Kronecker Recurrent Units

Cijo Jose, Moustapha Cisse, Francois Fleuret
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:2380-2389, 2018.

Abstract

Our work addresses two important issues with recurrent neural networks: (1) they are over-parametrized, and (2) the recurrent weight matrix is ill-conditioned. The former increases the sample complexity of learning and the training time. The latter causes the vanishing and exploding gradient problem. We present a flexible recurrent neural network model called Kronecker Recurrent Units (KRU). KRU achieves parameter efficiency in RNNs through a Kronecker factored recurrent matrix. It overcomes the ill-conditioning of the recurrent matrix by enforcing soft unitary constraints on the factors. Thanks to the small dimensionality of the factors, maintaining these constraints is computationally efficient. Our experimental results on seven standard data-sets reveal that KRU can reduce the number of parameters by three orders of magnitude in the recurrent weight matrix compared to the existing recurrent models, without trading the statistical performance. These results in particular show that while there are advantages in having a high dimensional recurrent space, the capacity of the recurrent part of the model can be dramatically reduced.

Cite this Paper

BibTeX
@InProceedings{pmlr-v80-jose18a, title = {{K}ronecker Recurrent Units}, author = {Jose, Cijo and Cisse, Moustapha and Fleuret, Francois}, booktitle = {Proceedings of the 35th International Conference on Machine Learning}, pages = {2380--2389}, year = {2018}, editor = {Dy, Jennifer and Krause, Andreas}, volume = {80}, series = {Proceedings of Machine Learning Research}, month = {10--15 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v80/jose18a/jose18a.pdf}, url = {https://proceedings.mlr.press/v80/jose18a.html}, abstract = {Our work addresses two important issues with recurrent neural networks: (1) they are over-parametrized, and (2) the recurrent weight matrix is ill-conditioned. The former increases the sample complexity of learning and the training time. The latter causes the vanishing and exploding gradient problem. We present a flexible recurrent neural network model called Kronecker Recurrent Units (KRU). KRU achieves parameter efficiency in RNNs through a Kronecker factored recurrent matrix. It overcomes the ill-conditioning of the recurrent matrix by enforcing soft unitary constraints on the factors. Thanks to the small dimensionality of the factors, maintaining these constraints is computationally efficient. Our experimental results on seven standard data-sets reveal that KRU can reduce the number of parameters by three orders of magnitude in the recurrent weight matrix compared to the existing recurrent models, without trading the statistical performance. These results in particular show that while there are advantages in having a high dimensional recurrent space, the capacity of the recurrent part of the model can be dramatically reduced.} }
Endnote
%0 Conference Paper %T Kronecker Recurrent Units %A Cijo Jose %A Moustapha Cisse %A Francois Fleuret %B Proceedings of the 35th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2018 %E Jennifer Dy %E Andreas Krause %F pmlr-v80-jose18a %I PMLR %P 2380--2389 %U https://proceedings.mlr.press/v80/jose18a.html %V 80 %X Our work addresses two important issues with recurrent neural networks: (1) they are over-parametrized, and (2) the recurrent weight matrix is ill-conditioned. The former increases the sample complexity of learning and the training time. The latter causes the vanishing and exploding gradient problem. We present a flexible recurrent neural network model called Kronecker Recurrent Units (KRU). KRU achieves parameter efficiency in RNNs through a Kronecker factored recurrent matrix. It overcomes the ill-conditioning of the recurrent matrix by enforcing soft unitary constraints on the factors. Thanks to the small dimensionality of the factors, maintaining these constraints is computationally efficient. Our experimental results on seven standard data-sets reveal that KRU can reduce the number of parameters by three orders of magnitude in the recurrent weight matrix compared to the existing recurrent models, without trading the statistical performance. These results in particular show that while there are advantages in having a high dimensional recurrent space, the capacity of the recurrent part of the model can be dramatically reduced.
APA
Jose, C., Cisse, M. & Fleuret, F.. (2018). Kronecker Recurrent Units. Proceedings of the 35th International Conference on Machine Learning, in Proceedings of Machine Learning Research 80:2380-2389 Available from https://proceedings.mlr.press/v80/jose18a.html.

Related Material