On orthogonality and learning recurrent networks with long term dependencies
This addresses the vanishing/exploding gradient problem in deep learning, but the findings are incremental as they refine existing orthogonality-based approaches.
The paper tackles the challenge of training recurrent neural networks with long-term dependencies by analyzing the effects of orthogonality constraints on optimization convergence, speed, and gradient stability, finding that hard constraints can negatively impact convergence speed and model performance.
It is well known that it is challenging to train deep neural networks and recurrent neural networks for tasks that exhibit long term dependencies. The vanishing or exploding gradient problem is a well known issue associated with these challenges. One approach to addressing vanishing and exploding gradients is to use either soft or hard constraints on weight matrices so as to encourage or enforce orthogonality. Orthogonal matrices preserve gradient norm during backpropagation and may therefore be a desirable property. This paper explores issues with optimization convergence, speed and gradient stability when encouraging or enforcing orthogonality. To perform this analysis, we propose a weight matrix factorization and parameterization strategy through which we can bound matrix norms and therein control the degree of expansivity induced during backpropagation. We find that hard constraints on orthogonality can negatively affect the speed of convergence and model performance.