Adaptive Approximation

Adaptive approximation focuses on efficiently representing functions or data using methods that adjust their complexity or precision based on the input or desired accuracy. Current research explores this through various approaches, including randomized low-rank matrix approximations for optimizing deep learning models, adaptive algorithms for approximating monotone functions with optimal sample complexity, and the use of sparse deep neural networks for solving partial differential equations. These advancements improve the efficiency and accuracy of computations in diverse fields, ranging from machine learning optimization to numerical solutions of complex equations, by tailoring the approximation to the specific problem at hand.