Gauss Newton

Gauss-Newton methods are iterative optimization algorithms that approximate the Hessian matrix, a crucial component in Newton's method, to efficiently find the minimum of a function. Current research focuses on applying and improving Gauss-Newton methods within various machine learning contexts, including training neural networks (especially deep and overparameterized ones), solving inverse problems, and data assimilation in fields like weather forecasting. These advancements aim to improve the speed and accuracy of optimization, leading to more efficient training of complex models and enhanced performance in diverse applications. The resulting algorithms often leverage techniques like automatic differentiation, Hessian approximations (e.g., Kronecker-factored), and adaptive step-size strategies to achieve scalability and robustness.