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The rise of deep neural networks has led to several breakthroughs for semantic segmentation. In spite of this, a model trained on source domain often fails to work properly in new challenging domains, that is directly concerned with the…

Computer Vision and Pattern Recognition · Computer Science 2022-05-31 Jin Kim , Jiyoung Lee , Jungin Park , Dongbo Min , Kwanghoon Sohn

We present a continuous formulation of machine learning, as a problem in the calculus of variations and differential-integral equations, in the spirit of classical numerical analysis. We demonstrate that conventional machine learning models…

Numerical Analysis · Mathematics 2020-10-02 Weinan E , Chao Ma , Lei Wu

Focusing on the practical configuration needs of optimization algorithms in deep learning, this article concentrates on five major algorithms: SGD, Mini-batch SGD, Momentum, Adam, and Lion. It systematically analyzes the core advantages,…

Machine Learning · Computer Science 2025-11-27 Deng Fucheng , Wang Wanjie , Gong Ao , Wang Xiaoqi , Wang Fan

We present Gradient Activation Maps (GAM) - a machinery for explaining predictions made by visual similarity and classification models. By gleaning localized gradient and activation information from multiple network layers, GAM offers…

Computer Vision and Pattern Recognition · Computer Science 2021-09-03 Oren Barkan , Omri Armstrong , Amir Hertz , Avi Caciularu , Ori Katz , Itzik Malkiel , Noam Koenigstein

Machine unlearning in foundation models (e.g., language and vision transformers) is essential for privacy and safety; however, existing approaches are unstable and unreliable. A widely used strategy, the gradient difference method, applies…

Machine Learning · Computer Science 2026-03-19 Arpit Garg , Hemanth Saratchandran , Ravi Garg , Simon Lucey

A set of accelerated first order algorithms with memory are proposed for minimising strongly convex functions. The algorithms are differentiated by their use of the iterate history for the gradient step. The increased convergence rate of…

Optimization and Control · Mathematics 2018-08-31 Ross Drummond , Stephen Duncan

A number of results have recently demonstrated the benefits of incorporating various constraints when training deep architectures in vision and machine learning. The advantages range from guarantees for statistical generalization to better…

Machine Learning · Computer Science 2019-05-27 Sathya N. Ravi , Tuan Dinh , Vishnu Lokhande , Vikas Singh

Learning rate adaptation is a popular topic in machine learning. Gradient Descent trains neural nerwork with a fixed learning rate. Learning rate adaptation is proposed to accelerate the training process through adjusting the step size in…

Machine Learning · Computer Science 2022-10-20 Bozhou Chen , Hongzhi Wang , Chenmin Ba

While deep learning has been successfully applied to the data-driven classification of anomalous diffusion mechanisms, how the algorithm achieves the feat still remains a mystery. In this study, we use a well-known technique aimed at…

Machine Learning · Computer Science 2024-10-23 Jaeyong Bae , Yongjoo Baek , Hawoong Jeong

This paper shows that a wide class of effective learning rules -- those that improve a scalar performance measure over a given time window -- can be rewritten as natural gradient descent with respect to a suitably defined loss function and…

Machine Learning · Computer Science 2024-09-26 Lucas Shoji , Kenta Suzuki , Leo Kozachkov

Recently, learning algorithms motivated from sharpness of loss surface as an effective measure of generalization gap have shown state-of-the-art performances. Nevertheless, sharpness defined in a rigid region with a fixed radius, has a…

Machine Learning · Computer Science 2021-06-30 Jungmin Kwon , Jeongseop Kim , Hyunseo Park , In Kwon Choi

Gradient descent is one of the most widely used iterative algorithms in modern statistical learning. However, its precise algorithmic dynamics in high-dimensional settings remain only partially understood, which has limited its broader…

Statistics Theory · Mathematics 2025-11-19 Qiyang Han , Xiaocong Xu

We build a theoretical framework for designing and understanding practical meta-learning methods that integrates sophisticated formalizations of task-similarity with the extensive literature on online convex optimization and sequential…

Machine Learning · Computer Science 2019-12-10 Mikhail Khodak , Maria-Florina Balcan , Ameet Talwalkar

We describe an alternative learning method for neural networks, which we call Blind Descent. By design, Blind Descent does not face problems like exploding or vanishing gradients. In Blind Descent, gradients are not used to guide the…

Machine Learning · Computer Science 2020-08-27 Akshat Gupta , Prasad N R

In this work, we consider smooth unconstrained optimization problems and we deal with the class of gradient methods with momentum, i.e., descent algorithms where the search direction is defined as a linear combination of the current…

Optimization and Control · Mathematics 2025-12-04 Matteo Lapucci , Giampaolo Liuzzi , Stefano Lucidi , Davide Pucci , Marco Sciandrone

The concept of the value-gradient is introduced and developed in the context of reinforcement learning. It is shown that by learning the value-gradients exploration or stochastic behaviour is no longer needed to find locally optimal…

Neural and Evolutionary Computing · Computer Science 2008-03-26 Michael Fairbank

The performance of optimization methods is often tied to the spectrum of the objective Hessian. Yet, conventional assumptions, such as smoothness, do often not enable us to make finely-grained convergence statements -- particularly not for…

Optimization and Control · Mathematics 2024-02-08 Nikita Doikov , Sebastian U. Stich , Martin Jaggi

Probabilistic graphical models are traditionally known for their successes in generative modeling. In this work, we advocate layered graphical models (LGMs) for probabilistic discriminative learning. To this end, we design LGMs in close…

Machine Learning · Computer Science 2019-02-04 Yuesong Shen , Tao Wu , Csaba Domokos , Daniel Cremers

We develop the mathematical foundations of the stochastic modified equations (SME) framework for analyzing the dynamics of stochastic gradient algorithms, where the latter is approximated by a class of stochastic differential equations with…

Machine Learning · Computer Science 2018-11-06 Qianxiao Li , Cheng Tai , Weinan E

This work is a rigorous development of a complete and general-purpose deep learning framework from the ground up. The fundamental components of deep learning - automatic differentiation and gradient methods of optimizing multivariable…

Mathematical Software · Computer Science 2020-11-18 Andrei Nicolae