Seminar Details
2022-03-01 (14h) : Exploring geometry for deep learning
At Euler building (room a.002)
Organized by Mathematical Engineering
Speaker :
Massart, Estelle
Abstract :
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. Time permitting, I will also present another application of geometry in deep learning, namely, exploiting invariant curves in the loss landscape when training Wasserstein generative adversarial neural networks.