functions (AFs) in pool-based Active Learning (AL) is querying by the model's uncertainty. However, we recognize that…

Machine Learning · Computer Science 2025-10-06 Ha Manh Bui , Iliana Maifeld-Carucci , Anqi Liu

We prove that the active-set method needs an exponential number of iterations in the worst-case to maximize a convex quadratic function subject to linear constraints, regardless of the pivot rule used. This substantially improves over the…

Discrete Mathematics · Computer Science 2025-10-23 Eleon Bach , Yann Disser , Sophie Huiberts , Nils Mosis

In standard passive imitation learning, the goal is to learn a target policy by passively observing full execution trajectories of it. Unfortunately, generating such trajectories can require substantial expert effort and be impractical in…

Machine Learning · Computer Science 2012-10-19 Kshitij Judah , Alan Fern , Thomas G. Dietterich

We prove that if an activation function satisfies some mild conditions and number of neurons in a two-layered fully connected neural network with this activation function is beyond a certain threshold, then gradient descent on quadratic…

Optimization and Control · Mathematics 2019-11-14 Biswarup Das , Eugene. A. Golikov

Active learning methods aim to improve sample complexity in machine learning. In this work, we investigate an active learning scheme via a novel gradient-free cutting-plane training method for ReLU networks of arbitrary depth and develop a…

Machine Learning · Computer Science 2025-06-26 Erica Zhang , Fangzhao Zhang , Mert Pilanci

The stunning empirical successes of neural networks currently lack rigorous theoretical explanation. What form would such an explanation take, in the face of existing complexity-theoretic lower bounds? A first step might be to show that…

Machine Learning · Computer Science 2017-07-18 Le Song , Santosh Vempala , John Wilmes , Bo Xie

Active learning, an iterative process of selecting the most informative data points for exploration, is crucial for efficient characterization of materials and chemicals property space. Neural networks excel at predicting these properties…

Disordered Systems and Neural Networks · Physics 2025-06-02 Sarah I. Allec , Maxim Ziatdinov