Second Order Neural Network Optimization: Meta Analysis

Second-order optimization algorithms have garnered significant interest in deep learning due to their ability to leverage curvature information, leading to faster convergence and enhanced generalization compared to first-order methods. This paper provides a comprehensive review of recent advancements in second-order optimization techniques tailored for deep neural networks, emphasizing their scalability, efficiency, and applicability across various tasks. We categorize these methods into Quasi-Newton methods, Generalized Gauss-Newton methods, and Parameter Subset Optimization methods, each offering unique strategies to balance computational cost and the advantages of second-order information. Despite their potential, these techniques face challenges such as high computational and memory demands, sensitivity to hyperparameters, and integration complexities in large-scale models. We discuss the innovative approaches employed by these algorithms to address these challenges, including structured approximations and adaptive updates, and provide insights into their theoretical foundations and empirical evaluations. The analysis highlights the critical role of second-order methods in advancing neural network optimization and outlines future research directions aimed at enhancing their scalability and practical adoption in deep learning applications.