The paper explores the relevance of smoothness in Kolmogorov-Arnold Networks (KANs) and proposes that smooth, structurally informed KANs can achieve equivalence to multi-layer perceptrons (MLPs) in specific function classes. While KANs offer an efficient and interpretable alternative to MLPs due to their finite network topology, the representation of generic smooth functions by KANs using analytic functions constrained to a finite number of cutoff points is not exact, limiting their convergence during training. The authors discuss the role of smoothness in the representation of generic functions using finite networks of nested smooth functions and its consequences for generalized KANs. They argue that leveraging inherent structural knowledge can reduce the data required for training and mitigate the risk of generating hallucinated predictions, enhancing model reliability and performance in computational biomedicine. The paper also presents experimental results demonstrating the effectiveness of structured, smooth KANs in various applications, including chemical engineering and bioinformatics.The paper explores the relevance of smoothness in Kolmogorov-Arnold Networks (KANs) and proposes that smooth, structurally informed KANs can achieve equivalence to multi-layer perceptrons (MLPs) in specific function classes. While KANs offer an efficient and interpretable alternative to MLPs due to their finite network topology, the representation of generic smooth functions by KANs using analytic functions constrained to a finite number of cutoff points is not exact, limiting their convergence during training. The authors discuss the role of smoothness in the representation of generic functions using finite networks of nested smooth functions and its consequences for generalized KANs. They argue that leveraging inherent structural knowledge can reduce the data required for training and mitigate the risk of generating hallucinated predictions, enhancing model reliability and performance in computational biomedicine. The paper also presents experimental results demonstrating the effectiveness of structured, smooth KANs in various applications, including chemical engineering and bioinformatics.