Kolmogorov-Arnold Networks (KAN) Guide

Overview

Kolmogorov-Arnold Networks (KANs) are a novel neural network architecture that places learnable activation functions on edges (weights) instead of fixed activations on nodes. Based on the Kolmogorov-Arnold representation theorem, KANs use B-spline functions as learnable edge activations, achieving better accuracy and interpretability than MLPs with fewer parameters in certain domains. This collection tracks the rapidly growing KAN literature.

Core Concept

Traditional MLP:
  x → [fixed activation(linear transform)] → y
  Activations on nodes, weights on edges

KAN:
  x → [learnable spline functions on edges] → sum → y
  Each edge learns its own activation function (B-spline)

Kolmogorov-Arnold Theorem:
  f(x₁,...,xₙ) = Σ Φᵢ(Σ φᵢⱼ(xⱼ))