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Recurrent Neural Networks (RNNs) are among the most popular models insequential data analysis. Yet, in the foundational PAC learning language, whatconcept class can it learn? Moreover, how can the same recurrent unitsimultaneously learn functions from different input tokens to different outputtokens, without affecting each other? Existing generalization bounds for RNNscale exponentially with the input length, significantly limiting theirpractical implications.  In this paper, we show using the vanilla stochastic gradient descent (SGD),RNN can actually learn some notable concept class efficiently, meaning thatboth time and sample complexity scale polynomially in the input length (oralmost polynomially, depending on the concept). This concept class at leastincludes functions where each output token is generated from inputs of earliertokens using a smooth two-layer neural network.

Can SGD Learn Recurrent Neural Networks with Provable Generalization?