Quaternion Approximate Network

This paper introduces Quaternion Approximate Networks (QUAN), a novel deep learning framework that leverages quaternion algebra for rotation equivariant image classification and object detection. Quaternion networks are studied for their inherent rotation equivariance, enabling them to capture richer spatial relationships and geometric structures compared to real-valued convolutions. Unlike conventional quaternion neural networks that operate entirely in the quaternion domain, QUAN utilizes the Hamilton product to approximate quaternion convolution while maintaining real-valued operations. This approach preserves both semantic and geometric information while reducing computational overhead, allowing for efficient implementation within standard deep learning frameworks. Additionally, quaternion operations are extended to spatial attention mechanisms, and Independent Quaternion Batch Normalization is introduced to enhance feature characterization stability.

The effectiveness of QUAN is evaluated in two experimental settings: image classification and rotated object detection. In classification tasks on CIFAR-10 and CIFAR-100, QUAN achieves higher accuracy with fewer parameters and faster convergence compared to existing convolution and quaternion-based models. For rotated object detection, performance is assessed on a real-world robotic assembly dataset, where a UR5 robot executes manipulation tasks with oriented bounding box outputs. By integrating quaternion-based representations into both classification and detection tasks, QUAN demonstrates improved parameter efficiency and rotation handling over standard Convolution Neural Networks (CNNs) and improved accuracy over existing quaternion CNNs. These results highlight its potential for deployment in resource-constrained robotic systems and provide a foundation for further exploration on larger benchmark datasets.

Recommended citation: B. Grant and P. Wang, “Quaternion Approximate Networks,” arXiv.org, Mar. 1, 2025.
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