Deformable Kolmogorov-Arnold Networks for Medical Image Segmentation

Medical image segmentation remains difficult when boundaries are faint and anatomy varies across modalities. U-Net variants replace the bottleneck with a transformer, an MLP, a state-space model, or a Kolmogorov-Arnold network (KAN). These variants still evaluate that operator on the encoder's fixed, downsampled grid. We present UKAD, a deformable KAN encoder-decoder. Its Kolmogorov-Arnold Displacement (KAD) bottleneck predicts a content-adaptive grid, resamples the bottleneck features on that grid, and then applies a learnable activation. That activation is a low-degree group-rational function, and we share it within each channel group, so its parameter count does not grow with network width. UKAD also uses it in the skip gates and in a hybrid decoder. We train UKAD in one stage, without pretraining or distillation, and with one hyperparameter setting across datasets, resolutions, and widths. We retrain fourteen U-Net, MLP, state-space, and KAN baselines on four public datasets under one protocol. UKAD-L has the highest mean IoU and Dice, 83.11 and 90.25. AdaKAN reaches 82.36 and 89.78, and Rolling-UNet reaches 82.25 mean IoU. UKAD-B reaches 82.59 mean IoU with 45% fewer parameters than AdaKAN. We release the code at https://anonymous.4open.science/r/UKAD.