Kolmogorov GAM Networks Are All You Need!

Area of Science:

• Artificial Intelligence
• Machine Learning
• Deep Learning

Background:

• Kolmogorov GAM (K-GAM) networks are efficient architectures for training and inference.
• They offer an alternative to Transformer architectures in machine learning.
• K-GAMs are based on Kolmogorov's superposition theorem (KST), providing efficient multivariate function representation.

Purpose of the Study:

• To interpret KST-based representations in a machine learning context for AI applications.
• To present a novel K-GAM architecture as an alternative to Transformers.
• To demonstrate a computationally attractive and parameter-efficient learning procedure.

Main Methods:

• Developed a K-GAM architecture equivalent to a topological embedding and a generalized additive model (GAM) layer.
• Utilized KST for efficient representation of multivariate functions.
• Applied the methodology to the iris dataset for illustration.

Main Results:

• The K-GAM architecture provides a class of learning procedures with significantly fewer parameters than deep learning algorithms.
• The additive model with non-linear embedding serves as a statistical alternative to Transformer architectures (kernel smoothers).
• The proposed algorithms are parallelizable and computationally attractive.

Conclusions:

• Additive KAN models present a natural and efficient alternative to Transformer architectures.
• The K-GAM approach offers a promising direction for future research in AI and machine learning.
• This methodology enables efficient encoding of dictionaries and function approximation.