Limited-Memory BFGS Optimization of Recurrent Neural Network Language Models for Speech Recognition

Abstract

Recurrent neural network language models (RNNLM) have become an increasingly popular choice for state-of-the-art speech recognition systems. RNNLMs are normally trained by minimizing the cross entropy (CE) using the stochastic gradient descent (SGD) algorithm. The SGD method only uses first-order derivatives and no higher order gradient information is used to consider the correlation between model parameters. It is unable to fully capture the curvature of the error cost function. This can lead to slow convergence in model training. In this paper, a limited-memory Broyden Fletcher Goldfarb Shannon (L-BFGS) based second order optimization technique is proposed for RNNLMs. This method efficiently approximates the matrix-vector product between the inverse Hessian and gradient vector via a recursion over past gradients with a compact memory requirement. Consistent perplexity and error rate reductions are obtained over the SGD method on two speech recognition tasks: Switchboard English and Babel Cantonese. A faster convergence and speed up in RNNLM training time was also obtained. Index Terms: recurrent neural network, language model, second order optimization, limited-memory BFGS, speech recognition