Input-Output Equivalence of Unitary and Contractive RNNs
Abstract
Unitary recurrent neural networks (URNNs) have been proposed as a method to overcome the vanishing and exploding gradient problem in modeling data with long-term dependencies. A basic question is how restrictive is the unitary constraint on the possible input-output mappings of such a network? This work shows that for any contractive RNN with ReLU activations, there is a URNN with at most twice the number of hidden states and the identical input-output mapping. Hence, with ReLU activations, URNNs are as expressive as general RNNs. In contrast, for certain smooth activations, it is shown that the input-output mapping of an RNN cannot be matched with a URNN, even with an arbitrary number of states. The theoretical results are supported by experiments on modeling of slowly-varying dynamical systems.
Keywords
Cite
@article{arxiv.1910.13672,
title = {Input-Output Equivalence of Unitary and Contractive RNNs},
author = {M. Emami and M. Sahraee-Ardakan and S. Rangan and A. K. Fletcher},
journal= {arXiv preprint arXiv:1910.13672},
year = {2019}
}