  Our work addresses two important issues with recurrent neural networks: (1)
they are over-parameterized, and (2) the recurrence 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.
