DGKAN:Dynamic-Grid Kolmogorov-Arnold Networks

We introduce DGKAN, a dynamic-grid Kolmogorov-Arnold Network that learns to redistribute a fixed number of grid points across the input domain. Existing KAN use uniformly spaced, predefined grids, implicitly assigning the same representational resolution to all regions. This allocation can be inefficient when function complexity and feature distributions are heterogeneous, motivating the problem of how to optimally allocate a limited grid budget across the domain. DGKAN addresses this problem through backward-guided grid adaptation: output-layer grids are relocated according to local prediction errors, while intermediate-layer grids adapt to the empirical distribution of latent features. To support non-uniform grids, we develop adaptive radial basis functions with grid-dependent bandwidths and selectively introduce variational Bayesian modeling into the Radial Basis Function (RBF) branch for localized shrinkage and uncertainty estimation. Experiments and ablation studies demonstrate the effectiveness of dynamic grid allocation, while generalization tests across diverse tasks validate the generality of DGKAN.