HVT: A Comprehensive Vision Framework for Learning in Non-Euclidean Space
Keywords: hyperbolic, topology, vit, transformer, vision, manifold
TL;DR: ViTs can benefit from hyperbolic spaces to preserve location importance and enhance hierarchical structures
Abstract: 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.
Primary Area: applications to computer vision, audio, language, and other modalities
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Submission Number: 800
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