KAN-Matrix: Visualizing Nonlinear Pairwise and Multivariate Contributions for Physical Insight

TL;DR

This paper introduces KAN-Matrix, a set of visualization tools based on Kolmogorov-Arnold Networks that improve interpretability of complex, high-dimensional datasets by revealing nonlinear relationships and variable contributions.

Contribution

The paper presents novel PKAN and MKAN matrices that outperform traditional correlation methods in capturing nonlinear associations and feature importance for physical data analysis.

Findings

PKAN and MKAN outperform Pearson Correlation and Mutual Information.

They effectively reveal nonlinear relationships and variable contributions.

Tools support model explanation and physical insight discovery.

Abstract

Interpreting complex datasets remains a major challenge for scientists, particularly due to high dimensionality and collinearity among variables. We introduce a novel application of Kolmogorov-Arnold Networks (KANs) to enhance interpretability and parsimony beyond what traditional correlation analyses offer. We present two interpretable, color-coded visualization tools: the Pairwise KAN Matrix (PKAN) and the Multivariate KAN Contribution Matrix (MKAN). PKAN characterizes nonlinear associations between pairs of variables, while MKAN serves as a nonlinear feature-ranking tool that quantifies the relative contributions of inputs in predicting a target variable. These tools support pre-processing (e.g., feature selection, redundancy analysis) and post-processing (e.g., model explanation, physical insights) in model development workflows. Through experimental comparisons, we demonstrate that PKAN and MKAN yield more robust and informative results than Pearson Correlation and Mutual Information. By capturing the strength and functional forms of relationships, these matrices facilitate the discovery of hidden physical patterns and promote domain-informed model development.