Coordinate descent on the orthogonal group for recurrent neural network training
This work addresses training efficiency for recurrent neural networks, but it is incremental as it builds on existing optimization methods with specific adaptations.
The authors tackled the problem of training recurrent neural networks by proposing a stochastic Riemannian coordinate descent algorithm on the orthogonal group, which rotates columns of the recurrent matrix using Givens matrices, and demonstrated its effectiveness on a benchmark problem with faster variants based on sparse gradient structures.
We propose to use stochastic Riemannian coordinate descent on the orthogonal group for recurrent neural network training. The algorithm rotates successively two columns of the recurrent matrix, an operation that can be efficiently implemented as a multiplication by a Givens matrix. In the case when the coordinate is selected uniformly at random at each iteration, we prove the convergence of the proposed algorithm under standard assumptions on the loss function, stepsize and minibatch noise. In addition, we numerically demonstrate that the Riemannian gradient in recurrent neural network training has an approximately sparse structure. Leveraging this observation, we propose a faster variant of the proposed algorithm that relies on the Gauss-Southwell rule. Experiments on a benchmark recurrent neural network training problem are presented to demonstrate the effectiveness of the proposed algorithm.