Clifford Kolmogorov-Arnold Networks

TL;DR

ClKAN is a novel neural network architecture designed for efficient function approximation in high-dimensional Clifford algebra spaces, utilizing randomized grid generation and new normalization strategies, with applications in scientific and engineering tasks.

Contribution

The paper introduces ClKAN, a new architecture that addresses exponential scaling in high-dimensional Clifford algebras using randomized grid methods and innovative normalization techniques.

Findings

Effective in synthetic and physics-inspired tasks

Handles high-dimensional Clifford algebra spaces efficiently

Introduces new batch normalization strategies

Abstract

We introduce Clifford Kolmogorov-Arnold Network (ClKAN), a flexible and efficient architecture for function approximation in arbitrary Clifford algebra spaces. We propose the use of Randomized Quasi Monte Carlo grid generation as a solution to the exponential scaling associated with higher dimensional algebras. Our ClKAN also introduces new batch normalization strategies to deal with variable domain input. ClKAN finds application in scientific discovery and engineering, and is validated in synthetic and physics inspired tasks.