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Stochastic gradient methods are among the most widely used algorithms for large-scale optimization and machine learning. A key technique for improving the statistical efficiency and stability of these methods is the use of averaging schemes…

Optimization and Control · Mathematics 2026-03-11 K. Lakshmanan

Stochastic gradient descent (SGD) is an immensely popular approach for online learning in settings where data arrives in a stream or data sizes are very large. However, despite an ever-increasing volume of work on SGD, much less is known…

Machine Learning · Statistics 2025-03-06 Weijie J. Su , Yuancheng Zhu

Sharpness-aware Minimization (SAM) has been proposed recently to improve model generalization ability. However, SAM calculates the gradient twice in each optimization step, thereby doubling the computation costs compared to stochastic…

Computer Vision and Pattern Recognition · Computer Science 2024-03-15 Jiaxin Deng , Junbiao Pang , Baochang Zhang , Tian Wang

We present a novel optimization-based decoding algorithm for LDPC codes that is suitable for hardware architectures specialized to feed-forward neural networks. The algorithm is based on the projected gradient descent algorithm with a…

Information Theory · Computer Science 2019-01-16 Tadashi Wadayama , Satoshi Takabe

In this paper, we introduce StochGradAdam, a novel optimizer designed as an extension of the Adam algorithm, incorporating stochastic gradient sampling techniques to improve computational efficiency while maintaining robust performance.…

Machine Learning · Computer Science 2025-03-19 Juyoung Yun

Stochastic neurons and hard non-linearities can be useful for a number of reasons in deep learning models, but in many cases they pose a challenging problem: how to estimate the gradient of a loss function with respect to the input of such…

Machine Learning · Computer Science 2013-08-16 Yoshua Bengio , Nicholas Léonard , Aaron Courville

Gradient descent method, as one of the major methods in numerical optimization, is the key ingredient in many machine learning algorithms. As one of the most fundamental way to solve the optimization problems, it promises the function value…

Quantum Physics · Physics 2021-02-01 Keren Li , Shijie Wei , Feihao Zhang , Pan Gao , Zengrong Zhou , Tao Xin , Xiaoting Wang , Guilu Long

We provide new gradient-based methods for efficiently solving a broad class of ill-conditioned optimization problems. We consider the problem of minimizing a function $f : \mathbb{R}^d \rightarrow \mathbb{R}$ which is implicitly…

Optimization and Control · Mathematics 2021-11-08 Jonathan Kelner , Annie Marsden , Vatsal Sharan , Aaron Sidford , Gregory Valiant , Honglin Yuan

This paper studies interpretability of convolutional networks by means of saliency maps. Most approaches based on Class Activation Maps (CAM) combine information from fully connected layers and gradient through variants of backpropagation.…

Computer Vision and Pattern Recognition · Computer Science 2024-04-24 Felipe Torres Figueroa , Hanwei Zhang , Ronan Sicre , Yannis Avrithis , Stephane Ayache

Mini-batch algorithms have been proposed as a way to speed-up stochastic convex optimization problems. We study how such algorithms can be improved using accelerated gradient methods. We provide a novel analysis, which shows how standard…

Machine Learning · Computer Science 2011-06-24 Andrew Cotter , Ohad Shamir , Nathan Srebro , Karthik Sridharan

The most successful methods such as ReLU transfer functions, batch normalization, Xavier initialization, dropout, learning rate decay, or dynamic optimizers, have become standards in the field due, particularly, to their ability to increase…

Machine Learning · Computer Science 2020-10-26 Yurika Sakai , Andrey Kormilitzin , Qiang Liu , Alejo Nevado-Holgado

Stochastic gradient descent (SGD) is one of the most widely used optimization methods for parallel and distributed processing of large datasets. One of the key limitations of distributed SGD is the need to regularly communicate the…

Optimization and Control · Mathematics 2018-10-25 Xiaojian Xu , Ulugbek S. Kamilov

Deep learning models offer superior performance compared to other machine learning techniques for a variety of tasks and domains, but pose their own challenges. In particular, deep learning models require larger training times as the depth…

Machine Learning · Computer Science 2023-05-31 Sunitha Basodi , Krishna Pusuluri , Xueli Xiao , Yi Pan

The policy gradient approach is a flexible and powerful reinforcement learning method particularly for problems with continuous actions such as robot control. A common challenge in this scenario is how to reduce the variance of policy…

Machine Learning · Computer Science 2013-01-18 Tingting Zhao , Hirotaka Hachiya , Voot Tangkaratt , Jun Morimoto , Masashi Sugiyama

We consider the problem of approximating a function by an element of a nonlinear manifold which admits a differentiable parametrization, typical examples being neural networks with differentiable activation functions or tensor networks.…

Machine Learning · Computer Science 2026-04-20 Anthony Nouy , Agustín Somacal

Existing work has linked properties of a function's gradient to the difficulty of function approximation. Motivated by these insights, we study how gradient information can be leveraged to improve neural network's ability to approximate…

Machine Learning · Computer Science 2026-02-11 Yangchen Pan , Qizhen Ying , Philip Torr , Bo Liu

Stochastic gradient optimization is the dominant learning paradigm for a variety of scenarios, from classical supervised learning to modern self-supervised learning. We consider stochastic gradient algorithms for learning problems whose…

Machine Learning · Statistics 2025-08-29 Facheng Yu , Ronak Mehta , Alex Luedtke , Zaid Harchaoui

Gradient descent has been a central training principle for artificial neural networks from the early beginnings to today's deep learning networks. The most common implementation is the backpropagation algorithm for training feed-forward…

Machine Learning · Computer Science 2020-06-09 Stefan Jaeger

We introduce a notion of inexact model of a convex objective function, which allows for errors both in the function and in its gradient. For this situation, a gradient method with an adaptive adjustment of some parameters of the model is…

Optimization and Control · Mathematics 2021-10-12 Fedor S. Stonyakin

We introduce a method called TracIn that computes the influence of a training example on a prediction made by the model. The idea is to trace how the loss on the test point changes during the training process whenever the training example…

Machine Learning · Computer Science 2020-11-17 Garima Pruthi , Frederick Liu , Mukund Sundararajan , Satyen Kale
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