Path-Decoupled Hyperbolic Flow Matching for Few-Shot Adaptation
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arXiv
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| Auteurs principaux: | , , , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911464317517824 |
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| author | Li, Lin Jiang, Ziqi Ye, Gefan He, Zhenqi Li, Jiahui Xiao, Jun Cheng, Kwang-Ting Chen, Long |
| author_facet | Li, Lin Jiang, Ziqi Ye, Gefan He, Zhenqi Li, Jiahui Xiao, Jun Cheng, Kwang-Ting Chen, Long |
| contents | Recent advances in cross-modal few-shot adaptation treat visual-semantic alignment as a continuous feature transport problem via Flow Matching (FM). However, we argue that Euclidean-based FM overlooks fundamental limitations of flat geometry, where polynomial volume growth fails to accommodate diverse feature distributions, leading to severe path entanglement. To this end, we propose path-decoupled Hyperbolic Flow Matching (HFM), leveraging the Lorentz manifold's exponential expansion for trajectory decoupling. HFM structures the transport via two key designs: 1) Centripetal hyperbolic alignment: It constructs a centripetal hierarchy by anchoring textual roots, which pushes visual leaves to the boundary to initialize orderly flows. 2) Path-decoupled objective: It acts as a ``semantic guardrail'' rigidly confining trajectories within isolated class-specific geodesic corridors via step-wise supervision. Furthermore, we devise an adaptive diameter-based stopping to prevent over-transportation into the crowded origin based on the intrinsic semantic scale. Extensive ablations on 11 benchmarks have shown that HFM establishes a new state-of-the-art, consistently outperforming its Euclidean counterparts. Our codes and models will be released. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20479 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Path-Decoupled Hyperbolic Flow Matching for Few-Shot Adaptation Li, Lin Jiang, Ziqi Ye, Gefan He, Zhenqi Li, Jiahui Xiao, Jun Cheng, Kwang-Ting Chen, Long Computer Vision and Pattern Recognition Recent advances in cross-modal few-shot adaptation treat visual-semantic alignment as a continuous feature transport problem via Flow Matching (FM). However, we argue that Euclidean-based FM overlooks fundamental limitations of flat geometry, where polynomial volume growth fails to accommodate diverse feature distributions, leading to severe path entanglement. To this end, we propose path-decoupled Hyperbolic Flow Matching (HFM), leveraging the Lorentz manifold's exponential expansion for trajectory decoupling. HFM structures the transport via two key designs: 1) Centripetal hyperbolic alignment: It constructs a centripetal hierarchy by anchoring textual roots, which pushes visual leaves to the boundary to initialize orderly flows. 2) Path-decoupled objective: It acts as a ``semantic guardrail'' rigidly confining trajectories within isolated class-specific geodesic corridors via step-wise supervision. Furthermore, we devise an adaptive diameter-based stopping to prevent over-transportation into the crowded origin based on the intrinsic semantic scale. Extensive ablations on 11 benchmarks have shown that HFM establishes a new state-of-the-art, consistently outperforming its Euclidean counterparts. Our codes and models will be released. |
| title | Path-Decoupled Hyperbolic Flow Matching for Few-Shot Adaptation |
| topic | Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2602.20479 |