Path-Decoupled Hyperbolic Flow Matching for Few-Shot Adaptation
- URL: http://arxiv.org/abs/2602.20479v1
- Date: Tue, 24 Feb 2026 02:12:58 GMT
- Title: Path-Decoupled Hyperbolic Flow Matching for Few-Shot Adaptation
- Authors: Lin Li, Ziqi Jiang, Gefan Ye, Zhenqi He, Jiahui Li, Jun Xiao, Kwang-Ting Cheng, Long Chen,
- Abstract summary: We argue that Euclidean-based Flow Matching overlooks fundamental limitations of flat geometry.<n>We propose path-decoupled Hyperbolic Flow Matching, leveraging the Lorentz manifold's exponential expansion for trajectory decoupling.<n>Our codes and models will be released.
- Score: 36.30669615593167
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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.
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