  Recurrent neural networks (RNNs) are a class of neural networks used in
sequential tasks. However, in general, RNNs have a large number of parameters
and involve enormous computational costs by repeating the recurrent structures
in many time steps. As a method to overcome this difficulty, RNN pruning has
attracted increasing attention in recent years, and it brings us benefits in
terms of the reduction of computational cost as the time step progresses.
However, most existing methods of RNN pruning are heuristic. The purpose of
this paper is to study the theoretical scheme for RNN pruning method. We
propose an appropriate pruning algorithm for RNNs inspired by "spectral
pruning", and provide the generalization error bounds for compressed RNNs. We
also provide numerical experiments to demonstrate our theoretical results and
show the effectiveness of our pruning method compared with existing methods.
