用双曲几何解构少样本跨模态对齐路径纠缠问题
Path-Decoupled Hyperbolic Flow Matching for Few-Shot Adaptation
- 引入双曲流匹配，通过洛伦兹流形的指数扩张实现路径解耦
- 在11个基准上超越欧氏方法，显著提升少样本对齐性能
- 适合做跨模态少样本学习的研究者和工程师参考
近期跨模态少样本适应将视觉-语义对齐视为连续特征传输问题，采用流匹配（FM）方法。然而我们指出，基于欧几里得空间的FM忽视了平坦几何的根本局限：多项式体积增长无法适应多样的特征分布，导致严重路径纠缠。为此，本文提出路径解耦的双曲流匹配（HFM），利用洛伦兹流形的指数扩张实现轨迹解耦。HFM通过两项关键设计构建运输过程：1）向心双曲对齐：以文本根节点为锚点构建向心层次结构，推动视觉叶节点向边界移动，初始化有序流；2）路径解耦目标：作为“语义护栏”，通过分步监督严格约束轨迹在独立类特定测地线通道内。此外，我们设计基于自适应直径的停止机制，依据内在语义尺度防止过度传输至拥挤原点。在11个基准上的大量消融实验表明，HFM建立了新最优性能，持续优于其欧氏对应方法。代码与模型将公开发布。
原文摘要 · Abstract (English)
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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