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Stochastic gradient descent (SGD) and its variants enable modern artificial intelligence. However, theoretical understanding lags far behind their empirical success. It is widely believed that SGD has a curious ability to avoid sharp local…

Machine Learning · Computer Science 2025-10-27 Xingyu Wang , Chang-Han Rhee

We perform an experimental study of the dynamics of Stochastic Gradient Descent (SGD) in learning deep neural networks for several real and synthetic classification tasks. We show that in the initial epochs, almost all of the performance…

Machine Learning · Computer Science 2019-05-29 Preetum Nakkiran , Gal Kaplun , Dimitris Kalimeris , Tristan Yang , Benjamin L. Edelman , Fred Zhang , Boaz Barak

Learning in deep neural networks (DNNs) is implemented through minimizing a highly non-convex loss function, typically by a stochastic gradient descent (SGD) method. This learning process can effectively find good wide minima without being…

Machine Learning · Computer Science 2021-07-27 Guozhang Chen , Cheng Kevin Qu , Pulin Gong

Theoretically understanding stochastic gradient descent (SGD) in overparameterized models has led to the development of several optimization algorithms that are widely used in practice today. Recent work by~\citet{zou2021benign} provides…

Machine Learning · Computer Science 2025-06-19 Alexandru Meterez , Depen Morwani , Costin-Andrei Oncescu , Jingfeng Wu , Cengiz Pehlevan , Sham Kakade

We study a distributed consensus-based stochastic gradient descent (SGD) algorithm and show that the rate of convergence involves the spectral properties of two matrices: the standard spectral gap of a weight matrix from the network…

Optimization and Control · Mathematics 2016-09-02 Avleen S. Bijral , Anand D. Sarwate , Nathan Srebro

One crucial factor behind the success of deep learning lies in the implicit bias induced by noise inherent in gradient-based training algorithms. Motivated by empirical observations that training with noisy labels improves model…

Machine Learning · Computer Science 2026-03-12 Tongcheng Zhang , Zhanpeng Zhou , Mingze Wang , Andi Han , Wei Huang , Taiji Suzuki , Junchi Yan

In deep multi-task learning, weights of task-specific networks are shared between tasks to improve performance on each single one. Since the question, which weights to share between layers, is difficult to answer, human-designed…

Machine Learning · Computer Science 2020-03-24 Jonas Prellberg , Oliver Kramer

Deep neural networks (DNNs) have demonstrated dominating performance in many fields; since AlexNet, networks used in practice are going wider and deeper. On the theoretical side, a long line of works has been focusing on training neural…

Machine Learning · Computer Science 2019-06-18 Zeyuan Allen-Zhu , Yuanzhi Li , Zhao Song

With rise of machine learning (ML) and the proliferation of smart mobile devices, recent years have witnessed a surge of interest in performing ML in wireless edge networks. In this paper, we consider the problem of jointly improving data…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-03-31 Xin Zhang , Minghong Fang , Jia Liu , Zhengyuan Zhu

We present novel empirical observations regarding how stochastic gradient descent (SGD) navigates the loss landscape of over-parametrized deep neural networks (DNNs). These observations expose the qualitatively different roles of learning…

Machine Learning · Statistics 2018-05-31 Chen Xing , Devansh Arpit , Christos Tsirigotis , Yoshua Bengio

Understanding the properties of neural networks trained via stochastic gradient descent (SGD) is at the heart of the theory of deep learning. In this work, we take a mean-field view, and consider a two-layer ReLU network trained via SGD for…

Machine Learning · Computer Science 2022-05-02 Alexander Shevchenko , Vyacheslav Kungurtsev , Marco Mondelli

Stochastic gradient descent (SGD) is a widely adopted iterative method for optimizing differentiable objective functions. In this paper, we propose and discuss a novel approach to scale up SGD in applications involving non-convex functions…

Machine Learning · Statistics 2022-10-07 Saad Mohamad , Hamad Alamri , Abdelhamid Bouchachia

We consider learning two layer neural networks using stochastic gradient descent. The mean-field description of this learning dynamics approximates the evolution of the network weights by an evolution in the space of probability…

Machine Learning · Statistics 2019-02-19 Song Mei , Theodor Misiakiewicz , Andrea Montanari

We consider the dynamics of gradient descent (GD) in overparameterized single hidden layer neural networks with a squared loss function. Recently, it has been shown that, under some conditions, the parameter values obtained using GD achieve…

Machine Learning · Computer Science 2021-05-17 Siddhartha Satpathi , R Srikant

Analyzing neural network dynamics via stochastic gradient descent (SGD) is crucial to building theoretical foundations for deep learning. Previous work has analyzed structured inputs within the \textit{hidden manifold model}, often under…

Machine Learning · Statistics 2025-12-01 Jaeyong Bae , Hawoong Jeong

We consider the approximation of functions by 2-layer neural networks with a small number of hidden weights based on the squared loss and small datasets. Due to the highly non-convex energy landscape, gradient-based training often suffers…

Machine Learning · Computer Science 2025-08-14 Johannes Hertrich , Sebastian Neumayer

We study diffusion and consensus based optimization of a sum of unknown convex objective functions over distributed networks. The only access to these functions is through stochastic gradient oracles, each of which is only available at a…

Numerical Analysis · Computer Science 2015-09-01 N. Denizcan Vanli , Muhammed O. Sayin , Suleyman S. Kozat

Stochastic gradient descent (SGD) is widely used in deep learning due to its computational efficiency, but a complete understanding of why SGD performs so well remains a major challenge. It has been observed empirically that most…

Machine Learning · Statistics 2022-06-20 Carmina Fjellström , Kaj Nyström

Deep neural networks (DNNs) have achieved remarkable success in computer vision; however, training DNNs for satisfactory performance remains challenging and suffers from sensitivity to empirical selections of an optimization algorithm for…

Computer Vision and Pattern Recognition · Computer Science 2020-12-22 Haichao Zhang , Kuangrong Hao , Lei Gao , Bing Wei , Xuesong Tang

In the last decade, deep learning has become a major component of artificial intelligence. The workhorse of deep learning is the optimization of loss functions by stochastic gradient descent (SGD). Traditionally in deep learning, neural…

Machine Learning · Computer Science 2021-04-27 Benjamin Scellier