Quaternion Approximate Networks for Enhanced Image Classification and Oriented Object Detection

Quaternion-valued neural networks and variational quantum circuits (VQCs) both derive local transformations from $\mathrm{SU}(2)$ geometry, yet their performance on classical supervised learning remains poorly understood. We compare real-valued, quaternion-valued, and quantum classification heads on identical frozen features across MNIST, FashionMNIST, and CIFAR-10. CIFAR-10 uses a learned 16-dimensional bottleneck and frozen ImageNet-pretrained ResNet18 features to separate architecture from representation quality. Quaternion classifiers match or approach real-valued baselines while outperforming shallow VQCs. On MNIST and FashionMNIST, quaternion networks nearly equal real-valued MLPs, whereas product-state VQCs show lower accuracy and higher cost. On CIFAR-10, quaternion networks retain 94--97% of real-valued performance and remain stable under a 32-fold increase in dimensionality. Product-state circuits underperform quaternion classifiers, while entanglement gives modest grayscale gains but reverses under pretrained CNN features (9.25 pp degradation vs.\ product-state). Fubini--Study/QFI natural gradients improve geometric alignment but not short-horizon loss reduction vs.\ Adam. A Friedman test on five-seed MNIST detects model differences ($χ^2=12.796$, $p=0.0051$, $n=5$), with Wilcoxon tests yielding large effect sizes ($d>5$) for QuatNet vs.\ quantum comparisons. For FashionMNIST and CIFAR-10, large effects ($d>2.0$) are the primary statistic given $n=3$. These results indicate that quaternion networks provide efficient, stable $\mathrm{SU}(2)$ alternatives to shallow VQCs on tasks lacking intrinsic quantum structure. Shared local $\mathrm{SU}(2)$ geometry and shallow entanglement are insufficient, within the regime studied, to confer practical quantum advantage. Conclusions are limited to shallow, measurement-limited circuits on such tasks.

Recent real-time detection transformers have gained popularity due to their simplicity and efficiency. However, these detectors do not explicitly model object rotation, especially in remote sensing imagery where objects appear at arbitrary angles, leading to challenges in angle representation, matching cost, and training stability. In this paper, we propose a real-time oriented object detection transformer, the first real-time end-to-end oriented object detector to the best of our knowledge, that addresses the above issues. Specifically, angle distribution refinement is proposed to reformulate angle regression as an iterative refinement of probability distributions, thereby capturing the uncertainty of object rotation and providing a more fine-grained angle representation. Then, we incorporate a Chamfer distance cost into bipartite matching, measuring box distance via vertex sets, enabling more accurate geometric alignment and eliminating ambiguous matches. Moreover, we propose oriented contrastive denoising to stabilize training and analyze four noise modes. We observe that a ground truth can be assigned to different index queries across different decoder layers, and analyze this issue using the proposed instability metric. We design a series of model variants and experiments to validate the proposed method. Notably, our O2-DFINE-L, O2-RTDETR-R50 and O2-DEIM-R50 achieve 77.73%/78.45%/80.15% AP50 on DOTA1.0 and 132/119/119 FPS on the 2080ti GPU. Code is available at https://github.com/wokaikaixinxin/ai4rs.

Camouflaged object detection (COD) depends on weak texture and boundary cues that can be destroyed by aggressive post-training quantization (PTQ). Existing PTQ methods mainly optimize quantizers or reconstruct network blocks, while using a single precision-allocation domain throughout hierarchical backbones. Instead, we introduce AxisQ, a depth-adaptive bit-allocation framework motivated by the observation that the useful allocation axis changes with feature depth. Under a fixed per-layer average activation-bit budget, AxisQ allocates precision in the channel domain for shallow features and in the local-frequency domain for deep features, using COD-aware sensitivity to better preserve subtle foreground regions and ambiguous boundaries. We also formulate a boundary-aware Hessian approximation for reconstruction by incorporating boundary-weighted gradient and error statistics. Experiments across multiple COD models and diverse benchmarks demonstrate improved accuracy over the strongest baselines at low bit widths, with relative weighted F-measure gains of 12.7% for CFRN and 33.3% for CamoFormer-P on CAMO under W2A2 quantization. These results support adapting the allocation domain to feature depth as a transferable quantization strategy for hierarchical COD models.