Stochastic Gradient Flow

Stochastic gradient flow (SGF) studies the continuous-time limit of stochastic gradient descent (SGD), a fundamental algorithm for training machine learning models. Current research focuses on analyzing SGF's dynamics, particularly its convergence properties and implicit biases, often using tools from stochastic differential equations and optimal transport. This analysis helps explain the generalization performance of SGD, especially in high-dimensional and non-convex settings, and informs the development of improved optimization algorithms like accelerated and robust variants of SGD. Understanding SGF provides crucial insights into the behavior of widely used machine learning methods and guides the design of more efficient and effective training procedures.