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Gradient-based algorithms, popular strategies to optimization problems, are essential for many modern machine-learning techniques. Theoretically, extreme points of certain cost functions can be found iteratively along the directions of the…

Quantum Physics · Physics 2021-04-07 Keren Li , Pan Gao , Shijie Wei , Jiancun Gao , Guilu Long

Many machine learning algorithms have been developed under the assumption that data sets are already available in batch form. Yet in many application domains data is only available sequentially overtime via compute nodes in different…

Optimization and Control · Mathematics 2020-09-10 Alfredo Garcia , Luochao Wang , Jeff Huang , Lingzhou Hong

The demand for artificially generated data for the development, training and testing of new algorithms is omnipresent. Quantum computing (QC), does offer the hope that its inherent probabilistic functionality can be utilised in this field…

Machine Learning · Computer Science 2025-09-03 Tobias Rohe , Florian Burger , Michael Kölle , Sebastian Wölckert , Maximilian Zorn , Claudia Linnhoff-Popien

A major obstacle to achieving global convergence in distributed and federated learning is the misalignment of gradients across clients, or mini-batches due to heterogeneity and stochasticity of the distributed data. In this work, we show…

Machine Learning · Computer Science 2021-12-14 Yatin Dandi , Luis Barba , Martin Jaggi

Today's deep learning methods focus on how to design the most appropriate objective functions so that the prediction results of the model can be closest to the ground truth. Meanwhile, an appropriate architecture that can facilitate…

Computer Vision and Pattern Recognition · Computer Science 2024-03-01 Chien-Yao Wang , I-Hau Yeh , Hong-Yuan Mark Liao

In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…

Dynamical Systems · Mathematics 2025-07-08 Dennis Chemnitz , Maximilian Engel , Christian Kuehn , Sara-Viola Kuntz

Quantum neural networks (QNNs) provide expressive probabilistic models by leveraging quantum superposition and entanglement, yet their practical training remains challenging due to highly oscillatory loss landscapes and noise inherent to…

Quantum Physics · Physics 2026-01-26 Jaemin Seo

Generative Adversarial Networks (GANs), as a framework for estimating generative models via an adversarial process, have attracted huge attention and have proven to be powerful in a variety of tasks. However, training GANs is well known for…

Machine Learning · Computer Science 2017-11-09 Zi-Yi Dou

Due to the substantial computational cost, training state-of-the-art deep neural networks for large-scale datasets often requires distributed training using multiple computation workers. However, by nature, workers need to frequently…

Machine Learning · Computer Science 2018-02-21 Yusuke Tsuzuku , Hiroto Imachi , Takuya Akiba

In many real-world applications of Machine Learning it is of paramount importance not only to provide accurate predictions, but also to ensure certain levels of robustness. Adversarial Training is a training procedure aiming at providing…

Machine Learning · Computer Science 2019-10-09 Matteo Terzi , Gian Antonio Susto , Pratik Chaudhari

Modern machine learning and deep learning models are shown to be vulnerable when testing data are slightly perturbed. Existing theoretical studies of adversarial training algorithms mostly focus on either adversarial training losses or…

Machine Learning · Statistics 2021-04-07 Yue Xing , Qifan Song , Guang Cheng

Ridgeless regression has garnered attention among researchers, particularly in light of the ``Benign Overfitting'' phenomenon, where models interpolating noisy samples demonstrate robust generalization. However, kernel ridgeless regression…

Machine Learning · Computer Science 2024-06-04 Fan He , Mingzhen He , Lei Shi , Xiaolin Huang , Johan A. K. Suykens

We propose self-adaptive training -- a unified training algorithm that dynamically calibrates and enhances training processes by model predictions without incurring an extra computational cost -- to advance both supervised and…

Machine Learning · Computer Science 2022-10-17 Lang Huang , Chao Zhang , Hongyang Zhang

Spiking Neural Networks (SNNs) have been proposed as biologically plausible and energy-efficient alternatives to conventional Artificial Neural Networks (ANNs). However, the training of SNN usually relies on surrogate gradients due to the…

Neural and Evolutionary Computing · Computer Science 2026-05-11 Himanshu Udupi , Xiaocong Yang , ChengXiang Zhai

A multilayer perceptron can behave as a generative classifier by applying bidirectional learning (BL). It consists of training an undirected neural network to map input to output and vice-versa; therefore it can produce a classifier in one…

Machine Learning · Computer Science 2019-10-25 Sidney Pontes-Filho , Marcus Liwicki

Traditional classification algorithms assume that training and test data come from similar distributions. This assumption is violated in adversarial settings, where malicious actors modify instances to evade detection. A number of custom…

Computer Science and Game Theory · Computer Science 2016-11-29 Bo Li , Yevgeniy Vorobeychik , Xinyun Chen

There are several applications of stochastic optimization where one can benefit from a robust estimate of the gradient. For example, domains such as distributed learning with corrupted nodes, the presence of large outliers in the training…

Machine Learning · Statistics 2025-10-30 Fabian Schaipp , Guillaume Garrigos , Umut Simsekli , Robert Gower

We introduce a general method for improving the convergence rate of gradient-based optimizers that is easy to implement and works well in practice. We demonstrate the effectiveness of the method in a range of optimization problems by…

Machine Learning · Computer Science 2018-08-23 Atilim Gunes Baydin , Robert Cornish , David Martinez Rubio , Mark Schmidt , Frank Wood

Natural gradient descent is a principled method for adapting the parameters of a statistical model on-line using an underlying Riemannian parameter space to redefine the direction of steepest descent. The algorithm is examined via methods…

Disordered Systems and Neural Networks · Physics 2009-10-31 Magnus Rattray , David Saad

Arguably the biggest challenge in applying neural networks is tuning the hyperparameters, in particular the learning rate. The sensitivity to the learning rate is due to the reliance on backpropagation to train the network. In this paper we…

Machine Learning · Statistics 2018-08-08 Francois Fagan , Garud Iyengar