Kolmogorov-Arnold Networks (KANs) offer an efficient and interpretable alternative to traditional multi-layer perceptrons (MLPs) 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. 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. The Kolmogorov-Arnold representation theorem guarantees that finite KANs with a priori defined topology can represent all functions. However, the loss of smoothness of the univariate nonlinear functions, even if the overall functions f to be represented are smooth, prohibits efficient implementations. Recent results show that deep KAN topologies reduce the numerical challenges arising from the loss of smoothness, paving the way for efficient and interpretable alternatives to MLPs. However, the interference of smoothness and the representation of generic functions by finite, a priori defined networks may be essential for efficient training rates. Smoothness and finite nested functions are crucial for the representation of generic functions. Vitushkin proved that even analytic functions cannot be represented by KANs using differentiable node functions. The smoothness of the node functions is restricted by the upper bound, resulting in a loss of smoothness. If the smoothness of the inner nodes does not satisfy the Vitushkin conditions, the equivalence to universal MLPs is no longer guaranteed. Representing even smooth high-dimensional functions using low-dimensional node functions requires the implementation of highly irregular node functions, reducing convergence rates of training. The local representation of a function by KAN with a given, finite KAN structure requires reproducibility of any derivatives of f by the respective derivatives of the KAN. The p-th derivative of any u_j at a fixed point can be given as a function depending on the values of {u^(0), ..., u^(p)} and the linear parameters. The dimension of the vector space of the local p-th derivatives is limited by N_p for all combinations of partial derivatives. As the number of combinations of p-th derivatives grows with O(p^{n-1}), for n ≥ 3, the number of combinations has the lower bound. Hence, for each KAN with fixed topology, the KAN cannot represent all possible p-th local derivatives if the number of combinations exceeds N_p. In conclusion, deep KAN architectures may provide a promising route towards interpretable and efficient implementations of representations of high-dimensional functions. However, the role of smoothness should be taken into account because of the specific, non-intuitive interaction between networkKolmogorov-Arnold Networks (KANs) offer an efficient and interpretable alternative to traditional multi-layer perceptrons (MLPs) 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. 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. The Kolmogorov-Arnold representation theorem guarantees that finite KANs with a priori defined topology can represent all functions. However, the loss of smoothness of the univariate nonlinear functions, even if the overall functions f to be represented are smooth, prohibits efficient implementations. Recent results show that deep KAN topologies reduce the numerical challenges arising from the loss of smoothness, paving the way for efficient and interpretable alternatives to MLPs. However, the interference of smoothness and the representation of generic functions by finite, a priori defined networks may be essential for efficient training rates. Smoothness and finite nested functions are crucial for the representation of generic functions. Vitushkin proved that even analytic functions cannot be represented by KANs using differentiable node functions. The smoothness of the node functions is restricted by the upper bound, resulting in a loss of smoothness. If the smoothness of the inner nodes does not satisfy the Vitushkin conditions, the equivalence to universal MLPs is no longer guaranteed. Representing even smooth high-dimensional functions using low-dimensional node functions requires the implementation of highly irregular node functions, reducing convergence rates of training. The local representation of a function by KAN with a given, finite KAN structure requires reproducibility of any derivatives of f by the respective derivatives of the KAN. The p-th derivative of any u_j at a fixed point can be given as a function depending on the values of {u^(0), ..., u^(p)} and the linear parameters. The dimension of the vector space of the local p-th derivatives is limited by N_p for all combinations of partial derivatives. As the number of combinations of p-th derivatives grows with O(p^{n-1}), for n ≥ 3, the number of combinations has the lower bound. Hence, for each KAN with fixed topology, the KAN cannot represent all possible p-th local derivatives if the number of combinations exceeds N_p. In conclusion, deep KAN architectures may provide a promising route towards interpretable and efficient implementations of representations of high-dimensional functions. However, the role of smoothness should be taken into account because of the specific, non-intuitive interaction between network