Unpacking Kolmogorov-Arnold Networks

Author(s): Shenggang Li

Originally published on Towards AI.

Edge-Based Activation: Exploring the Mathematical Foundations and Practical Implications of KANs
Photo by JJ Ying on Unsplash

Researchers at MIT recently introduced a new neural network architecture called Kolmogorov-Arnold Networks (KANs). Unlike traditional neural networks that use activation functions at the nodes, KANs place these functions along the connections between nodes. This method is based on the Kolmogorov-Arnold representation theorem which decomposes a complex multivariate function into sequences of simpler univariate functions connected by binary operations. As a result, the Kolmogorov-Arnold representation can express any complex ‘shape’ using a series of simpler, countable ‘shapes’:

Decomposing Complexity: Summation of Basic Shapes

In this post, I will illustrate the innovative structure of Kolmogorov-Arnold Networks (KANs) through clear examples and straightforward insights, aiming to make these advanced concepts understandable and accessible to a broader audience.

The Kolmogorov-Arnold Representation introduces a concept within a mathematical framework: any complex pattern can be decomposed into simpler elements. These basic components are universal, similar to mosaic tiles that remain constant regardless of the specific scene they represent.

Kolmogorov-Arnold Networks (KANs) are based on the profound principles of the Kolmogorov-Arnold representation theorem, which states that any multivariate continuous function can be decomposed into a series of univariate functions. This implies that if f is a multivariate continuous function:

, there exists a series of univariate… Read the full blog for free on Medium.

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Published via Towards AI