| title | MC-RFM: Geometry-Aware Few-Shot Adaptation via Mixed-Curvature Riemannian Flow Matching |
|---|---|
| authors | Salim Khazem, Ibrahim Mohamed Serouis, Zakaria Ezzahed |
| date | 2026-05-08 |
| venue | arXiv (preprint, not peer reviewed) |
| id | arXiv:2605.08557 |
| affiliation | Talan |
| upvotes | 3 (Hugging Face Daily Papers, 2026-11-01) |
| links | abs pdf hf code |
| abstract | 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. |
cite
@misc{khazem2026mc,
title={MC-RFM: Geometry-Aware Few-Shot Adaptation via Mixed-Curvature Riemannian Flow Matching},
author={Salim Khazem and Ibrahim Mohamed Serouis and Zakaria Ezzahed},
year={2026},
eprint={2605.08557},
archivePrefix={arXiv},
url={https://arxiv.org/abs/2605.08557}
}