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Implicit deep learning has recently become popular in the machine learning community since these implicit models can achieve competitive performance with state-of-the-art deep networks while using significantly less memory and computational…

Machine Learning · Computer Science 2022-05-17 Tianxiang Gao , Hongyang Gao

In this paper, we consider a general stochastic optimization problem which is often at the core of supervised learning, such as deep learning and linear classification. We consider a standard stochastic gradient descent (SGD) method with a…

Machine Learning · Statistics 2018-12-27 Lam M. Nguyen , Nam H. Nguyen , Dzung T. Phan , Jayant R. Kalagnanam , Katya Scheinberg

Aimed at explaining the surprisingly good generalization behavior of overparameterized deep networks, recent works have developed a variety of generalization bounds for deep learning, all based on the fundamental learning-theoretic…

Machine Learning · Computer Science 2021-10-19 Vaishnavh Nagarajan , J. Zico Kolter

We prove limitations on what neural networks trained by noisy gradient descent (GD) can efficiently learn. Our results apply whenever GD training is equivariant, which holds for many standard architectures and initializations. As…

Machine Learning · Computer Science 2022-10-17 Emmanuel Abbe , Enric Boix-Adsera

Polynomial regression is a basic primitive in learning and statistics. In its most basic form the goal is to fit a degree $d$ polynomial to a response variable $y$ in terms of an $n$-dimensional input vector $x$. This is extremely…

Data Structures and Algorithms · Computer Science 2020-04-30 Sitan Chen , Raghu Meka

Deep neural networks' remarkable ability to correctly fit training data when optimized by gradient-based algorithms is yet to be fully understood. Recent theoretical results explain the convergence for ReLU networks that are wider than…

Machine Learning · Computer Science 2021-02-09 Asaf Noy , Yi Xu , Yonathan Aflalo , Lihi Zelnik-Manor , Rong Jin

Recent advances have significantly improved our understanding of the generalization performance of gradient descent (GD) methods in deep neural networks. A natural and fundamental question is whether GD can achieve generalization rates…

Machine Learning · Computer Science 2026-04-14 Yuanfan Li , Yunwen Lei , Zheng-Chu Guo , Yiming Ying

We consider the problem of learning the best-fitting single neuron as measured by the expected square loss $\mathbb{E}_{(x,y)\sim \mathcal{D}}[(\sigma(w^\top x)-y)^2]$ over some unknown joint distribution $\mathcal{D}$ by using gradient…

Machine Learning · Computer Science 2020-09-01 Spencer Frei , Yuan Cao , Quanquan Gu

We give the first provably efficient algorithms for learning neural networks with distribution shift. We work in the Testable Learning with Distribution Shift framework (TDS learning) of Klivans et al. (2024), where the learner receives…

Data Structures and Algorithms · Computer Science 2025-02-25 Gautam Chandrasekaran , Adam R. Klivans , Lin Lin Lee , Konstantinos Stavropoulos

This paper analyzes the convergence and generalization of training a one-hidden-layer neural network when the input features follow the Gaussian mixture model consisting of a finite number of Gaussian distributions. Assuming the labels are…

Machine Learning · Computer Science 2023-01-30 Hongkang Li , Shuai Zhang , Meng Wang

A main puzzle of deep networks revolves around the absence of overfitting despite large overparametrization and despite the large capacity demonstrated by zero training error on randomly labeled data. In this note, we show that the dynamics…

We consider the natural problem of learning a ReLU network from queries, which was recently remotivated by model extraction attacks. In this work, we present a polynomial-time algorithm that can learn a depth-two ReLU network from queries…

Machine Learning · Computer Science 2023-03-07 Amit Daniely , Elad Granot

We study the problem of estimating the mean of an identity covariance Gaussian in the truncated setting, in the regime when the truncation set comes from a low-complexity family $\mathcal{C}$ of sets. Specifically, for a fixed but unknown…

Data Structures and Algorithms · Computer Science 2024-03-05 Ilias Diakonikolas , Daniel M. Kane , Thanasis Pittas , Nikos Zarifis

Understanding when neural networks can be learned efficiently is a fundamental question in learning theory. Existing hardness results suggest that assumptions on both the input distribution and the network's weights are necessary for…

Machine Learning · Computer Science 2023-10-05 Amit Daniely , Nathan Srebro , Gal Vardi

Image classification based on over-parametrized convolutional neural networks with a global average-pooling layer is considered. The weights of the network are learned by gradient descent. A bound on the rate of convergence of the…

Machine Learning · Statistics 2024-05-14 Michael Kohler , Adam Krzyzak , Benjamin Walter

Machine Unlearning aims to remove specific data from trained models, addressing growing privacy and ethical concerns. We provide a theoretical analysis of a simple and widely used method - gradient ascent - used to reverse the influence of…

Machine Learning · Computer Science 2025-10-17 Odelia Melamed , Gilad Yehudai , Gal Vardi

This work aims to provide understandings on the remarkable success of deep convolutional neural networks (CNNs) by theoretically analyzing their generalization performance and establishing optimization guarantees for gradient descent based…

Machine Learning · Computer Science 2018-05-29 Pan Zhou , Jiashi Feng

Implicit neural networks have become increasingly attractive in the machine learning community since they can achieve competitive performance but use much less computational resources. Recently, a line of theoretical works established the…

Machine Learning · Computer Science 2022-10-03 Tianxiang Gao , Hongyang Gao

Two aspects of neural networks that have been extensively studied in the recent literature are their function approximation properties and their training by gradient descent methods. The approximation problem seeks accurate approximations…

Machine Learning · Computer Science 2022-09-20 R. Gentile , G. Welper

We show that the standard stochastic gradient decent (SGD) algorithm is guaranteed to learn, in polynomial time, a function that is competitive with the best function in the conjugate kernel space of the network, as defined in Daniely,…

Machine Learning · Computer Science 2017-05-23 Amit Daniely