# KAN: Kolmogorov-Arnold Networks

**Authors:** Ziming Liu, Yixuan Wang, Sachin Vaidya, Fabian Ruehle, James Halverson, Marin Soljačić, Thomas Y. Hou, Max Tegmark  
**arXiv:** [2404.19756](https://arxiv.org/abs/2404.19756)  
**Date:** 2024-04-30  
**Summary page:** https://www.summarizepaper.com/en/paper/2404.19756v5/

## Key points

- Kolmogorov-Arnold Networks (KANs) developed as an alternative to Multi-Layer Perceptrons (MLPs)
- KANs have learnable activation functions on edges, outperforming MLPs in accuracy and interpretability
- Faster neural scaling laws and easier visualization for human users
- Assist scientists in discovering mathematical and physical laws through examples in mathematics and physics
- Symbolic formulas can be automatically discovered by training KANs with different shapes
- Unsupervised learning mode of KANs uncovers additional relations in knot invariants
- Achieve better accuracy with fewer parameters compared to Deepmind's MLP architecture
- Potential for AI + Science tasks to be less computationally demanding, enabling new scientific discoveries even on personal laptops

## Summary

Researchers have developed Kolmogorov-Arnold Networks (KANs) as a promising alternative to Multi-Layer Perceptrons (MLPs), inspired by the Kolmogorov-Arnold representation theorem. Unlike MLPs, KANs have learnable activation functions on edges instead of fixed ones on nodes. This simple change allows KANs to outperform MLPs in terms of accuracy and interpretability. Additionally, KANs possess faster neural scaling laws and are more easily visualized and interacted with by human users. Through examples in mathematics and physics, researchers demonstrate how KANs can assist scientists in discovering or rediscovering mathematical and physical laws. By training KANs with different shapes, symbolic formulas can be automatically discovered, providing a balance between simplicity and accuracy. In the field of "AI for Math," KANs' unsupervised learning mode can also uncover additional relations in knot invariants. In comparison to Deepmind's MLP architecture, researchers find that KANs achieve better accuracy with fewer parameters in signature classification problems. This discovery highlights the potential for AI + Science tasks to be less computationally demanding than previously thought, opening up possibilities for new scientific discoveries even on personal laptops. Overall, this study showcases the capabilities of Kolmogorov-Arnold Networks as promising alternatives to Multi-Layer Perceptrons. They offer improved performance in accuracy and interpretability across various scientific domains.