Explore a novel interacting particle system for implementing expectation maximization (EM) in latent variable models. Delve into the continuous-time system's properties, its relation to Langevin diffusion, and how it enables non-asymptotic concentration bounds for optimization error. Compare this approach to existing methods, examine the proof structure, and discuss potential generalizations. Cover topics such as simulated annealing, Langevin dynamics, target measures, and convergence results. Gain insights from Tim Johnston and Francesca Crucinio's research on optimizing parameters in latent variable models using this innovative particle system approach.