Directional Derivative

The directional derivative measures the rate of change of a function along a specific direction, a fundamental concept in calculus with broad applications in optimization and machine learning. Current research focuses on leveraging directional derivatives in novel ways, such as developing stochastic gradient descent methods using nonlocal directional derivatives for improved generalization in deep learning, and employing randomized forward mode automatic differentiation for efficient gradient estimation. These advancements are impacting various fields, including deep learning model training, where techniques like Mixup are being refined through a directional derivative lens to enhance generalization performance, and distributed computing, where coded computation strategies utilize directional derivatives for robust and asynchronous gradient updates.