# Quantized Approximately Orthogonal Recurrent Neural Networks

arXiv: https://arxiv.org/abs/2402.04012 · HTML: https://mlsanity.com/paper/2402.04012/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 77 references that are in the map.
- First posted on arXiv 5 Feb 2024.

## Builds on (most cited first, 30 of 54)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [Long Range Arena: A Benchmark for Efficient Transformers](https://mlsanity.com/paper/2011.04006/) (2020)
- [Speech Recognition with Deep Recurrent Neural Networks](https://mlsanity.com/paper/1303.5778/) (2013)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [BinaryConnect: Training Deep Neural Networks with binary weights during propagations](https://mlsanity.com/paper/1511.00363/) (2015)
- [Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations](https://mlsanity.com/paper/1609.07061/) (2016)
- [Q-BERT: Hessian Based Ultra Low Precision Quantization of BERT](https://mlsanity.com/paper/1909.05840/) (2019)
- [Unitary Evolution Recurrent Neural Networks](https://mlsanity.com/paper/1511.06464/) (2015)
- [A Survey on Model Compression for Large Language Models](https://mlsanity.com/paper/2308.07633/) (2023)
- [Repeat After Me: Transformers are Better than State Space Models at Copying](https://mlsanity.com/paper/2402.01032/) (2024)
- [Sorting out Lipschitz function approximation](https://mlsanity.com/paper/1811.05381/) (2018)
- [Independently Recurrent Neural Network (IndRNN): Building A Longer and Deeper RNN](https://mlsanity.com/paper/1803.04831/) (2018)
- [Cheap Orthogonal Constraints in Neural Networks: A Simple Parametrization of the Orthogonal and Unitary Group](https://mlsanity.com/paper/1901.08428/) (2019)
- [AntisymmetricRNN: A Dynamical System View on Recurrent Neural Networks](https://mlsanity.com/paper/1902.09689/) (2019)
- [Full-Capacity Unitary Recurrent Neural Networks](https://mlsanity.com/paper/1611.00035/) (2016)
- [Lipschitz Recurrent Neural Networks](https://mlsanity.com/paper/2006.12070/) (2020)
- [On orthogonality and learning recurrent networks with long term dependencies](https://mlsanity.com/paper/1702.00071/) (2017)
- [Orthogonal Recurrent Neural Networks with Scaled Cayley Transform](https://mlsanity.com/paper/1707.09520/) (2017)
- [Dilated Recurrent Neural Networks](https://mlsanity.com/paper/1710.02224/) (2017)
- [Learning Long-Term Dependencies in Irregularly-Sampled Time Series](https://mlsanity.com/paper/2006.04418/) (2020)

## Built on by (most cited first, 1 of 1)

- [HadamRNN: Binary and Sparse Ternary Orthogonal RNNs](https://mlsanity.com/paper/2502.00047/) (2025)

## Abstract (arXiv)

In recent years, Orthogonal Recurrent Neural Networks (ORNNs) have gained popularity due to their ability to manage tasks involving long-term dependencies, such as the copy-task, and their linear complexity. However, existing ORNNs utilize full precision weights and activations, which prevents their deployment on compact devices.In this paper, we explore the quantization of the weight matrices in ORNNs, leading to Quantized approximately Orthogonal RNNs (QORNNs). The construction of such networks remained an open problem, acknowledged for its inherent instability. We propose and investigate two strategies to learn QORNN by combining quantization-aware training (QAT) and orthogonal projections. We also study post-training quantization of the activations for pure integer computation of the recurrent loop. The most efficient models achieve results similar to state-of-the-art full-precision ORNN, LSTM and FastRNN on a variety of standard benchmarks, even with 4-bits quantization.