HVT: A Comprehensive Vision Framework for Learning in Non-Euclidean Space
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866929515972788224 |
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| author | Fein-Ashley, Jacob Feng, Ethan Pham, Minh |
| author_facet | Fein-Ashley, Jacob Feng, Ethan Pham, Minh |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16897 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | HVT: A Comprehensive Vision Framework for Learning in Non-Euclidean Space Fein-Ashley, Jacob Feng, Ethan Pham, Minh Computer Vision and Pattern Recognition 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. |
| title | HVT: A Comprehensive Vision Framework for Learning in Non-Euclidean Space |
| topic | Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2409.16897 |