High-resolution UAV photogrammetry has become a key technology for precision agriculture, enabling centimeter-level crop monitoring and point-level plant localization. However, point-level maize localization in UAV imagery remains challenging due to (1) extremely small object-to-pixel ratios, typically less than 0.1%, (2) prohibitive computational costs of quadratic attention on ultra-high-resolution images larger than 3000 x 4000 pixels, and (3) agricultural scene-specific complexities such as sparse object distribution and environmental variability that are poorly handled by general-purpose vision models. To address these challenges, we propose the Additive Kolmogorov-Arnold Transformer (AKT), which replaces conventional multilayer perceptrons with Pade Kolmogorov-Arnold Network (PKAN) modules to enhance functional expressivity for small-object feature extraction, and introduces PKAN Additive Attention (PAA) to model multiscale spatial dependencies with reduced computational complexity. In addition, we present the Point-based Maize Localization (PML) dataset, consisting of 1,928 high-resolution UAV images with approximately 501,000 point annotations collected under real field conditions. Extensive experiments show that AKT achieves an average F1-score of 62.8%, outperforming state-of-the-art methods by 4.2%, while reducing FLOPs by 12.6% and improving inference throughput by 20.7%. For downstream tasks, AKT attains a mean absolute error of 7.1 in stand counting and a root mean square error of 1.95-1.97 cm in interplant spacing estimation. These results demonstrate that integrating Kolmogorov-Arnold representation theory with efficient attention mechanisms offers an effective framework for high-resolution agricultural remote sensing.