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Operator learning for time-dependent partial differential equations (PDEs) has seen rapid progress in recent years, enabling efficient approximation of complex spatiotemporal dynamics. However, most existing methods rely on fixed time step…

Machine Learning · Computer Science 2025-10-07 Zhikai Wu , Sifan Wang , Shiyang Zhang , Sizhuang He , Min Zhu , Anran Jiao , Lu Lu , David van Dijk

This paper proposes a set of new error criteria and learning approaches, Adaptive Normalized Risk-Averting Training (ANRAT), to attack the non-convex optimization problem in training deep neural networks (DNNs). Theoretically, we…

Machine Learning · Computer Science 2016-06-10 Zhiguang Wang , Tim Oates , James Lo

The training of deep neural networks is inherently a nonconvex optimization problem, yet standard approaches such as stochastic gradient descent (SGD) require simultaneous updates to all parameters, often leading to unstable convergence and…

Machine Learning · Computer Science 2025-08-07 Chengcheng Yan , Jiawei Xu , Zheng Peng , Qingsong Wang

Despite significant recent advances in deep neural networks, training them remains a challenge due to the highly non-convex nature of the objective function. State-of-the-art methods rely on error backpropagation, which suffers from several…

Deep neural networks and decision trees operate on largely separate paradigms; typically, the former performs representation learning with pre-specified architectures, while the latter is characterised by learning hierarchies over…

Neural and Evolutionary Computing · Computer Science 2019-06-11 Ryutaro Tanno , Kai Arulkumaran , Daniel C. Alexander , Antonio Criminisi , Aditya Nori

The DANE algorithm is an approximate Newton method popularly used for communication-efficient distributed machine learning. Reasons for the interest in DANE include scalability and versatility. Convergence of DANE, however, can be tricky;…

Machine Learning · Statistics 2019-08-07 Xiao-Tong Yuan , Ping Li

Designing an optimal deep neural network for a given task is important and challenging in many machine learning applications. To address this issue, we introduce a self-adaptive algorithm: the adaptive network enhancement (ANE) method,…

Numerical Analysis · Mathematics 2022-03-02 Zhiqiang Cai , Jingshuang Chen , Min Liu

Transformers have become the de facto backbone of modern deep learning, yet their training typically demands an advanced optimizer with adaptive learning rate like AdamW, rather than a momentum SGDW (mSGDW). Previous works show that it is…

Machine Learning · Computer Science 2025-07-24 Xianbiao Qi , Marco Chen , Wenjie Xiao , Jiaquan Ye , Yelin He , Chun-Guang Li , Zhouchen Lin

Scaling network depth has been a central driver behind the success of modern foundation models, yet recent investigations suggest that deep layers are often underutilized. This paper revisits the default mechanism for deepening neural…

Machine Learning · Computer Science 2026-02-10 Yilang Zhang , Bingcong Li , Niao He , Georgios B. Giannakis

The gradients used to train neural networks are typically computed using backpropagation. While an efficient way to obtain exact gradients, backpropagation is computationally expensive, hinders parallelization, and is biologically…

Machine Learning · Computer Science 2026-01-14 Katharina Flügel , Daniel Coquelin , Marie Weiel , Charlotte Debus , Achim Streit , Markus Götz

In recent years, the Deep Learning Alternating Minimization (DLAM), which is actually the alternating minimization applied to the penalty form of the deep neutral networks training, has been developed as an alternative algorithm to overcome…

Machine Learning · Computer Science 2021-02-02 Linbo Qiao , Tao Sun , Hengyue Pan , Dongsheng Li

The accuracy of deep learning (e.g., convolutional neural networks) for an image classification task critically relies on the amount of labeled training data. Aiming to solve an image classification task on a new domain that lacks labeled…

Computer Vision and Pattern Recognition · Computer Science 2019-01-01 Xianghong Fang , Haoli Bai , Ziyi Guo , Bin Shen , Steven Hoi , Zenglin Xu

Quantization is a technique for reducing deep neural networks (DNNs) training and inference times, which is crucial for training in resource constrained environments or applications where inference is time critical. State-of-the-art (SOTA)…

Machine Learning · Computer Science 2023-05-24 Lorenz Kummer , Kevin Sidak , Tabea Reichmann , Wilfried Gansterer

In the last decade, motivated by the success of Deep Learning, the scientific community proposed several approaches to make the learning procedure of Neural Networks more effective. When focussing on the way in which the training data are…

Machine Learning · Computer Science 2021-06-22 Simone Marullo , Matteo Tiezzi , Marco Gori , Stefano Melacci

Current artificial neural networks are trained with parameters encoded as floating point numbers that occupy lots of memory space at inference time. Due to the increase in the size of deep learning models, it is becoming very difficult to…

Machine Learning · Computer Science 2024-08-09 Ben Crulis , Barthelemy Serres , Cyril de Runz , Gilles Venturini

Current deep neural networks (DNNs) are vulnerable to adversarial attacks, where adversarial perturbations to the inputs can change or manipulate classification. To defend against such attacks, an effective and popular approach, known as…

Machine Learning · Computer Science 2022-09-08 Gaoyuan Zhang , Songtao Lu , Yihua Zhang , Xiangyi Chen , Pin-Yu Chen , Quanfu Fan , Lee Martie , Lior Horesh , Mingyi Hong , Sijia Liu

In this paper we propose a new family of algorithms, ATENT, for training adversarially robust deep neural networks. We formulate a new loss function that is equipped with an additional entropic regularization. Our loss function considers…

Machine Learning · Computer Science 2021-02-22 Gauri Jagatap , Ameya Joshi , Animesh Basak Chowdhury , Siddharth Garg , Chinmay Hegde

Motivated by the gap between theoretical optimal approximation rates of deep neural networks (DNNs) and the accuracy realized in practice, we seek to improve the training of DNNs. The adoption of an adaptive basis viewpoint of DNNs leads to…

Machine Learning · Computer Science 2019-12-11 Eric C. Cyr , Mamikon A. Gulian , Ravi G. Patel , Mauro Perego , Nathaniel A. Trask

Quantization is a technique to reduce the computation and memory cost of DNN models, which are getting increasingly large. Existing quantization solutions use fixed-point integer or floating-point types, which have limited benefits, as both…

Machine Learning · Computer Science 2022-08-31 Cong Guo , Chen Zhang , Jingwen Leng , Zihan Liu , Fan Yang , Yunxin Liu , Minyi Guo , Yuhao Zhu

Large-scale deep neural networks (DNN) have been successfully used in a number of tasks from image recognition to natural language processing. They are trained using large training sets on large models, making them computationally and…

Machine Learning · Computer Science 2017-03-28 Sek Chai , Aswin Raghavan , David Zhang , Mohamed Amer , Tim Shields
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