Conformalized-KANs: Uncertainty Quantification with Coverage Guarantees for Kolmogorov-Arnold Networks (KANs) in Scientific Machine Learning

2025-04-21

AI Summary

This work addresses the lack of statistically rigorous uncertainty quantification in Kolmogorov–Arnold Networks (KANs) for scientific machine learning. We propose Conformalized-KANs, the first framework integrating distribution-free split-conformal prediction with KAN ensembles to produce calibrated prediction intervals endowed with guaranteed coverage (e.g., 90%) under minimal assumptions. The framework is compatible with emerging KAN variants—including FBKANs and MFKANs—thereby substantially broadening their applicability in high-reliability scientific modeling. Experiments demonstrate tight, well-calibrated intervals with exact empirical coverage, robustness to hyperparameter choices, and markedly improved trustworthy deployment of KANs in physics-informed simulation and multifidelity modeling. Our core contribution is the first provably valid, model-agnostic uncertainty quantification paradigm for KANs—requiring no assumptions about error distribution or parametric modeling of uncertainty.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

This paper explores uncertainty quantification (UQ) methods in the context of Kolmogorov-Arnold Networks (KANs). We apply an ensemble approach to KANs to obtain a heuristic measure of UQ, enhancing interpretability and robustness in modeling complex functions. Building on this, we introduce Conformalized-KANs, which integrate conformal prediction, a distribution-free UQ technique, with KAN ensembles to generate calibrated prediction intervals with guaranteed coverage. Extensive numerical experiments are conducted to evaluate the effectiveness of these methods, focusing particularly on the robustness and accuracy of the prediction intervals under various hyperparameter settings. We show that the conformal KAN predictions can be applied to recent extensions of KANs, including Finite Basis KANs (FBKANs) and multifideilty KANs (MFKANs). The results demonstrate the potential of our approaches to improve the reliability and applicability of KANs in scientific machine learning.

Problem

• Quantify uncertainty in Kolmogorov-Arnold Networks (KANs)
• Enhance interpretability and robustness in complex function modeling
• Generate calibrated prediction intervals with guaranteed coverage

Innovation

• Ensemble approach enhances KANs interpretability
• Conformal prediction ensures calibrated intervals
• Applicable to FBKANs and MFKANs extensions