Interpretable and Efficient Diffusion Model for Complex Data Reconstruction

Abstract

This work aimsto present an experimental-computational approach designed to evaluate the performance of the Kolmogorov-Arnold Network Splines (KANS) architecture, capable of reconstructing complex data while preserving model interpretability. This networkis based on the Kolmogorov–Arnold representation theorem, which allows the decomposition of multivariate functions into compositions of univariate functions modeled through adaptive splines. A KAN was implemented using Python/PyTorch, and its performance was evaluated in comparison to multilayer perceptrons (MLPs) in tasks involving noise removal and reconstruction of the synthetic Swiss Roll dataset. The resultsshow that KANS outperform MLPs in terms of accuracy , computational efficiency , and the number of required parameters. In addition, KANS demonstrate greater generalization capabilities and superior explainability by enabling the identification of critical data points through the learned splines. It is concludedthat the KANS architecture offers anefficient and interpretable alternative in contexts where data is limited and decision-making transparency is essential, such as in clinical or engineering applications. Finally, future research directions are proposed, including integration with attention mechanisms and validation in real-world high-dimensional environments.