Definition: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
Input: <lb>We show that any model trained by a stochastic gradient method with few iterations has<lb>vanishing generalization error. We prove this by showing the method is algorithmically stable<lb>in the sense of Bousquet and Elisseeff. Our analysis only employs elementary tools from convex<lb>and continuous optimization. Our results apply to both convex and non-convex optimization<lb>under standard Lipschitz and smoothness assumptions.<lb>Applying our results to the convex case, we provide new explanations for why multiple<lb>epochs of stochastic gradient descent generalize well in practice. In the nonconvex case, we<lb>provide a new interpretation of common practices in neural networks, and provide a formal<lb>rationale for stability-promoting mechanisms in training large, deep models. Conceptually, our<lb>findings underscore the importance of reducing training time beyond its obvious benefit.

Stability of stochastic gradient descent