Optimal Stable Nonlinear Approximation

While it is well-known that nonlinear methods of approximation can often perform dramatically better than linear methods, there are still questions on how to measure the optimal performance possible for such methods. This paper studies compatible with numerical implementation in they required be numerically stable. A performance, called stable manifold widths, approximating a model class K Banach space X by introduced. Fundamental inequalities between these widths and entropy established. The effects requiring stability settings deep learning compressed sensing discussed.