MC-RFM: Geometry-Aware Few-Shot Adaptation via Mixed-Curvature Riemannian Flow Matching

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few-shot-adaptation geometry-aware riemannian-flow-matching mixed-curvature visual-recognition pretrained-models

Summary

MC-RFM proposes a novel Riemannian flow-matching framework for few-shot adaptation that models feature displacement on a mixed-curvature manifold combining hyperbolic and Euclidean spaces, outperforming existing methods across multiple visual recognition benchmarks.

Parameter-efficient adaptation of pretrained vision models is commonly performed through linear probes, prompts, low-rank updates, or lightweight residual modules. While effective, these methods usually treat adaptation as a discrete Euclidean perturbation of frozen representations, without explicitly modeling the geometry of the task-induced feature displacement. We propose MC-RFM, a mixed-curvature Riemannian flow-matching framework for few-shot adaptation of frozen visual backbones. The key idea is to represent adapted features on a product manifold combining a hyperbolic factor, which captures hierarchy-sensitive semantic structure, and a Euclidean factor, which preserves locally discriminative visual variation. Adaptation is formulated as a task-conditioned continuous transport from frozen features to support-set prototypes, trained with a flow-matching objective and coupled to a hybrid prototype-linear classifier. The method is lightweight, backbone-agnostic, and operates entirely on cached frozen features. Across seven visual recognition benchmarks, five frozen backbones, and 1/4/16-shot regimes, MC-RFM is the best-performing method in a majority of evaluated settings, with the strongest gains on Transformer backbones and fine-grained datasets. Ablations show that the mixed-curvature head, task conditioning, adaptive branch gating, prototype shrinkage, and discriminative supervision each contribute to performance. These results suggest that few-shot adaptation benefits not only from deciding which parameters to update, but also from modeling how representations should move through a geometry matched to the structure of the downstream task.
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Paper page - MC-RFM: Geometry-Aware Few-Shot Adaptation via Mixed-Curvature Riemannian Flow Matching

Source: https://huggingface.co/papers/2605.08557

Abstract

A novel Riemannian flow-matching framework for few-shot adaptation that models feature displacement on a mixed-curvature manifold combining hyperbolic and Euclidean spaces, outperforming existing methods across multiple benchmarks.

Parameter-efficient adaptationof pretrainedvision modelsis commonly performed through linear probes, prompts, low-rank updates, or lightweight residual modules. While effective, these methods usually treat adaptation as a discrete Euclidean perturbation of frozen representations, without explicitly modeling the geometry of the task-inducedfeature displacement. We propose MC-RFM, a mixed-curvatureRiemannian flow-matchingframework forfew-shot adaptationoffrozen visual backbones. The key idea is to represent adapted features on aproduct manifoldcombining ahyperbolic factor, which captures hierarchy-sensitive semantic structure, and aEuclidean factor, which preserves locally discriminative visual variation. Adaptation is formulated as a task-conditioned continuous transport from frozen features to support-set prototypes, trained with aflow-matching objectiveand coupled to ahybrid prototype-linear classifier. The method is lightweight, backbone-agnostic, and operates entirely on cached frozen features. Across seven visual recognition benchmarks, five frozen backbones, and 1/4/16-shot regimes, MC-RFM is the best-performing method in a majority of evaluated settings, with the strongest gains on Transformer backbones and fine-grained datasets. Ablations show that the mixed-curvature head, task conditioning, adaptive branch gating, prototype shrinkage, and discriminative supervision each contribute to performance. These results suggest thatfew-shot adaptationbenefits not only from deciding which parameters to update, but also from modeling how representations should move through a geometry matched to the structure of the downstream task.

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