Clifford Kolmogorov-Arnold Networks
This work addresses function approximation challenges in scientific discovery and engineering, but appears incremental as it builds on existing Kolmogorov-Arnold Networks with Clifford algebra extensions.
The paper tackles the problem of function approximation in Clifford algebra spaces by introducing Clifford Kolmogorov-Arnold Networks (ClKAN), which use Randomized Quasi Monte Carlo grid generation to address exponential scaling in higher dimensions and new batch normalization for variable domain inputs, achieving validation in synthetic and physics-inspired tasks.
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.