# Smooth Kolmogorov Arnold networks enabling structural knowledge representation

arXiv: https://arxiv.org/abs/2405.11318 · HTML: https://mlsanity.com/paper/2405.11318/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 14 references that are in the map.
- First posted on arXiv 18 May 2024.

## Builds on (most cited first, 1 of 1)

- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)

## Built on by (most cited first, 22 of 22)

- [A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks](https://mlsanity.com/paper/2406.02917/) (2024)
- [A Survey on Kolmogorov-Arnold Network](https://mlsanity.com/paper/2411.06078/) (2024)
- [fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functions](https://mlsanity.com/paper/2406.07456/) (2024)
- [Exploring the Potential of Polynomial Basis Functions in Kolmogorov-Arnold Networks: A Comparative Study of Different Groups of Polynomials](https://mlsanity.com/paper/2406.02583/) (2024)
- [rKAN: Rational Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.14495/) (2024)
- [iKAN: Global Incremental Learning with KAN for Human Activity Recognition Across Heterogeneous Datasets](https://mlsanity.com/paper/2406.01646/) (2024)
- [SPIKANs: Separable Physics-Informed Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2411.06286/) (2024)
- [Surrogate Learning in Meta-Black-Box Optimization: A Preliminary Study](https://mlsanity.com/paper/2503.18060/) (2025)
- [Architectural Scaling Surpass Basis Complexity? Efficient KANs with Single-Parameter Design](https://mlsanity.com/paper/2410.14951/) (2024)
- [Inelastic Constitutive Kolmogorov-Arnold Networks: A generalized framework for automated discovery of interpretable inelastic material models](https://mlsanity.com/paper/2602.17750/) (2026)
- [FourierKAN outperforms MLP on Text Classification Head Fine-tuning](https://mlsanity.com/paper/2408.08803/) (2024)
- [KAN we improve on HEP classification tasks? Kolmogorov-Arnold Networks applied to an LHC physics example](https://mlsanity.com/paper/2408.02743/) (2024)
- [KAN v.s. MLP for Offline Reinforcement Learning](https://mlsanity.com/paper/2409.09653/) (2024)
- [Physics-informed KAN PointNet: Deep learning for simultaneous solutions to inverse problems in incompressible flow on numerous irregular geometries](https://mlsanity.com/paper/2504.06327/) (2025)
- [Kolmogorov Arnold Networks in Fraud Detection: Bridging the Gap Between Theory and Practice](https://mlsanity.com/paper/2408.10263/) (2024)
- [iTFKAN: Interpretable Time Series Forecasting with Kolmogorov-Arnold Network](https://mlsanity.com/paper/2504.16432/) (2025)
- [KAT to KANs: A Review of Kolmogorov-Arnold Networks and the Neural Leap Forward](https://mlsanity.com/paper/2411.10622/) (2024)
- [Flexible Swarm Learning May Outpace Foundation Models in Essential Tasks](https://mlsanity.com/paper/2510.06349/) (2025)
- [PO-CKAN:Physics Informed Deep Operator Kolmogorov Arnold Networks with Chunk Rational Structure](https://mlsanity.com/paper/2510.08795/) (2025)
- [HKAN: Hierarchical Kolmogorov-Arnold Network without Backpropagation](https://mlsanity.com/paper/2501.18199/) (2025)
- [Learning Fair Representations with Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2511.11767/) (2025)
- [KANs need curvature: penalties for compositional smoothness](https://mlsanity.com/paper/2605.02190/) (2026)

## Abstract (arXiv)

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.