MC-RFM: Geometry-Aware Few-Shot Adaptation via Mixed-Curvature Riemannian Flow Matching
Researchers have introduced MC-RFM, a novel framework for parameter-efficient few-shot adaptation of pretrained vision models. Unlike traditional methods that treat adaptation as discrete Euclidean perturbations, MC-RFM employs a mixed-curvature Riemannian flow-matching approach. It represents adapted features on a product manifold combining hyperbolic geometry for hierarchical semantic structures and Euclidean geometry for local visual variations. The method formulates adaptation as a task-conditioned continuous transport from frozen features to support-set prototypes, utilizing a flow-matching objective and a hybrid classifier. Operating entirely on cached frozen features, MC-RFM is lightweight and backbone-agnostic. Extensive evaluations across seven visual recognition benchmarks and five backbones demonstrate its superior performance, particularly in 1/4/16-shot regimes with Transformer backbones and fine-grained datasets. Ablation studies confirm the contributions of mixed-curvature heads, task conditioning, and other components. This work highlights the importance of modeling representation movement through geometry matched to downstream task structures, offering a significant advancement in efficient computer vision model adaptation without requiring extensive parameter updates.
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MC-RFM: Geometry-Aware Few-Shot Adaptation via Mixed-Curvature Riemannian Flow Matching
Researchers have introduced MC-RFM, a novel framework for parameter-efficient few-shot adaptation of pretrained vision models. Unlike traditional methods that treat adaptation as discrete Euclidean perturbations, MC-RFM employs a mixed-curvature Riemannian flow-matching approach. It represents adapted features on a product manifold combining hyperbolic geometry for hierarchical semantic structures and Euclidean geometry for local visual variations. The method formulates adaptation as a task-conditioned continuous transport from frozen features to support-set prototypes, utilizing a flow-matching objective and a hybrid classifier. Operating entirely on cached frozen features, MC-RFM is lightweight and backbone-agnostic. Extensive evaluations across seven visual recognition benchmarks and five backbones demonstrate its superior performance, particularly in 1/4/16-shot regimes with Transformer backbones and fine-grained datasets. Ablation studies confirm the contributions of mixed-curvature heads, task conditioning, and other components. This work highlights the importance of modeling representation movement through geometry matched to downstream task structures, offering a significant advancement in efficient computer vision model adaptation without requiring extensive parameter updates.
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