On the Provable Generalization of Recurrent Neural Networks

Recurrent Neural Network (RNN) is a fundamental structure in deep learning. Recently, some works study the training process of over-parameterized neural networks, and show that over-parameterized networks can learn functions in some notable concept classes with a provable generalization error bound. In this paper, we analyze the training and generalization for RNNs with random initialization, and provide the following improvements over recent works:(1) For a RNN with input sequence x (X_1,X_2,...,X_L), previous works study to learn functions that are summation of f(\beta T_lX_l) and require normalized conditions that X_l \leq\epsilon with some very small \epsilon depending on the complexity of f . In this paper, using detailed analysis about the neural tangent kernel matrix, we prove a generalization error bound to learn such functions without normalized conditions and show that some notable concept classes are learnable with the numbers of iterations and samples scaling almost-polynomially in the input length L .(2) Moreover, we prove a novel result to learn N-variables functions of input sequence with the form f(\beta T[X_{l_1},...,X_{l_N}]), which do not belong to the additive'' concept class, i,e., the summation of function f(X_l) .