Path-Decoupled Hyperbolic Flow Matching for Few-Shot Adaptation

Lin Li; Ziqi Jiang; Gefan Ye; Zhenqi He; Jiahui Li; Jun Xiao; Kwang-Ting Cheng; Long Chen

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arXiv · 2602.20479

Path-Decoupled Hyperbolic Flow Matching for Few-Shot Adaptation

Lin Li·Ziqi Jiang·Gefan Ye·Zhenqi He·Jiahui Li·Jun Xiao·Kwang-Ting Cheng·Long Chen

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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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BibTeX RIS

Lin Li, Ziqi Jiang, Gefan Ye, Zhenqi He, Jiahui Li, Jun Xiao, Kwang-Ting Cheng, Long Chen. 2026-02-24. Path-Decoupled Hyperbolic Flow Matching for Few-Shot Adaptation. https://arxiv.org/abs/2602.20479

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