kolmogorov-arnold-networks-guide

npx skills add brycewang-stanford/Auto-Empirical-Research-Skills --skill kolmogorov-arnold-networks-guide --agent claude-code

Same command for any agent — swap --agent for codex, cursor, copilot.

# 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)) Any multivariate continuous function = composition of univariate functions and addition ``` ## Key Papers ```bibtex @article{liu2024kan, title={KAN: Kolmogorov-Arnold Networks}, author={Liu, Ziming and Wang, Yixuan and Vaidya, Sachin and Ruehle, Fabian and Halverson, James and Solja{\v{c}}i{\'c}, Marin and Hou, Thomas Y. and Tegmark, Max}, journal={arXiv:2404.19756}, year={2024} } ``` ## Implementation ``