Kolmogorov-Arnold Classifier Systems

Abstract

Learning Classifier Systems (LCS), a family of evolutionary rule-based machine learning, are highly effective for complex function approximation problems. Based on the divide-and-conquer principle, they work by dividing the problem space into multiple subspaces and constructing local models (rules) optimized for each subspace. However, conventional LCS face a significant challenge: rule optimization becomes exceedingly difficult as the dimensionality of the problem increases. To address this challenge, this paper proposes a novel LCS based on the Kolmogorov-Arnold representation theorem, named KACS (Kolmogorov-Arnold Classifier System). This approach leverages the theorem to decompose a single n-dimensional problem into multiple 1-dimensional problems with theoretical rigor. It then constructs specialized rule sets for each 1-dimensional subproblem using evolutionary algorithms and gradient-based methods, thereby significantly reducing the difficulty of rule optimization. Evaluation experiments on benchmark functions and real-world datasets demonstrate that the proposed method significantly outperforms the conventional method (XCSF), which directly constructs n-dimensional rule sets. KACS showed a statistically significant advantage across all evaluated metrics: prediction accuracy (absolute error), model complexity (number of parameters), and the Akaike Information Criterion (combination of accuracy and complexity).