Kolmogorov–Arnold network

A neural networkneural network, n.: A kind of computer program that learns a task from examples by tuning thousands to billions of connections between simple number-crunching units, an arrangement loosely inspired by nerve cells in the brain. architecture inspired by the Kolmogorov–Arnold representation theorem, which states that any continuous function of several variables on a closed, bounded domain (such as the unit cube) can be written using only addition and compositions of continuous functions of one variable. Its learnable parts sit in a different place from a multilayer perceptronmultilayer perceptron, n.: A neural network made of several layers of artificial neurons, each connected to every neuron in the next layer. It is the simplest kind of deep network and a component of almost every modern model.'s: instead of learned linear weights on the connections and a fixed activation functionactivation function, n.: The simple rule each artificial neuron applies to its total input to decide its output, such as 'keep positive values, turn negatives into zero'. Without it, a deep network would be no smarter than a single layer. at each unit, every connection applies its own learned one-variable function, usually a B-spline plus a simple base function, and each unit just adds up what arrives. Its authors reported that small KANs could match much larger MLPs on function fitting and on solving partial differential equations, with better scaling in these settings, and that trained KANs can be pruned and converted into symbolic formulas, aiding scientific discovery. Follow-up studies found that at matched parameters or compute KANs mostly trail MLPs outside symbolic and low-dimensional scientific tasks, and spline evaluation makes them slow on GPUs; their value remains debated.

After pruning, the KAN's learned edge functions matched a sine and a square almost exactly.