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.

研究使用具有固定网络拓扑结构的 Kolmogorov-Arnold 网络（KAN）作为传统多层感知器（MLP）架构的高效可解释替代方法，探讨了 KAN 中平滑性的相关性，并提出了在特定函数类中，具有平滑且结构知情的 KAN 可以达到与 MLP 相等的效果，从而减少训练所需的数据，并降低生成虚假预测的风险，从而提高计算生物医学模型的可靠性和性能。