Deterministic convergence analysis for regularized long short-term memory and its application to regression and multi-classification problems

Long short-term memory (LSTM) is a recurrent neural network (RNN) framework designed to solve the gradient disappearance and explosion problems of traditional RNNs. In recent years, LSTM has become a state-of-the-art model for solving various machine-learning problems. This paper propose a novel regularized LSTM based on the batch gradient method. Specifically, the L₂ regularization is appended to the objective function as a systematic external force, effectively controlling the excessive growth of weights in the network and preventing the overfitting phenomenon. In addition, a rigorous convergence analysis of the proposed method is carried out, i.e., monotonicity, weak convergence, and strong convergence results are obtained. Finally, comparative simulations are conducted on the benchmark data set for regression and classification problems, and the simulation results verify the effectiveness of the method.