MC-RFM: Geometry-Aware Few-Shot Adaptation via Mixed-Curvature Riemannian Flow Matching
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917475206037504 |
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| author | Khazem, Salim Serouis, Ibrahim Mohamed Ezzahed, Zakaria |
| author_facet | Khazem, Salim Serouis, Ibrahim Mohamed Ezzahed, Zakaria |
| contents | 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 \textsc{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, \textsc{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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_08557 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | MC-RFM: Geometry-Aware Few-Shot Adaptation via Mixed-Curvature Riemannian Flow Matching Khazem, Salim Serouis, Ibrahim Mohamed Ezzahed, Zakaria Computer Vision and Pattern Recognition Artificial Intelligence Machine Learning 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 \textsc{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, \textsc{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. |
| title | MC-RFM: Geometry-Aware Few-Shot Adaptation via Mixed-Curvature Riemannian Flow Matching |
| topic | Computer Vision and Pattern Recognition Artificial Intelligence Machine Learning |
| url | https://arxiv.org/abs/2605.08557 |