# Quaternion Approximation Networks for Enhanced Image Classification and Oriented Object Detection

arXiv: https://arxiv.org/abs/2509.05512 · HTML: https://mlsanity.com/paper/2509.05512/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 39 references that are in the map.
- First posted on arXiv 5 Sep 2025.

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

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [DOTA: A Large-scale Dataset for Object Detection in Aerial Images](https://mlsanity.com/paper/1711.10398/) (2017)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [YOLOv11: An Overview of the Key Architectural Enhancements](https://mlsanity.com/paper/2410.17725/) (2024)
- [DenseFusion: 6D Object Pose Estimation by Iterative Dense Fusion](https://mlsanity.com/paper/1901.04780/) (2019)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [BOP: Benchmark for 6D Object Pose Estimation](https://mlsanity.com/paper/1808.08319/) (2018)
- [PVN3D: A Deep Point-wise 3D Keypoints Voting Network for 6DoF Pose Estimation](https://mlsanity.com/paper/1911.04231/) (2019)
- [R3Det: Refined Single-Stage Detector with Feature Refinement for Rotating Object](https://mlsanity.com/paper/1908.05612/) (2019)
- [Gliding vertex on the horizontal bounding box for multi-oriented object detection](https://mlsanity.com/paper/1911.09358/) (2019)
- [Geoopt: Riemannian Optimization in PyTorch](https://mlsanity.com/paper/2005.02819/) (2020)
- [Rotation equivariant vector field networks](https://mlsanity.com/paper/1612.09346/) (2016)
- [Oriented Response Networks](https://mlsanity.com/paper/1701.01833/) (2017)
- [Deep Quaternion Networks](https://mlsanity.com/paper/1712.04604/) (2017)
- [Quaternion Convolutional Neural Networks](https://mlsanity.com/paper/1903.00658/) (2019)
- [Quaternion Recurrent Neural Networks](https://mlsanity.com/paper/1806.04418/) (2018)
- [Large-scale 6D Object Pose Estimation Dataset for Industrial Bin-Picking](https://mlsanity.com/paper/1912.12125/) (2019)
- [Quaternion Convolutional Neural Networks for Detection and Localization of 3D Sound Events](https://mlsanity.com/paper/1812.06811/) (2018)
- [A Quaternion-Valued Variational Autoencoder](https://mlsanity.com/paper/2010.11647/) (2020)
- [Hyperbolic-constraint Point Cloud Reconstruction from Single RGB-D Images](https://mlsanity.com/paper/2412.09055/) (2024)
- [Quaternion Convolutional Neural Networks: Current Advances and Future Directions](https://mlsanity.com/paper/2307.08663/) (2023)
- [Improving Quaternion Neural Networks with Quaternionic Activation Functions](https://mlsanity.com/paper/2406.16481/) (2024)

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

- [QC-GAN: A Parameter-Efficient Quaternion Conformer GAN for High-Fidelity Speech Enhancement](https://mlsanity.com/paper/2606.18611/) (2026)

## Abstract (arXiv)

This paper introduces Quaternion Approximate Networks (QUAN), a novel deep learning framework that leverages quaternion algebra for rotation equivariant image classification and object detection. Unlike conventional quaternion neural networks attempting to operate entirely in the quaternion domain, QUAN approximates quaternion convolution through Hamilton product decomposition using real-valued operations. This approach preserves geometric properties while enabling efficient implementation with custom CUDA kernels. We introduce Independent Quaternion Batch Normalization (IQBN) for training stability and extend quaternion operations to spatial attention mechanisms. QUAN is evaluated on image classification (CIFAR-10/100, ImageNet), object detection (COCO, DOTA), and robotic perception tasks. In classification tasks, QUAN achieves higher accuracy with fewer parameters and faster convergence compared to existing convolution and quaternion-based models. For objection detection, QUAN demonstrates improved parameter efficiency and rotation handling over standard Convolutional Neural Networks (CNNs) while establishing the SOTA for quaternion CNNs in this downstream task. These results highlight its potential for deployment in resource-constrained robotic systems requiring rotation-aware perception and application in other domains.