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Evaluating Kolmogorov–Arnold Networks for Scientific Discovery: A Simple Yet Effective Approach
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Version 1
: Received: 14 August 2024 / Approved: 15 August 2024 / Online: 19 August 2024 (18:13:54 CEST)
How to cite: Sun, J. Evaluating Kolmogorov–Arnold Networks for Scientific Discovery: A Simple Yet Effective Approach. Preprints 2024, 2024081184. https://doi.org/10.20944/preprints202408.1184.v1 Sun, J. Evaluating Kolmogorov–Arnold Networks for Scientific Discovery: A Simple Yet Effective Approach. Preprints 2024, 2024081184. https://doi.org/10.20944/preprints202408.1184.v1
Abstract
Kolmogorov–Arnold Network (KAN) is an emerging interpretable neural network compared to fully black-box MLPs. Recently, emerging works focus on comprehensive and fair comparisons between KAN and MLP in various tasks. However, these works didn't focus on the strongest advantage of KAN: generating symbolic outputs. The ability of KAN to provide scientific insights or even discover new science is under-examined. In this work, we propose several novel metrics to measure how well a KAN performs on symbolic function fitting: R^2-Mean, weighted R^2-complexity loss, and ranking metrics. We also propose a metric to determine mathematical complexity of a target function and evaluate KAN with several functions of different mathematical complexity. Additionally, we also tried inputs with different ranges to find the effect of normalization.
Keywords
Machine Learning; Neural Networks; Interpretable AI; AI4Science
Subject
Computer Science and Mathematics, Artificial Intelligence and Machine Learning
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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