# Higher Order Recurrent Neural Networks

arXiv: https://arxiv.org/abs/1605.00064 · HTML: https://mlsanity.com/paper/1605.00064/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Apr 2016.

## Built on by (most cited first, 11 of 11)

- [BasicVSR++: Improving Video Super-Resolution with Enhanced Propagation and Alignment](https://mlsanity.com/paper/2104.13371/) (2021)
- [Event-Based Motion Magnification](https://mlsanity.com/paper/2402.11957/) (2024)
- [Higher Order Recurrent Space-Time Transformer for Video Action Prediction](https://mlsanity.com/paper/2104.08665/) (2021)
- [On the Memory Mechanism of Tensor-Power Recurrent Models](https://mlsanity.com/paper/2103.01521/) (2021)
- [Entangled Residual Mappings](https://mlsanity.com/paper/2206.01261/) (2022)
- [Inductive Attention for Video Action Anticipation](https://mlsanity.com/paper/2212.08830/) (2022)
- [Memory Capacity of Recurrent Neural Networks with Matrix Representation](https://mlsanity.com/paper/2104.07454/) (2021)
- [Forecasting of COVID-19 Cases, Using an Evolutionary Neural Architecture Search Approach](https://mlsanity.com/paper/2109.13062/) (2021)
- [Learning Sequence Representations by Non-local Recurrent Neural Memory](https://mlsanity.com/paper/2207.09710/) (2022)
- [Trading Complexity for Expressivity Through Structured Generalized Linear Token Mixing](https://mlsanity.com/paper/2605.31367/) (2026)
- [Learning infinite context windows in recurrent architectures via spatial neural computing](https://mlsanity.com/paper/2610.10690/) (2026)

## Abstract (arXiv)

In this paper, we study novel neural network structures to better model long term dependency in sequential data. We propose to use more memory units to keep track of more preceding states in recurrent neural networks (RNNs), which are all recurrently fed to the hidden layers as feedback through different weighted paths. By extending the popular recurrent structure in RNNs, we provide the models with better short-term memory mechanism to learn long term dependency in sequences. Analogous to digital filters in signal processing, we call these structures as higher order RNNs (HORNNs). Similar to RNNs, HORNNs can also be learned using the back-propagation through time method. HORNNs are generally applicable to a variety of sequence modelling tasks. In this work, we have examined HORNNs for the language modeling task using two popular data sets, namely the Penn Treebank (PTB) and English text8 data sets. Experimental results have shown that the proposed HORNNs yield the state-of-the-art performance on both data sets, significantly outperforming the regular RNNs as well as the popular LSTMs.