\Varepsilon$ Cover

Epsilon (ε)-covers are used in various fields to approximate complex structures or functions within a specified tolerance. Current research focuses on developing efficient algorithms for computing ε-covers, particularly in high-dimensional spaces and for kernel range spaces where the goal is to approximate the effect of a kernel function on a set of points. This work is significant because efficient ε-cover computation improves the scalability of machine learning algorithms, enables faster approximate solutions to partial differential equations, and offers theoretical insights into generalization bounds for stochastic gradient descent. The resulting approximations offer a trade-off between computational cost and accuracy, impacting diverse applications from computer vision to machine learning.