A Practitioner's Guide to Kolmogorov-Arnold Networks

2026-04-16 · Source: cs.AI updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences, Engineering & Applied Sciences · Depth: Expert, extended

Summary

This practitioner's guide provides a comprehensive overview of Kolmogorov-Arnold Networks (KANs), a promising alternative to traditional Multilayer Perceptrons (MLPs) for scientific machine learning. KANs utilize learnable univariate basis functions on edges, offering enhanced expressivity and interpretability compared to MLPs' fixed activation functions. The review systematically synthesizes KANs' theoretical foundations, architectural variants, and practical implementation strategies, categorizing advancements in accuracy, efficiency, and regularization. It details various basis functions like B-splines, Chebyshev, Jacobi, ReLU compositions, Gaussian RBFs, and Fourier series, analyzing their trade-offs. The guide also covers techniques such as physics-informed loss design, adaptive sampling, domain decomposition, and hybrid architectures, concluding with a "Choose-Your-KAN" guide and identifying research gaps. An associated GitHub repository complements the paper, serving as a structured reference for ongoing KAN research.

Key takeaway

For AI Engineers developing models for scientific computing or complex function approximation, KANs offer a powerful, configurable alternative to MLPs. You should carefully select your KAN's basis functions and architectural enhancements based on the problem's specific characteristics, such as function smoothness, periodicity, or presence of discontinuities. Prioritize GPU-friendly bases and parallelization for efficiency, and leverage physics-informed losses and adaptive sampling for accuracy, especially in PDE-driven tasks, to achieve superior performance and interpretability.

Key insights

KANs offer enhanced expressivity and interpretability over MLPs by using learnable univariate basis functions on network edges.

Principles

• Basis function choice critically influences KAN performance.
• KANs exhibit superior parameter efficiency compared to MLPs.
• Spectral bias is reduced in KANs, improving high-frequency learning.

Method

Implement KANs by selecting basis functions (e.g., B-splines, Chebyshev, Gaussian) based on target function properties, applying adaptive sampling, and using hybrid optimization strategies for improved accuracy and stability.

In practice

• Use cubic B-spline KANs as a robust default for general tasks.
• Employ `tanh` normalization for Chebyshev/Jacobi bases to stabilize training.
• Combine Adam with L-BFGS for stiff PDE problems to improve convergence.

Topics

• Kolmogorov-Arnold Networks
• Basis Functions
• Physics-Informed Learning
• Spectral Bias
• Parameter Efficiency

Code references

• AmirNoori68/kan-review
• yu-rp/KANbeFair
• afrah/pinn_learnable_activation
• mintisan/awesome-kan
• AntonioTepsich/Convolutional-KANs

Best for: AI Engineer, AI Scientist, Machine Learning Engineer, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.AI updates on arXiv.org.