Smooth Kolmogorov Arnold networks enabling structural knowledge representation
This work addresses the problem of improving model reliability and performance in computational biomedicine, but it appears incremental as it builds on existing KAN frameworks with a focus on smoothness and structural knowledge.
The paper tackles the limitation of Kolmogorov-Arnold Networks (KANs) in representing smooth functions exactly, proposing that smooth, structurally informed KANs can achieve equivalence to MLPs in specific function classes, potentially reducing training data and mitigating hallucinated predictions in computational biomedicine.
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.