Building and Visualising Kolmogorov–Arnold Networks

Kolmogorov–Arnold Networks (KANs) are a neural network architecture that replaces the scalar weights of traditional networks with learnable univariate functions on the connections between nodes. This design is inspired by the Kolmogorov–Arnold representation theorem, which allows complex multivariate functions to be constructed from simpler one-dimensional functions. The process of building a KAN is demonstrated, starting with simple quadratic functions and progressing to more flexible B-splines and Chebyshev polynomials. The network's effectiveness is explored by attempting to model and recover the Lorenz Equations from synthetic data, highlighting the potential for KANs to not just predict but also reveal underlying mathematical structures.