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Deep learning optimization relies heavily on the assumption of smooth loss landscapes, a condition systematically violated by modern architectures due to non-smooth components such as ReLU activations and quantization operators. In such…

Machine Learning · Computer Science 2026-05-29 Ruoran Xu , Borong She , Xiaobo Jin , Qiufeng Wang

Gradient descent based optimization methods are the methods of choice to train deep neural networks in machine learning. Beyond the standard gradient descent method, also suitable modified variants of standard gradient descent involving…

Optimization and Control · Mathematics 2025-04-29 Steffen Dereich , Arnulf Jentzen , Adrian Riekert

The choice of optimiser is important in deep learning, as it strongly influences model efficiency and speed of convergence. However, many commonly used optimisers encounter difficulties when applied to imbalanced and sequential datasets,…

We observe that the traditional use of DP with the Adam optimizer introduces a bias in the second moment estimation, due to the addition of independent noise in the gradient computation. This bias leads to a different scaling for low…

Machine Learning · Computer Science 2023-04-25 Qiaoyue Tang , Mathias Lécuyer

Adam is a widely used optimization method for training deep learning models. It computes individual adaptive learning rates for different parameters. In this paper, we propose a generalization of Adam, called Adambs, that allows us to also…

Machine Learning · Computer Science 2020-10-27 Rui Liu , Tianyi Wu , Barzan Mozafari

The insufficient generalization of adaptive moment estimation (Adam) has hindered its broader application. Recent studies have shown that flat minima in loss landscapes are highly associated with improved generalization. Inspired by the…

Machine Learning · Computer Science 2024-12-18 Long Jin , Han Nong , Liangming Chen , Zhenming Su

This work introduces NOVAK, a modular gradient-based optimization algorithm that integrates adaptive moment estimation, rectified learning-rate scheduling, decoupled weight regularization, multiple variants of Nesterov momentum, and…

Machine Learning · Computer Science 2026-01-14 Sergii Kavun

Stochastic optimizers are central to deep learning, yet widely used methods such as Adam and Adan can degrade in non-stationary or noisy environments, partly due to their reliance on momentum-based magnitude estimates. We introduce Ano, a…

Machine Learning · Computer Science 2025-11-11 Adrien Kegreisz

Adam is applied widely to train neural networks. Different kinds of Adam methods with different features pop out. Recently two new adam optimizers, AdaBelief and Padam are introduced among the community. We analyze these two adam optimizers…

Computer Vision and Pattern Recognition · Computer Science 2021-10-05 Zhaoyang Zhu , Haozhe Sun , Chi Zhang

Federated learning on edge devices must cope with non-IID client data and tight memory budgets. Adaptive optimizers like Adam stabilize training under data heterogeneity but require storing full-precision momentum and variance states, often…

Machine Learning · Computer Science 2026-05-19 Vedant Waykole , Haroon R. Lone

This paper studies a class of adaptive gradient based momentum algorithms that update the search directions and learning rates simultaneously using past gradients. This class, which we refer to as the "Adam-type", includes the popular…

Machine Learning · Computer Science 2019-03-12 Xiangyi Chen , Sijia Liu , Ruoyu Sun , Mingyi Hong

Although adaptive optimization algorithms such as Adam show fast convergence in many machine learning tasks, this paper identifies a problem of Adam by analyzing its performance in a simple non-convex synthetic problem, showing that Adam's…

Machine Learning · Computer Science 2020-05-06 Wenjie Li , Zhaoyang Zhang , Xinjiang Wang , Ping Luo

Adam is a popular variant of stochastic gradient descent for finding a local minimizer of a function. In the constant stepsize regime, assuming that the objective function is differentiable and non-convex, we establish the convergence in…

Machine Learning · Statistics 2020-05-15 Anas Barakat , Pascal Bianchi

In this paper, we present a comprehensive study on the convergence properties of Adam-family methods for nonsmooth optimization, especially in the training of nonsmooth neural networks. We introduce a novel two-timescale framework that…

Optimization and Control · Mathematics 2024-02-20 Nachuan Xiao , Xiaoyin Hu , Xin Liu , Kim-Chuan Toh

Momentum based optimizers are central to a wide range of machine learning applications. These typically rely on an Exponential Moving Average (EMA) of gradients, which decays exponentially the present contribution of older gradients. This…

Machine Learning · Computer Science 2024-10-01 Matteo Pagliardini , Pierre Ablin , David Grangier

NOMAD (Navigating Optimal Model Application for Datastreams) is an intelligent framework for data enrichment during ingestion that optimizes realtime multiclass classification by dynamically constructing model chains, i.e ,sequences of…

Deep neural networks are commonly trained using stochastic non-convex optimization procedures, which are driven by gradient information estimated on fractions (batches) of the dataset. While it is commonly accepted that batch size is an…

Machine Learning · Computer Science 2016-04-26 Ilya Loshchilov , Frank Hutter

Modern deep learning systems do not generalize well when the test data distribution is slightly different to the training data distribution. While much promising work has been accomplished to address this fragility, a systematic study of…

Efficient stochastic optimization typically integrates an update direction that performs well in the deterministic regime with a mechanism adapting to stochastic perturbations. While Adam uses adaptive moment estimates to promote stability,…

Machine Learning · Computer Science 2026-02-23 Minxin Zhang , Yuxuan Liu , Hayden Schaeffer

Stochastic gradient descent (SGD) optimization methods are nowadays the method of choice for the training of deep neural networks (DNNs) in artificial intelligence systems. In practically relevant training problems, usually not the plain…

Optimization and Control · Mathematics 2024-08-01 Steffen Dereich , Arnulf Jentzen
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