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 five 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.

我们提出了称为Kronecker循环单元（KRU）的灵活的递归神经网络模型，它通过Kronecker分解循环矩阵实现RNNs的参数效率，并通过对因子施加软幺正约束克服循环矩阵的病态条件，从而克服递归神经网络过度参数化的问题。 KRU模型可以降低递归权重矩阵中的参数数量三个数量级，而不会牺牲统计性能。

Kronecker 循环单元