SGORNN: Combining Scalar Gates and Orthogonal Constraints in Recurrent Networks

William Keith Taylor-Melanson, Martha Dais Ferreira, Stan Matwin

Keywords: Deep Learning, Recurrent Neural Networks, Exploding Gradient Problem, Deep Learning Generalization, Orthogonal RNNs

Abstract: Recurrent Neural Network (RNN) models have been applied in different domains, producing high accuracies on time-dependent data. However, RNNs have long suffered from exploding gradients during training, mainly due to their recurrent process. In this context, we propose a variant of the scalar gated FastRNN architecture, called Scalar Gated Orthogonal Recurrent Neural Networks (SGORNN). SGORNN utilizes orthogonal linear transformations at the recurrent step. In our experiments, SGORNN forms its recurrent weights through a strategy inspired by Volume Preserving RNNs (VPRNN), though our architecture allows the use of any orthogonal constraint mechanism. We present a simple constraint on the scalar gates of SGORNN, which is easily enforced at training time to provide a theoretical generalization ability for SGORNN similar to that of FastRNN. Our constraint is further motivated by success in experimental settings. Next, we provide bounds on the gradients of SGORNN, to show the impossibility of (exponentially) exploding gradients. Our experimental results on the addition problem confirm that our combination of orthogonal and scalar gated RNNs are able to outperform both predecessor models on long sequences using only a single RNN cell. We further evaluate SGORNN on the HAR-2 classification task, where it improves slightly upon the accuracy of both FastRNN and VPRNN using far fewer parameters than FastRNN. Finally, we evaluate SGORNN on the Penn Treebank word-level language modelling task, where it again outperforms its predecessor architectures. Overall, this architecture shows higher representation capacity than VPRNN, suffers from less overfitting than the other two models in our experiments, benefits from a decrease in parameter count, and alleviates exploding gradients when compared with FastRNN on the addition problem.