# Kronecker Recurrent Units

arXiv: https://arxiv.org/abs/1705.10142 · HTML: https://mlsanity.com/paper/1705.10142/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2017.

## Built on by (most cited first, 13 of 13)

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- [Improve Long-term Memory Learning Through Rescaling the Error Temporally](https://mlsanity.com/paper/2307.11462/) (2023)
- [Quantized Approximately Orthogonal Recurrent Neural Networks](https://mlsanity.com/paper/2402.04012/) (2024)
- [Weaver: Kronecker Product Approximations of Spatiotemporal Attention for Traffic Network Forecasting](https://mlsanity.com/paper/2511.08888/) (2025)
- [Time-series Initialization and Conditioning for Video-agnostic Stabilization of Video Super-Resolution using Recurrent Networks](https://mlsanity.com/paper/2403.15832/) (2024)
- [HadamRNN: Binary and Sparse Ternary Orthogonal RNNs](https://mlsanity.com/paper/2502.00047/) (2025)

## Abstract (arXiv)

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.