A new type of neural network, called a Kolmogorov-Arnold network (KAN), can do almost everything a regular neural network can for a certain class of problems

A Kolmogorov-Arnold network ( KAN ) is based on a mathematical idea from the mid-20th century that has been rediscovered and reconfigured for deployment in the deep learning era.

KANs go about function fitting — connecting the dots of the network’s output — in a fundamentally different way than MLPs.

They’re also learnable, so they can be tweaked with far greater sensitivity than the simple numerical weights.

The Kolmogorov-Arnold theorem essentially provides a blueprint for such a structure.

The KAN can approximate smooth functions with smooth functions.

The biggest advantage that KANs hold over other forms of neural networks lies in their interpretability.

With each one, the network is able to align with a more complicated output function.

A paper by Yizheng Wang of Tsinghua University and others that appeared online in June showed that their neural network “significantly outperforms” MLPs for solving partial differential equations.

Liu and Tegmark ’s KAN paper quickly caused a stir, garnering 75 citations within about three months .

Liu is striving to make KANs more practical and easier to use.