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Recurrent Neural Networks (RNNs) are designed to handle sequential data butsuffer from vanishing or exploding gradients. Recent work on Unitary RecurrentNeural Networks (uRNNs) have been used to address this issue and in some cases,exceed the capabilities of Long Short-Term Memory networks (LSTMs). We proposea simpler and novel update scheme to maintain orthogonal recurrent weightmatrices without using complex valued matrices. This is done by parametrizingwith a skew-symmetric matrix using the Cayley transform. Such a parametrizationis unable to represent matrices with negative one eigenvalues, but thislimitation is overcome by scaling the recurrent weight matrix by a diagonalmatrix consisting of ones and negative ones. The proposed training schemeinvolves a straightforward gradient calculation and update step. In severalexperiments, the proposed scaled Cayley orthogonal recurrent neural network(scoRNN) achieves superior results with fewer trainable parameters than otherunitary RNNs.

Orthogonal Recurrent Neural Networks with Scaled Cayley Transform