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Despite the omnipresent use of stochastic gradient descent (SGD) optimization methods in the training of deep neural networks (DNNs), it remains, in basically all practically relevant scenarios, a fundamental open problem to provide a…

Machine Learning · Computer Science 2025-03-04 Thang Do , Arnulf Jentzen , Adrian Riekert

Optimization in Deep Learning is mainly dominated by first-order methods which are built around the central concept of backpropagation. Second-order optimization methods, which take into account the second-order derivatives are far less…

Machine Learning · Computer Science 2021-04-09 Fares B. Mehouachi , Chaouki Kasmi

Convolutional neural networks (CNNs) are trained using stochastic gradient descent (SGD)-based optimizers. Recently, the adaptive moment estimation (Adam) optimizer has become very popular due to its adaptive momentum, which tackles the…

Machine Learning · Computer Science 2023-09-12 S. K. Roy , M. E. Paoletti , J. M. Haut , S. R. Dubey , P. Kar , A. Plaza , B. B. Chaudhuri

Scaling deep neural network (DNN) training to more devices can reduce time-to-solution. However, it is impractical for users with limited computing resources. FOSI, as a hybrid order optimizer, converges faster than conventional optimizers…

Machine Learning · Computer Science 2025-08-05 Shunxian Gu , Chaoqun You , Bangbang Ren , Lailong Luo , Junxu Xia , Deke Guo

Second-order optimization methods have the ability to accelerate convergence by modifying the gradient through the curvature matrix. There have been many attempts to use second-order optimization methods for training deep neural networks.…

Machine Learning · Computer Science 2020-11-24 Kai-Xin Gao , Xiao-Lei Liu , Zheng-Hai Huang , Min Wang , Zidong Wang , Dachuan Xu , Fan Yu

While first-order methods are popular for solving optimization problems that arise in large-scale deep learning problems, they come with some acute deficiencies. To diminish such shortcomings, there has been recent interest in applying…

Machine Learning · Computer Science 2023-10-05 Mahsa Yousefi , Angeles Martinez

Deep learning methods - consisting of a class of deep neural networks (DNNs) trained by a stochastic gradient descent (SGD) optimization method - are nowadays key tools to solve data driven supervised learning problems. Despite the great…

Machine Learning · Computer Science 2025-02-18 Thang Do , Sonja Hannibal , Arnulf Jentzen

Solving massive-scale optimization problems requires scalable first-order methods with low per-iteration cost. This tutorial highlights a shift in optimization: using differentiable programming not only to execute algorithms but to learn…

Mathematical Software · Computer Science 2026-03-02 Liping Tao , Xindi Tong , Chee Wei Tan

The demand for high speed data transmission has increased rapidly, leading to advanced optical communication techniques. In the past few years, multiple equalizers based on neural network (NN) have been proposed to recover signal from…

Signal Processing · Electrical Eng. & Systems 2020-08-26 Qingyi Zhou , Fan Zhang , Chuanchuan Yang

Adam is a widely used stochastic optimization method for deep learning applications. While practitioners prefer Adam because it requires less parameter tuning, its use is problematic from a theoretical point of view since it may not…

Machine Learning · Computer Science 2020-11-25 Mingrui Liu , Wei Zhang , Francesco Orabona , Tianbao Yang

Deep learning optimizers are often motivated through a mix of convex and approximate second-order theory. We select three such methods -- Adam, Shampoo and Prodigy -- and argue that each method can instead be understood as a squarely…

Machine Learning · Computer Science 2024-12-09 Jeremy Bernstein , Laker Newhouse

We introduce Velocity-Regularized Adam (VRAdam), a physics-inspired optimizer for training deep neural networks that draws on ideas from quartic terms for kinetic energy with its stabilizing effects on various system dynamics. Previous…

Machine Learning · Computer Science 2026-05-13 Pranav Vaidhyanathan , Lucas Schorling , Natalia Ares , Michael A. Osborne

Stochastic gradient descent (SGD) optimization methods are nowadays the method of choice for the training of deep neural networks (DNNs) in artificial intelligence systems. In practically relevant training problems, usually not the plain…

Optimization and Control · Mathematics 2024-08-01 Steffen Dereich , Arnulf Jentzen

Kronecker-factored Approximate Curvature (K-FAC) has recently been shown to converge faster in deep neural network (DNN) training than stochastic gradient descent (SGD); however, K-FAC's larger memory footprint hinders its applicability to…

Machine Learning · Computer Science 2021-09-21 J. Gregory Pauloski , Qi Huang , Lei Huang , Shivaram Venkataraman , Kyle Chard , Ian Foster , Zhao Zhang

Modern convolutional networks, incorporating rectifiers and max-pooling, are neither smooth nor convex; standard guarantees therefore do not apply. Nevertheless, methods from convex optimization such as gradient descent and Adam are widely…

Machine Learning · Computer Science 2018-06-07 David Balduzzi , Brian McWilliams , Tony Butler-Yeoman

Neural fields encode continuous multidimensional signals as neural networks, enabling diverse applications in computer vision, robotics, and geometry. While Adam is effective for stochastic optimization, it often requires long training…

Computer Vision and Pattern Recognition · Computer Science 2025-05-26 Shin-Fang Chng , Hemanth Saratchandran , Simon Lucey

Deep neural networks (DNNs) have been increasingly deployed on and integrated with edge devices, such as mobile phones, drones, robots and wearables. To run DNN inference directly on edge devices (a.k.a. edge inference) with a satisfactory…

Machine Learning · Computer Science 2020-09-18 Bingqian Lu , Jianyi Yang , Shaolei Ren

Second-order methods for neural network optimization have several advantages over methods based on first-order gradient descent, including better scaling to large mini-batch sizes and fewer updates needed for convergence. But they are…

Machine Learning · Computer Science 2017-12-21 Huishuai Zhang , Caiming Xiong , James Bradbury , Richard Socher

Second-order optimizers hold intriguing potential for deep learning, but suffer from increased cost and sensitivity to the non-convexity of the loss surface as compared to gradient-based approaches. We introduce a coordinate descent method…

Machine Learning · Computer Science 2020-06-19 Ravi G. Patel , Nathaniel A. Trask , Mamikon A. Gulian , Eric C. Cyr

We present a genetic algorithm framework for automatically discovering deep learning optimization algorithms. Our approach encodes optimizers as genomes that specify combinations of primitive update terms (gradient, momentum, RMS…

Neural and Evolutionary Computing · Computer Science 2025-12-16 Mitchell Marfinetz
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