# Enhancing ResNet Image Classification Performance by using Parameterized Hypercomplex Multiplication

arXiv: https://arxiv.org/abs/2301.04623 · HTML: https://mlsanity.com/paper/2301.04623/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 31 references that are in the map.
- First posted on arXiv 11 Jan 2023.

## Builds on (most cited first, 12 of 12)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Improved Regularization of Convolutional Neural Networks with Cutout](https://mlsanity.com/paper/1708.04552/) (2017)
- [Escaping the Big Data Paradigm with Compact Transformers](https://mlsanity.com/paper/2104.05704/) (2021)
- [Deep Complex Networks](https://mlsanity.com/paper/1705.09792/) (2017)
- [Beyond Fully-Connected Layers with Quaternions: Parameterization of Hypercomplex Multiplications with 1/n Parameters](https://mlsanity.com/paper/2102.08597/) (2021)
- [Deep Quaternion Networks](https://mlsanity.com/paper/1712.04604/) (2017)
- [Quaternion Convolutional Neural Networks](https://mlsanity.com/paper/1903.00658/) (2019)
- [Quaternion Convolutional Neural Networks for End-to-End Automatic Speech Recognition](https://mlsanity.com/paper/1806.07789/) (2018)
- [Deep Octonion Networks](https://mlsanity.com/paper/1903.08478/) (2019)
- [Sign Language Fingerspelling Classification from Depth and Color Images using a Deep Belief Network](https://mlsanity.com/paper/1503.05830/) (2015)

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

- [Towards Hyperparameter-Agnostic DNN Training via Dynamical System Insights](https://mlsanity.com/paper/2310.13901/) (2023)

## Abstract (arXiv)

Recently, many deep networks have introduced hypercomplex and related calculations into their architectures. In regard to convolutional networks for classification, these enhancements have been applied to the convolution operations in the frontend to enhance accuracy and/or reduce the parameter requirements while maintaining accuracy. Although these enhancements have been applied to the convolutional frontend, it has not been studied whether adding hypercomplex calculations improves performance when applied to the densely connected backend. This paper studies ResNet architectures and incorporates parameterized hypercomplex multiplication (PHM) into the backend of residual, quaternion, and vectormap convolutional neural networks to assess the effect. We show that PHM does improve classification accuracy performance on several image datasets, including small, low-resolution CIFAR 10/100 and large high-resolution ImageNet and ASL, and can achieve state-of-the-art accuracy for hypercomplex networks.