---
title: "Yale and Hong Kong Baptist Researchers Finally Bring Order to the KAN Chaos"
subtitle: "A new review maps the sprawling Kolmogorov-Arnold Network ecosystem, offering theory, basis-function trade-offs, and a decision guide for picking the right variant."
url: "https://alphasignal.ai/news/yale-and-hong-kong-baptist-researchers-finally-bring-order-to-the-kan-chaos"
author: "AlphaSignal Newsroom"
author_url: "https://alphasignal.ai/editorial-team"
company: "AlphaSignal"
company_url: "https://alphasignal.ai/company/alphasignal"
published: "2026-04-15T00:00:00.000Z"
updated: "2026-08-23T23:19:51.870Z"
type: "Paper"
topics:
  - "Llms"
  - "Development"
subtopics:
  - "Small Models"
  - "Structured Output"
upvotes: 2564
source_url: "https://arxiv.org/abs/2510.25781"
comments: 0
truncated: true
---

# Yale and Hong Kong Baptist Researchers Finally Bring Order to the KAN Chaos

> A new review maps the sprawling Kolmogorov-Arnold Network ecosystem, offering theory, basis-function trade-offs, and a decision guide for picking the right variant.

The last two years have seen an explosion of Kolmogorov-Arnold Network (KAN) variants, each claiming to beat multilayer perceptrons on some task. A new review from researchers at Hong Kong Baptist University, Yale, and Universidad de Sevilla tries to bring order to that chaos, cataloguing the theory, the basis functions, and the practical tricks that actually move the needle. It also ships with a [companion repository](https://github.com/AmirNoori68/kan-review) that tracks the ecosystem.

## Too many KANs, too little guidance

KANs were introduced as a structured alternative to MLPs. Instead of applying a fixed activation at each node, they place learnable univariate functions along the edges of the network and sum them at the nodes. That switch from **mix-then-activate** to **activate-then-mix** gives you more interpretable, adaptable mappings, and it echoes the structure of the Kolmogorov superposition theorem, which says any continuous multivariate function can be written as sums of univariate functions.

[The paper](https://arxiv.org/abs/2510.25781) documents dozens of KAN variants with wildly different bases (B-splines, Chebyshev, Fourier, wavelets, Gaussians, Sinc, Jacobi, ReLU compositions, rational functions) and even more inconsistent benchmarks. [Fair comparisons](https://github.com/yu-rp/KANbeFair) often reach contradictory conclusions because the optimal basis depends heavily on the PDE or function being fit. The review argues KANs are best understood as a

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## Sources

- [A Practitioner's Guide to Kolmogorov-Arnold Networks](https://arxiv.org/abs/2510.25781)
- [kan-review GitHub repository](https://github.com/AmirNoori68/kan-review)
- [KAN: Kolmogorov-Arnold Networks (original paper repository)](https://github.com/KindXiaoming/pykan)
- [KANbeFair: Fair comparison of KANs and MLPs](https://github.com/yu-rp/KANbeFair)