{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/hvt-a-comprehensive-vision-framework-for","title":"HVT: A Comprehensive Vision Framework for Learning in Non-Euclidean Space","arxiv_id":"2409.16897","date":"2024-09-25","proceeding":null,"authors":["Jacob Fein-Ashley","Ethan Feng","Minh Pham"],"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 M\\\"obius 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.","url_abs":"https://arxiv.org/abs/2409.16897v2","url_pdf":"https://arxiv.org/pdf/2409.16897v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"hvt-a-comprehensive-vision-framework-for","repo_url":"https://github.com/hyperbolicvit/hyperbolicvit","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"image-classification","task_name":"Image Classification"},{"task_slug":"image-classification","task_name":"image-classification"}],"methods":[{"method_slug":"absolute-position-encodings","method_name":"Absolute Position Encodings"},{"method_slug":"adam","method_name":"Adam"},{"method_slug":"attention","method_name":"Attention"},{"method_slug":"bpe","method_name":"BPE"},{"method_slug":"dense-connections","method_name":"Dense Connections"},{"method_slug":"dropout","method_name":"Dropout"},{"method_slug":"label-smoothing","method_name":"Label Smoothing"},{"method_slug":"layer-normalization","method_name":"Layer Normalization"},{"method_slug":"linear-layer","method_name":"Linear Layer"},{"method_slug":"multi-head-attention","method_name":"Multi-Head Attention"},{"method_slug":"position-wise-feed-forward-layer","method_name":"Position-Wise Feed-Forward Layer"},{"method_slug":"residual-connection","method_name":"Residual Connection"},{"method_slug":"softmax","method_name":"Softmax"},{"method_slug":"transformer","method_name":"Transformer"},{"method_slug":"vision-transformer","method_name":"Vision Transformer"}],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/image-classification-on-imagenet","task":"Image Classification","dataset":"ImageNet","model":"HVT Huge","rank_in_archive_order":92,"of":1060,"metrics":{"Top 1 Accuracy":"87.4%"},"uses_additional_data":false},{"leaderboard":"/sota/image-classification-on-imagenet","task":"Image Classification","dataset":"ImageNet","model":"HVT Large","rank_in_archive_order":265,"of":1060,"metrics":{"Top 1 Accuracy":"85%"},"uses_additional_data":false},{"leaderboard":"/sota/image-classification-on-imagenet","task":"Image Classification","dataset":"ImageNet","model":"HVT Base","rank_in_archive_order":717,"of":1060,"metrics":{"Top 1 Accuracy":"80.1%"},"uses_additional_data":false}],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}