# PAKAN: Pixel Adaptive Kolmogorov-Arnold Network Modules for Pansharpening

arXiv: https://arxiv.org/abs/2603.15109 · HTML: https://mlsanity.com/paper/2603.15109/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 17 references that are in the map.
- First posted on arXiv 16 Mar 2026.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Pan-Mamba: Effective pan-sharpening with State Space Model](https://mlsanity.com/paper/2402.12192/) (2024)
- [A Multi-Scale and Multi-Depth Convolutional Neural Network for Remote Sensing Imagery Pan-Sharpening](https://mlsanity.com/paper/1712.09809/) (2017)
- [Pansharpening via Detail Injection Based Convolutional Neural Networks](https://mlsanity.com/paper/1806.08898/) (2018)
- [U2Net: A General Framework with Spatial-Spectral-Integrated Double U-Net for Image Fusion](https://mlsanity.com/paper/2212.06466/) (2022)

## Abstract (arXiv)

Pansharpening aims to fuse high-resolution spatial details from panchromatic images with the rich spectral information of multispectral images. Existing deep neural networks for this task typically rely on static activation functions, which limit their ability to dynamically model the complex, non-linear mappings required for optimal spatial-spectral fusion. While the recently introduced Kolmogorov-Arnold Network (KAN) utilizes learnable activation functions, traditional KANs lack dynamic adaptability during inference. To address this limitation, we propose a Pixel Adaptive Kolmogorov-Arnold Network framework. Starting from KAN, we design two adaptive variants: a 2D Adaptive KAN that generates spline summation weights across spatial dimensions and a 1D Adaptive KAN that generates them across spectral channels. These two components are then assembled into PAKAN 2to1 for feature fusion and PAKAN 1to1 for feature refinement. Extensive experiments demonstrate that our proposed modules significantly enhance network performance, proving the effectiveness and superiority of pixel-adaptive activation in pansharpening tasks.