Generative AI and large language models hold great promise in enhancing programming education by generating individualized feedback and hints for learners. Recent works have primarily focused on improving the quality of generated feedback to achieve human tutors' quality.

Deep neural networks have achieved impressive performance in many areas. Designing a fast and provable method for training neural networks is a fundamental question in machine learning. The classical training method requires paying Ω(mnd) cost for both forward computation and backward computation, where m is the width of the neural network, and we are given n training points in d-dimensional space.

In this paper, we show that the smoothness of the estimators, and not the dimension, is the key: benign overfitting is possible if and only if the estimator's derivatives are large enough.