Quantitative Propagation of Chaos for SGD in Wide Neural Networks S

Mean field approximation and propagation of chaos for mSGLD . . . . . . . . . . 4 S3 T echnical results 4 S4 Quantitative propagation of chaos 8 S4.1 Existence of strong solutions to the particle SDE . . . . . . . . . . . . . . . . . . If F = R, then we simply note C( E). S2.1 Presentation of the modified SGLD and its continuous counterpart The proof is postponed to Section S4.4 Consider now the mean-field SDE starting from a random variable W The proof is postponed to Section S4.4 Then, there exists L 0 such that the following hold. In what follows, we bound separately the two terms in the right-hand side.