Linear dependency automatic differentiation (AD) is a technique for calculating gradients and Hessians efficiently. By tracking linear dependencies between variables, AD algorithms, such as the vector-Jacobian (VJ) product and matrix-vector (MV) product, avoid unnecessary computations, making them significantly faster than traditional methods. This efficiency is crucial in applications like neural network training, where large-scale optimization requires fast and accurate gradient and Hessian calculations. By leveraging AD, researchers and practitioners can improve the speed and performance of optimization algorithms, enabling more effective model training and problem-solving.
