2021/07/30 by Estelle Massart, Massart, Estelle, Vinayak Abrol +1 · 1 citation
Computer Science · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning and ELM #Neural Networks and Applications #Optimization and Control (math.OC) #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2108.00051
openalex publication_date 2021/07/30 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
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.