Path-Decoupled Hyperbolic Flow Matching for Few-Shot Adaptation

TL;DR

This paper introduces Hyperbolic Flow Matching, a novel method for cross-modal few-shot adaptation that uses hyperbolic geometry to better handle diverse feature distributions and improve alignment accuracy.

Contribution

It proposes a path-decoupled hyperbolic flow matching approach with hierarchical alignment and semantic boundary constraints, addressing limitations of Euclidean geometry in feature transport.

Findings

Achieves state-of-the-art performance on 11 benchmarks.

Outperforms Euclidean flow matching methods consistently.

Demonstrates effective semantic boundary preservation.

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.