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Automatic differentiation (AD) has driven recent advances in machine learning, including deep neural networks and Hamiltonian Markov Chain Monte Carlo methods. Partially observed nonlinear stochastic dynamical systems have proved resistant…

Methodology · Statistics 2024-07-04 Kevin Tan , Giles Hooker , Edward L. Ionides

Neural network-based approaches have recently shown significant promise in solving partial differential equations (PDEs) in science and engineering, especially in scenarios featuring complex domains or incorporation of empirical data. One…

Machine Learning · Computer Science 2025-03-19 Chuqi Chen , Yahong Yang , Yang Xiang , Wenrui Hao

Deep learning is pervasive in our daily life, including self-driving cars, virtual assistants, social network services, healthcare services, face recognition, etc. However, deep neural networks demand substantial compute resources during…

Optimization theory serves as a pivotal scientific instrument for achieving optimal system performance, with its origins in economic applications to identify the best investment strategies for maximizing benefits. Over the centuries, from…

Machine Learning · Computer Science 2024-09-10 Yuhan Ma , Dan Sun , Erdi Gao , Ningjing Sang , Iris Li , Guanming Huang

Highly distributed training of Deep Neural Networks (DNNs) on future compute platforms (offering 100 of TeraOps/s of computational capacity) is expected to be severely communication constrained. To overcome this limitation, new gradient…

Machine Learning · Computer Science 2017-12-08 Chia-Yu Chen , Jungwook Choi , Daniel Brand , Ankur Agrawal , Wei Zhang , Kailash Gopalakrishnan

Optimizing neural networks with loss that contain high-dimensional and high-order differential operators is expensive to evaluate with back-propagation due to $\mathcal{O}(d^{k})$ scaling of the derivative tensor size and the…

Machine Learning · Computer Science 2025-01-14 Zekun Shi , Zheyuan Hu , Min Lin , Kenji Kawaguchi

The great success neural networks have achieved is inseparable from the application of gradient-descent (GD) algorithms. Based on GD, many variant algorithms have emerged to improve the GD optimization process. The gradient for…

Machine Learning · Computer Science 2023-05-29 Zefan Li , Bingbing Ni , Teng Li , WenJun Zhang , Wen Gao

Deep feedforward and recurrent networks have achieved impressive results in many perception and language processing applications. This success is partially attributed to architectural innovations such as convolutional and long short-term…

Machine Learning · Statistics 2015-11-24 Arvind Neelakantan , Luke Vilnis , Quoc V. Le , Ilya Sutskever , Lukasz Kaiser , Karol Kurach , James Martens

Online synaptic plasticity rules derived from gradient descent achieve high accuracy on a wide range of practical tasks. However, their software implementation often requires tediously hand-derived gradients or using gradient…

Neural and Evolutionary Computing · Computer Science 2025-01-22 Jamie Lohoff , Anil Kaya , Florian Assmuth , Emre Neftci

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

We address the challenging problem of deep representation learning--the efficient adaption of a pre-trained deep network to different tasks. Specifically, we propose to explore gradient-based features. These features are gradients of the…

Machine Learning · Computer Science 2020-04-14 Fangzhou Mu , Yingyu Liang , Yin Li

Multilayered artificial neural networks are becoming a pervasive tool in a host of application fields. At the heart of this deep learning revolution are familiar concepts from applied and computational mathematics; notably, in calculus,…

History and Overview · Mathematics 2018-01-19 Catherine F. Higham , Desmond J. Higham

Adaptive gradient methods, e.g. \textsc{Adam}, have achieved tremendous success in machine learning. Scaling the learning rate element-wisely by a certain form of second moment estimate of gradients, such methods are able to attain rapid…

Machine Learning · Computer Science 2022-02-10 Yizhou Wang , Yue Kang , Can Qin , Huan Wang , Yi Xu , Yulun Zhang , Yun Fu

Automatic differentiation (AD) is a technique for computing the derivative of a function represented by a program. This technique is considered as the de-facto standard for computing the differentiation in many machine learning and…

Programming Languages · Computer Science 2022-12-21 Amir Shaikhha , Mathieu Huot , Shabnam Ghasemirad , Andrew Fitzgibbon , Simon Peyton Jones , Dimitrios Vytiniotis

A major challenge in training large-scale machine learning models is configuring the training process to maximize model performance, i.e., finding the best training setup from a vast design space. In this work, we unlock a gradient-based…

Machine Learning · Statistics 2025-03-19 Logan Engstrom , Andrew Ilyas , Benjamin Chen , Axel Feldmann , William Moses , Aleksander Madry

Balancing convergence speed, generalization capability, and computational efficiency remains a core challenge in deep learning optimization. First-order gradient descent methods, epitomized by stochastic gradient descent (SGD) and Adam,…

Deep learning networks are typically trained by Stochastic Gradient Descent (SGD) methods that iteratively improve the model parameters by estimating a gradient on a very small fraction of the training data. A major roadblock faced when…

Machine Learning · Computer Science 2020-06-11 Tao Lin , Lingjing Kong , Sebastian U. Stich , Martin Jaggi

Detecting out-of-distribution (OOD) samples is essential for ensuring the reliability of deep neural networks (DNNs) in real-world scenarios. While previous research has predominantly investigated the disparity between in-distribution (ID)…

Computer Vision and Pattern Recognition · Computer Science 2024-07-23 Yingwen Wu , Tao Li , Xinwen Cheng , Jie Yang , Xiaolin Huang

In this paper, an adjustment to the original differentially private stochastic gradient descent (DPSGD) algorithm for deep learning models is proposed. As a matter of motivation, to date, almost no state-of-the-art machine learning…

Machine Learning · Computer Science 2021-07-13 Mehdi Amian

Adaptive optimizers, such as Adam, have achieved remarkable success in deep learning. A key component of these optimizers is the so-called preconditioning matrix, providing enhanced gradient information and regulating the step size of each…

Machine Learning · Computer Science 2024-12-10 Yun Yue , Zhiling Ye , Jiadi Jiang , Yongchao Liu , Ke Zhang