Generalized Tensor Models for Recurrent Neural Networks
This work addresses the theoretical understanding of RNNs for researchers, but it is incremental as it extends existing analysis to more practical nonlinearities.
The paper tackles the gap between theoretical efficiency and practical application in Recurrent Neural Networks (RNNs) by extending analysis to RNNs with nonlinearities like ReLU, showing they also have universality and depth efficiency properties, with results verified through computational experiments.
Recurrent Neural Networks (RNNs) are very successful at solving challenging problems with sequential data. However, this observed efficiency is not yet entirely explained by theory. It is known that a certain class of multiplicative RNNs enjoys the property of depth efficiency --- a shallow network of exponentially large width is necessary to realize the same score function as computed by such an RNN. Such networks, however, are not very often applied to real life tasks. In this work, we attempt to reduce the gap between theory and practice by extending the theoretical analysis to RNNs which employ various nonlinearities, such as Rectified Linear Unit (ReLU), and show that they also benefit from properties of universality and depth efficiency. Our theoretical results are verified by a series of extensive computational experiments.