A Lyapunov-Based Method of Reducing Activation Functions of Recurrent Neural Networks for Stability Analysis

This letter proposes a Lyapunov-based method of reducing the number of activation functions of a recurrent neural network (RNN) for its stability analysis. To the best of the authors’ knowledge, no method has been presented for pruning RNNs with respecting their stability properties. We are the first to present an effective solution method for this important problem in the control community and machine learning community. The proposed reduction method follows the intuitive policy: compose a reduced RNN by removing some activation functions whose “magnitudes” with respect to their weighted actions are “small” in some sense, and analyze its stability to guarantee the stability of the original RNN. Moreover, we theoretically justify this policy by proving several theorems that are applicable to general reduction methods. In addition, we propose a method of rendering the proposed reduction method less conservative, on the basis of semidefinite programming. The effectiveness of the proposed methods is demonstrated on a numerical example.