Recurrent Neural Networks (RNNs) are designed to handle sequential data but suffer from vanishing or exploding gradients.   Recent work on Unitary Recurrent Neural Networks (uRNNs) have been used to address this issue and in some cases, exceed the capabilities of Long Short-Term Memory networks (LSTMs).   We propose a simpler and novel update scheme to maintain orthogonal recurrent weight matrices without using complex valued matrices. This is done by parametrizing with a skew-symmetric matrix using the Cayley transform. Such a parametrization is unable to represent matrices with negative one eigenvalues, but this limitation is overcome by scaling the recurrent weight matrix by a diagonal matrix consisting of ones and negative ones.   The proposed training scheme involves a straightforward gradient calculation and update step. In several experiments, the proposed scaled Cayley orthogonal recurrent neural network (scoRNN) achieves superior results with fewer trainable parameters than other unitary RNNs.
A novel approach to maintain orthogonal recurrent weight matrices in a RNN. Introduces a scheme for learning the recurrent parameter matrix in a neural network that uses the Cayley transform and a scaling weight matrix.  This paper suggests an RNN reparametrization of the recurrent weights with a skew-symmetric matrix using Cayley transform to keep the recurrent weight matrix orthogonal. Novel parametrization of RNNs allows representing orthogonal weight matrices relatively easily.