Recurrent Highway Networks

Many sequential processing tasks require complex nonlinear transition functions from one step to the next. However, recurrent neural networks with 'deep' transition functions remain difficult to train, even when using Long Short-Term Memory (LSTM) networks. We introduce a novel theoretical analysis of recurrent networks based on Gersgorin's circle theorem that illuminates several modeling and optimization issues and improves our understanding of the LSTM cell. Based on this analysis we propose Recurrent Highway Networks, which are deep not only in time but also in space, extending the LSTM architecture to larger step-to-step transition depths. Experiments demonstrate that the proposed architecture results in powerful and efficient models benefiting from up to 10 layers in the recurrent transition. On the Penn Treebank language modeling corpus, a single network outperforms all previous ensemble results with a perplexity of 66.0 on the test set. On the larger Hutter Prize Wikipedia dataset, a single network again significantly outperforms all previous results with an entropy of 1.32 bits per character on the test set.