Adaptive optimizers are pivotal in guiding the weight updates of deep neural networks, yet they often face challenges such as poor generalization and oscillation issues. To counter these, we introduce sigSignGrad and tanhSignGrad, two novel optimizers that integrate adaptive friction coefficients based on the Sigmoid and Tanh functions, respectively. These algorithms leverage short-term gradient information, a feature overlooked in traditional Adam variants like diffGrad and AngularGrad, to enhance parameter updates and convergence.Our theoretical analysis demonstrates the wide-ranging adjustment capability of the friction coefficient S, which aligns with targeted parameter update strategies and outperforms existing methods in both optimization trajectory smoothness and convergence rate. Extensive experiments on CIFAR-10, CIFAR-100, and Mini-ImageNet datasets using ResNet50 and ViT architectures confirm the superior performance of our proposed optimizers, showcasing improved accuracy and reduced training time. The innovative approach of integrating adaptive friction coefficients as plug-ins into existing optimizers, exemplified by the sigSignAdamW and sigSignAdamP variants, presents a promising strategy for boosting the optimization performance of established algorithms. The findings of this study contribute to the advancement of optimizer design in deep learning.

Deep Neural Networks (DNNs) have achieved outstanding results across a wide range of hot-topic tasks in computer vision and natural language processing. These achievements however come with a high cost, as solving increasingly complex tasks requires increasingly deep neural network architectures. Moreover, today's deepening architectures not only increase the computational burden, they can also suffer from vanishing gradient problems. Recent efforts to tackle the vanishing gradient problem in DNN training have leveraged advanced optimizers such as the adaptive moment estimation (Adam) optimizer in model training, but such existing optimizers are unable to exploit any gradient angular information other than magnitude. To overcome these limitations, a team from the IEEE (Institute of Electrical and Electronics Engineers) has proposed AngularGrad -- a novel optimization algorithm that takes both gradient direction and angular information into consideration.

Convolutional neural networks (CNNs) are trained using stochastic gradient descent (SGD)-based optimizers. Recently, the adaptive moment estimation (Adam) optimizer has become very popular due to its adaptive momentum, which tackles the dying gradient problem of SGD. Nevertheless, existing optimizers are still unable to exploit the optimization curvature information efficiently. This paper proposes a new AngularGrad optimizer that considers the behavior of the direction/angle of consecutive gradients. This is the first attempt in the literature to exploit the gradient angular information apart from its magnitude. The proposed AngularGrad generates a score to control the step size based on the gradient angular information of previous iterations. Thus, the optimization steps become smoother as a more accurate step size of immediate past gradients is captured through the angular information. Two variants of AngularGrad are developed based on the use of Tangent or Cosine functions for computing the gradient angular information. Theoretically, AngularGrad exhibits the same regret bound as Adam for convergence purposes. Nevertheless, extensive experiments conducted on benchmark data sets against state-of-the-art methods reveal a superior performance of AngularGrad. The source code will be made publicly available at: https://github.com/mhaut/AngularGrad.