Kolmogorov-Arnold Networks

Kolmogorov-Arnold Networks replace fixed scalar weights and activations with learnable one-dimensional functions on network edges, commonly represented by splines, radial basis functions, or polynomials. Researchers develop new bases and architectures, combine KANs with convolution, attention, or recurrent components, and use physics-informed and weak-form training for scientific problems such as partial differential equations. The functional structure can make learned relationships easier to inspect and supports applications in forecasting, vision, and scientific modeling, alongside theoretical work on approximation and generalization. A central tension is that expressive edge functions can be costly to evaluate, and theoretical universality does not guarantee better accuracy or efficiency than MLPs; performance depends on target structure, basis choice, and deployment hardware.