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Recent advancements have suggested that neural radiance fields (NeRFs) show great potential in color editing within the 3D domain. However, most existing NeRF-based editing methods continue to face significant challenges in local region editing, which usually lead to imprecise local object boundaries, difficulties in maintaining multi-view consistency, and over-reliance on annotated data. To address these limitations, in this paper, we propose a novel weakly-supervised method called KaRF for local color editing, which facilitates high-fidelity and realistic appearance edits in arbitrary regions of 3D scenes. At the core of the proposed KaRF approach is a unified two-stage Kolmogorov-Arnold Networks (KANs)-based radiance fields framework, comprising a segmentation stage followed by a local recoloring stage. This architecture seamlessly integrates geometric priors from NeRF to achieve weakly-supervised learning, leading to superior performance. More specifically, we propose a residual adaptive gating KAN structure, which integrates KAN with residual connections, adaptive parameters, and gating mechanisms to effectively enhance segmentation accuracy and refine specific editing effects. Additionally, we propose a palette-adaptive reconstruction loss, which can enhance the accuracy of additive mixing results. Extensive experiments demonstrate that the proposed KaRF algorithm significantly outperforms many state-of-the-art methods both qualitatively and quantitatively. Our code and more results are available at: https://github.com/PaiDii/KARF.git.