Related papers: Adaptive Optimization via Momentum on Variance-Nor…
Cohen et al. (arXiv:2207.14484) observed that adaptive gradient methods such as Adam operate at the edge of stability. While there has been significant work on continuous-time modeling of gradient descent at the edge of stability, extending…
This paper investigates different vector step-size adaptation approaches for non-stationary online, continual prediction problems. Vanilla stochastic gradient descent can be considerably improved by scaling the update with a vector of…
Adaptive optimization methods, which perform local optimization with a metric constructed from the history of iterates, are becoming increasingly popular for training deep neural networks. Examples include AdaGrad, RMSProp, and Adam. We…
The best performing Binary Neural Networks (BNNs) are usually attained using Adam optimization and its multi-step training variants. However, to the best of our knowledge, few studies explore the fundamental reasons why Adam is superior to…
Here I present a small update to the bias-correction term in the Adam optimizer that has the advantage of making smaller gradient updates in the first several steps of training. With the default bias-correction, Adam may actually make…
Training large language models (LLMs) typically relies on adaptive optimizers like Adam (Kingma & Ba, 2015) which store additional state information to accelerate convergence but incur significant memory overhead. Recent efforts, such as…
Gradient orthogonalization is a simple strategy that shows great utility in speeding up gradient descent. The Muon optimizer (Jordan, Jin, et al., 2024) combines gradient orthogonalization with first-order momentum and achieves significant…
Optimizers that further adjust the scale of gradient, such as Adam, Natural Gradient (NG), etc., despite widely concerned and used by the community, are often found poor generalization performance, compared with Stochastic Gradient Descent…
Adaptive Moment Estimation (Adam) is a cornerstone optimization algorithm in deep learning, widely recognized for its flexibility with adaptive learning rates and efficiency in handling large-scale data. However, despite its practical…
Two major momentum-based techniques that have achieved tremendous success in optimization are Polyak's heavy ball method and Nesterov's accelerated gradient. A crucial step in all momentum-based methods is the choice of the momentum…
Stochastic gradient descent (SGD) is an inherently sequential training algorithm--computing the gradient at batch $i$ depends on the model parameters learned from batch $i-1$. Prior approaches that break this dependence do not honor them…
Most popular optimizers for deep learning can be broadly categorized as adaptive methods (e.g. Adam) and accelerated schemes (e.g. stochastic gradient descent (SGD) with momentum). For many models such as convolutional neural networks…
RMSProp and ADAM continue to be extremely popular algorithms for training neural nets but their theoretical convergence properties have remained unclear. Further, recent work has seemed to suggest that these algorithms have worse…
Adaptive gradient methods, such as AdaGrad, have become fundamental tools in deep learning. Despite their widespread use, the asymptotic convergence of AdaGrad remains poorly understood in non-convex scenarios. In this work, we present the…
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…
In this paper, we present a unified analysis of methods for such a wide class of problems as variational inequalities, which includes minimization problems and saddle point problems. We develop our analysis on the modified Extra-Gradient…
Adaptive gradient methods are workhorses in deep learning. However, the convergence guarantees of adaptive gradient methods for nonconvex optimization have not been thoroughly studied. In this paper, we provide a fine-grained convergence…
The development of machine learning is promoting the search for fast and stable minimization algorithms. To this end, we suggest a change in the current gradient descent methods that should speed up the motion in flat regions and slow it…
Training deep neural networks is challenging. To accelerate training and enhance performance, we propose PadamP, a novel optimization algorithm. PadamP is derived by applying the adaptive estimation of the p-th power of the second-order…
Optimal selection of optimization algorithms is crucial for training deep learning models. The Adam optimizer has gained significant attention due to its efficiency and wide applicability. However, to enhance the adaptability of optimizers…