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We analyze Elman-type Recurrent Reural Networks (RNNs) and their training inthe mean-field regime. Specifically, we show convergence of gradient descenttraining dynamics of the RNN to the corresponding mean-field formulation in thelarge width limit. We also show that the fixed points of the limitinginfinite-width dynamics are globally optimal, under some assumptions on theinitialization of the weights. Our results establish optimality forfeature-learning with wide RNNs in the mean-field regime

Global Optimality of Elman-type RNN in the Mean-Field Regime