# Path-Decoupled Hyperbolic Flow Matching for Few-Shot Adaptation Source: [Path-Decoupled Hyperbolic Flow Matching for Few-Shot Adaptation]() Collection index: [llms.txt]() Data updated: 2026-02-26T05:00:04.574Z Authors: Lin Li, Ziqi Jiang, Gefan Ye, Zhenqi He, Jiahui Li, Jun Xiao, Kwang-Ting Cheng, Long Chen Published: 2026-02-24T02:12:58.000Z ## 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Few-Shot Image Classification on FGVC Aircraft (test)](): Few-shot Image Classification; FGVC-Aircraft (test); Top-1 Accuracy: 62.1. - [Few-shot Image Classification on EuroSAT (test)](): Few-shot Image Classification; EuroSAT (test); 1-Shot Accuracy: 94.3. - [Few-shot Image Classification on ImageNet (test)](): Few-shot Image Classification; ImageNet (test); Accuracy (1-shot): not recorded. ## Original sources and implementation [Original paper]() [PDF]()