Quaternion Approximation Networks for Enhanced Image Classification and Oriented Object Detection

2025-09-05

AI Summary

Traditional quaternion neural networks suffer from complex-domain arithmetic operations, training instability, and low parameter efficiency. To address these issues, this paper proposes Quaternion Approximate Networks (QUAN): it approximates quaternion convolution via real-valued decomposition of the Hamilton product, enabling efficient rotation-equivariant learning entirely within the real domain for the first time; introduces Independent Quaternion Batch Normalization (IQBN) to enhance training stability; and designs a quaternion spatial attention mechanism to improve geometric awareness. QUAN consistently outperforms standard CNNs and existing quaternion CNNs on image classification (CIFAR-10/100, ImageNet) and oriented object detection (COCO, DOTA), achieving higher accuracy while significantly reducing both parameter count and computational cost—making it particularly suitable for resource-constrained robotic vision systems.

Technology Category

• Computer Vision: Adversarial Attacks & Robustness
• Machine Learning: Quantum Machine Learning
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

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.

Problem

• Enhancing rotation equivariant image classification and object detection
• Approximating quaternion convolution with real-valued operations
• Improving parameter efficiency and rotation handling in CNNs

Innovation

• Quaternion convolution via real-valued operations
• Independent Quaternion Batch Normalization for stability
• Spatial attention with quaternion operations