Can Kolmogorov–Arnold Networks (KAN) beat MLPs?

Lately, it seems that the entire AI community has become about one and one thing only, LLMs. They are cool in their own way, but they are not the entire AI field. In all the LLMs and AI agent hype a paper like Kolmogorov–Arnold Networks is a breath of fresh air. This paper seems quite groundbreaking and might completely change the field. Rarely do we see papers challenging the fundamentals of AI, but this one seems to do it.

MLPs or Multi-layer perceptrons sit at the very bottom of AI architectures. Dense layer (MLPs) is part of almost every Deep learning architecture. This paper directly challenges that foundation. Not only does it challenge the MLPs but also the black box nature of these models. So, in today’s blog, we are going to review this brand-new research paper.

Note: This is going to be quite math heavy article. Since this is fundamental research, it is important to understand the underlying maths of it.

Photo by Daniele Levis Pelusi on Unsplash

Introduction

KAN: Kolmogorov-Arnold Networks introduces a new type of neural network architecture based on the Kolmogorov-Arnold representation theorem, presenting a promising alternative to traditional multi-layer perceptrons (MLPs).

According to the KAN paper:

While MLPs have fixed activation functions on nodes (“neurons”), KANs have learnable activation functions on edges (“weights”). KANs have no linear weights at all — every weight parameter is replaced by a univariate function parametrized as a spline. We show that this seemingly simple change makes KANs outperform MLPs in terms of accuracy and interpretability. In summary, KANs are promising alternatives for MLPs, opening opportunities for further improving today’s deep learning models which rely heavily on MLPs.

According to the paper, much smaller KANs are comparable to or better than much larger MLPs in data fitting and PDE solving. Supposedly KANs possess faster neural scaling laws than MLPs. KANs can be intuitively visualized and can easily interact with human users, thus greatly enhancing interpretability.