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About this paper
Lin Li, Ziqi Jiang, Gefan Ye, Zhenqi He, Jiahui Li, Jun Xiao, Kwang-Ting Cheng, Long Chen
Path-Decoupled Hyperbolic Flow Matching (HFM) was developed to enhance few-shot adaptation of pre-trained vision-language models by addressing path entanglement in existing Euclidean-based flow matching. Leveraging the exponential volume growth of hyperbolic geometry, HFM spatially decouples feature transport trajectories, achieving superior classification performance and surpassing Euclidean Flow Matching (FMA) by 3.5% (1-shot) and 2.1% (16-shot) on challenging benchmarks.
Key insights
- Hyperbolic geometry, with its exponential volume growth, offers a geometrically structured approach to disentangle complex feature distributions more effectively than Euclidean space, mitigating path entanglement in cross-modal feature transport.
- Establishing a concentric hierarchy in the hyperbolic latent space, where visual features flow centripetally towards textual prototypes, transforms disordered transport into organized inward flows, significantly reducing trajectory collisions.
- A path-decoupled objective, enforcing step-wise consistency and inter-class repulsion, acts as a "semantic guardrail" to confine class-specific trajectories within isolated geodesic corridors, thereby preserving semantic discrimination.
Summary by alphaXiv.
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