  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.
