Dynamic 3D KAN Convolution with Adaptive Grid Optimization for Hyperspectral Image Classification

Abstract: Deep neural networks face several challenges in hyperspectral image classification, including high-dimensional data, sparse distribution of ground objects, and spectral redundancy, which often lead to classification overfitting and limited generalization capability. To more efficiently adapt to ground object distributions while extracting image features without introducing excessive parameters and skipping redundant information, this paper proposes KANet based on an improved 3D-DenseNet model, consisting of 3D KAN Conv and an adaptive grid update mechanism. By introducing learnable univariate B-spline functions on network edges, specifically by flattening three-dimensional neighborhoods into vectors and applying B-spline-parameterized nonlinear activation functions to replace the fixed linear weights of traditional 3D convolutional kernels, we precisely capture complex spectral-spatial nonlinear relationships in hyperspectral data. Simultaneously, through a dynamic grid adjustment mechanism, we adaptively update the grid point positions of B-splines based on the statistical characteristics of input data, optimizing the resolution of spline functions to match the non-uniform distribution of spectral features, significantly improving the model's accuracy in high-dimensional data modeling and parameter efficiency, effectively alleviating the curse of dimensionality. This characteristic demonstrates superior neural scaling laws compared to traditional convolutional neural networks and reduces overfitting risks in small-sample and high-noise scenarios. KANet enhances model representation capability through a 3D dynamic expert convolution system without increasing network depth or width. The proposed method demonstrates superior performance on IN, UP, and KSC datasets, outperforming mainstream hyperspectral image classification approaches.