# 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/2404.19756v1/

## Key points

- Kolmogorov-Arnold Networks (KANs) are innovative alternatives to traditional Multi-Layer Perceptrons (MLPs)
- KANs feature learnable activation functions on edges for enhanced accuracy and interpretability
- In mathematics, KANs have demonstrated the ability to rediscover known relations in an unsupervised mode
- KANs show promise in physics applications such as Anderson localization
- KANs aid in identifying models with mobility edges and contribute to resolving debates on localization in interacting systems
- A new paradigm of "AI for Math" is proposed using KANs' unsupervised learning mode to discover additional relations beyond knot invariants
- Through experimentation, it is evident that KANs offer a valuable tool for exploring complex mathematical relationships and advancing research in both mathematics and physics.

## Summary

Kolmogorov-Arnold Networks (KANs) are innovative alternatives to traditional Multi-Layer Perceptrons (MLPs), featuring learnable activation functions on edges for enhanced accuracy and interpretability. In mathematics, KANs have demonstrated the ability to rediscover known relations in an unsupervised mode, highlighting their reliability. They also show promise in physics applications such as Anderson localization, aiding in identifying models with mobility edges and contributing to resolving debates on localization in interacting systems. A new paradigm of "AI for Math" is proposed using KANs' unsupervised learning mode to discover additional relations beyond knot invariants. Through experimentation, it is evident that KANs offer a valuable tool for exploring complex mathematical relationships and advancing research in both mathematics and physics.