HVT: A Comprehensive Vision Framework for Learning in Non-Euclidean Space
This work addresses the challenge of capturing complex relationships in vision tasks for researchers and practitioners, though it appears incremental as it extends an existing method with a known geometric approach.
The paper tackles the problem of modeling hierarchical and relational dependencies in image data by introducing the Hyperbolic Vision Transformer (HVT), which integrates hyperbolic geometry into the Vision Transformer, resulting in improved performance for image classification on the ImageNet dataset.
Data representation in non-Euclidean spaces has proven effective for capturing hierarchical and complex relationships in real-world datasets. Hyperbolic spaces, in particular, provide efficient embeddings for hierarchical structures. This paper introduces the Hyperbolic Vision Transformer (HVT), a novel extension of the Vision Transformer (ViT) that integrates hyperbolic geometry. While traditional ViTs operate in Euclidean space, our method enhances the self-attention mechanism by leveraging hyperbolic distance and Möbius transformations. This enables more effective modeling of hierarchical and relational dependencies in image data. We present rigorous mathematical formulations, showing how hyperbolic geometry can be incorporated into attention layers, feed-forward networks, and optimization. We offer improved performance for image classification using the ImageNet dataset.