Following the last talk, we shall continue exploring the connection between the (deep) neural networks and the mean-field Langevin dynamics. By modelling the deep networks using a controlled dynamics, we view the training of the deep networks as solving the corresponding relaxed optimal control problems. Indeed, in an abstract framework, the relaxed optimal control problem can be considered as an optimization problem on the probability measure space with marginal constraint. Again, the mean-field Langevin dynamics turns out to be a natural tool to approximate the minimizer of such optimization.

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