<ul><li>This paper studies the convergence analysis of a class of neural stochastic differential equations (SDEs) and their associated optimal control problems.</li><li>The focus is on understanding the limiting behavior of the sampled optimal control problems as the sample size grows to infinity.</li><li>The paper analyzes the N-particle systems with centralized control and establishes uniform regularity estimates by solving the Hamilton-Jacobi-Bellman equation.</li><li>The research shows the convergence of both the objective functionals and optimal parameters of the neural SDEs as the sample size tends to infinity, with the limiting objects identified as suitable functions defined on the Wasserstein space of Borel probability measures.</li></ul>

Convergence analysis of controlled particle systems arising in deep learning: from finite to infinite sample size

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