Quaternion Approximate Networks for Enhanced Image Classification and Oriented Object Detection

Quaternion Approximate Networks for Enhanced Image Classification and Oriented Object Detection. By Bryce Grant and one other, from Case Western Reserve University. Published on the twenty-seventh of October.

An object seen at a new angle is still the same object, and a vision model that respects this is called rotation equivariant. Quaternion algebra suits that kind of geometry, and quaternion neural networks already exist. The catch the authors point to is how those networks are usually built: they attempt to operate entirely in the quaternion domain, while the authors want models efficient enough for robots with limited resources.

Quaternion Approximate Networks, or QUAN, take a different route. Instead of living fully in the quaternion domain, QUAN approximates quaternion convolution. It does so through a decomposition of the Hamilton product, the multiplication rule at the heart of quaternion algebra, expressed with ordinary real-valued operations. The aim is to keep the geometric properties that made quaternions attractive in the first place, while gaining an implementation that runs efficiently, here with custom CUDA kernels.

Two further pieces complete the framework. The first is Independent Quaternion Batch Normalization, called IQBN, introduced for training stability. The second extends quaternion operations into spatial attention mechanisms, so attention too can work with the same algebra.

The evaluation covers three kinds of task. For classification, the benchmarks are the two CIFAR sets, ten and one hundred, along with ImageNet. Here QUAN reaches higher accuracy with fewer parameters and faster convergence than existing convolutional and quaternion-based models. For detection, on COCO and DOTA, QUAN shows improved parameter efficiency and better rotation handling than standard Convolutional Neural Networks, and the authors report that it sets the state of the art for quaternion CNNs in this downstream task. Robotic perception tasks round out the evaluation.

A compromise sits at the centre of this work. Rather than insisting that every operation be a true quaternion operation, QUAN approximates one with real-valued arithmetic and keeps the geometry that matters. The authors see the payoff in resource-constrained robotic systems that need rotation-aware perception, and suggest the approach could carry over to other domains as well.