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Stochastic gradient descent (SGD) is widely used in machine learning. Although being commonly viewed as a fast but not accurate version of gradient descent (GD), it always finds better solutions than GD for modern neural networks. In order…

机器学习 · 计算机科学 2018-08-17 Robert Kleinberg , Yuanzhi Li , Yang Yuan

Stochastic Gradient Descent (SGD) is a known stochastic iterative method popular for large-scale convex optimization problems due to its simple implementation and scalability. Some objectives, such as those found in complex-valued neural…

机器学习 · 计算机科学 2026-05-26 Natanael Alpay , Emeric Battaglia

Despite being the cornerstone of deep learning, backpropagation is criticized for its inherent sequentiality, which can limit the scalability of very deep models. Such models faced convergence issues due to vanishing gradient, later…

机器学习 · 计算机科学 2025-04-01 Erwan Fagnou , Paul Caillon , Blaise Delattre , Alexandre Allauzen

Backward propagation of errors (backpropagation) is a method to minimize objective functions (e.g., loss functions) of deep neural networks by identifying optimal sets of weights and biases. Imposing constraints on weight precision is often…

机器学习 · 计算机科学 2021-10-26 Guhyun Kim , Doo Seok Jeong

In this paper, we introduce proximal gradient temporal difference learning, which provides a principled way of designing and analyzing true stochastic gradient temporal difference learning algorithms. We show how gradient TD (GTD)…

机器学习 · 计算机科学 2020-06-09 Bo Liu , Ian Gemp , Mohammad Ghavamzadeh , Ji Liu , Sridhar Mahadevan , Marek Petrik

Stochastic Gradient Decent (SGD) is one of the core techniques behind the success of deep neural networks. The gradient provides information on the direction in which a function has the steepest rate of change. The main problem with basic…

Graduated optimization is a global optimization technique that is used to minimize a multimodal nonconvex function by smoothing the objective function with noise and gradually refining the solution. This paper experimentally evaluates the…

机器学习 · 计算机科学 2024-12-17 Naoki Sato , Hideaki Iiduka

Despite exceptional achievements, training neural networks remains computationally expensive and is often plagued by instabilities that can degrade convergence. While learning rate schedules can help mitigate these issues, finding optimal…

机器学习 · 计算机科学 2026-03-30 Benoit Dherin , Benny Avelin , Anders Karlsson , Hanna Mazzawi , Javier Gonzalvo , Michael Munn

Mini-batch stochastic gradient descent (SGD) is state of the art in large scale distributed training. The scheme can reach a linear speedup with respect to the number of workers, but this is rarely seen in practice as the scheme often…

最优化与控制 · 数学 2019-05-06 Sebastian U. Stich

Large models are prevalent in modern machine learning scenarios, including deep learning, recommender systems, etc., which can have millions or even billions of parameters. Parallel algorithms have become an essential solution technique to…

机器学习 · 计算机科学 2018-10-23 Rui Zhu , Di Niu

Backpropagation (BP) is the standard algorithm for training the deep neural networks that power modern artificial intelligence including large language models. However, BP is energy inefficient and unlikely to be implemented by the brain.…

机器学习 · 计算机科学 2025-10-30 Francesco Innocenti

Optimal Transport has sparked vivid interest in recent years, in particular thanks to the Wasserstein distance, which provides a geometrically sensible and intuitive way of comparing probability measures. For computational reasons, the…

机器学习 · 计算机科学 2024-03-19 Eloi Tanguy

Sampling from an unnormalized target distribution is an essential problem with many applications in probabilistic inference. Stein Variational Gradient Descent (SVGD) has been shown to be a powerful method that iteratively updates a set of…

机器学习 · 计算机科学 2023-02-13 Hoang Phan , Ngoc Tran , Trung Le , Toan Tran , Nhat Ho , Dinh Phung

Equilibrium Propagation (EP) is a biologically-inspired algorithm for convergent RNNs with a local learning rule that comes with strong theoretical guarantees. The parameter updates of the neural network during the credit assignment phase…

神经与进化计算 · 计算机科学 2020-06-09 Axel Laborieux , Maxence Ernoult , Benjamin Scellier , Yoshua Bengio , Julie Grollier , Damien Querlioz

Over the last four decades, the amazing success of deep learning has been driven by the use of Stochastic Gradient Descent (SGD) as the main optimization technique. The default implementation for the computation of the gradient for SGD is…

神经与进化计算 · 计算机科学 2024-12-31 Qianli Liao , Liu Ziyin , Yulu Gan , Brian Cheung , Mark Harnett , Tomaso Poggio

Spiking neural networks combine analog computation with event-based communication using discrete spikes. While the impressive advances of deep learning are enabled by training non-spiking artificial neural networks using the backpropagation…

神经元与认知 · 定量生物学 2021-06-22 Timo C. Wunderlich , Christian Pehle

The question of how to parallelize the stochastic gradient descent (SGD) method has received much attention in the literature. In this paper, we focus instead on batch methods that use a sizeable fraction of the training set at each…

最优化与控制 · 数学 2016-10-26 Albert S. Berahas , Jorge Nocedal , Martin Takáč

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…

机器学习 · 计算机科学 2021-04-27 Benjamin Scellier

Differential Privacy (DP) provides a formal privacy guarantee preventing adversaries with access to a machine learning model from extracting information about individual training points. Differentially Private Stochastic Gradient Descent…

机器学习 · 计算机科学 2022-06-17 Soham De , Leonard Berrada , Jamie Hayes , Samuel L. Smith , Borja Balle

A very popular approach for solving stochastic optimization problems is the stochastic gradient descent method (SGD). Although the SGD iteration is computationally cheap and the practical performance of this method may be satisfactory under…

最优化与控制 · 数学 2017-06-21 Andrei Patrascu , Ion Necoara