Hybrid Gromov-Wasserstein Embedding for Capsule Learning.

Area of Science:

• Computer Vision
• Machine Learning
• Deep Learning

Background:

• Capsule networks (CapsNets) offer hierarchical object representation but are computationally expensive.
• Current CapsNets underperform compared to deep convolutional neural networks (CNNs) on complex tasks.
• Existing models lack efficiency and broad applicability in intricate vision problems.

Purpose of the Study:

• To develop an efficient capsule learning approach that overcomes the limitations of current CapsNets.
• To enhance CapsNet performance and applicability to complex, high-dimensional vision tasks.
• To achieve superior performance compared to both CNNs and existing capsule baselines.

Main Methods:

• Introduction of subcapsules for input vector projection.
• Implementation of the hybrid Gromov-Wasserstein (HGW) framework for dissimilarity quantification and optimal transport (OT) based alignment.
• Leveraging component distribution similarity for defining input-subcapsule alignment.

Main Results:

• The proposed HGW capsules (HGWCapsules) demonstrate superior performance over canonical CapsNet baselines and high-performing CNNs.
• HGWCapsules exhibit enhanced robustness against affine transformations and scalability to larger datasets.
• The model maintains interpretability and hierarchical structure while improving efficiency.

Conclusions:

• The HGW framework provides an efficient and effective method for learning capsules.
• This approach enables CapsNets to tackle more intricate vision tasks, including object detection.
• HGWCapsules represent a significant advancement, outperforming existing models in demanding vision tasks.