Kolmogorov-Arnold Networks (KANs) offer an efficient and interpretable alternative to traditional multi-layer perceptron (MLP) architectures due to their finite network topology. However, according to the results of Kolmogorov and Vitushkin, the representation of generic smooth functions by KAN implementations using analytic functions constrained to a finite number of cutoff points cannot be exact. Hence, the convergence of KAN throughout the training process may be limited. This paper explores the relevance of smoothness in KANs, proposing that smooth, structurally informed KANs can achieve equivalence to MLPs in specific function classes. By leveraging inherent structural knowledge, KANs may reduce the data required for training and mitigate the risk of generating hallucinated predictions, thereby enhancing model reliability and performance in computational biomedicine.

翻译：Kolmogorov-Arnold网络（KANs）凭借其有限的网络拓扑结构，为传统的多层感知机（MLP）架构提供了一种高效且可解释的替代方案。然而，根据Kolmogorov和Vitushkin的研究结果，使用解析函数并在有限个截断点处受约束的KAN实现无法精确表示一般的平滑函数。因此，KAN在整个训练过程中的收敛性可能受限。本文探讨了光滑性在KAN中的相关性，提出光滑的、具有结构先验知识的KAN能够在特定函数类中达到与MLP的等价性。通过利用内在的结构知识，KAN可以减少训练所需的数据量，并降低产生幻觉预测的风险，从而在计算生物医学领域提升模型的可靠性与性能。