Neural networks have become a fundamental tool for solving complex problems, from image processing and speech recognition to time series prediction and large-scale data classification. However, traditional neural architectures suffer from interpretability problems due to their opaque representations and lack of explicit interaction between linear and nonlinear transformations. To address these limitations, Kolmogorov–Arnold Networks (KAN) have emerged as a mathematically grounded approach capable of efficiently representing complex nonlinear functions. Based on the principles established by Kolmogorov and Arnold, KAN offer an alternative to traditional architectures, mitigating issues such as overfitting and lack of interpretability. Despite their solid theoretical basis, practical implementations of KAN face challenges, such as optimal function selection and computational efficiency. This paper provides a systematic review that goes beyond previous surveys by consolidating the diverse structural variants of KAN (e.g., Wavelet-KAN, Rational-KAN, MonoKAN, Physics-KAN, Linear Spline KAN, and Orthogonal Polynomial KAN) into a unified framework. In addition, we emphasize their mathematical foundations, compare their advantages and limitations, and discuss their applicability across domains. From this review, three main conclusions can be drawn: (i) spline-based KAN remain the most widely used due to their stability and simplicity, (ii) rational and wavelet-based variants provide greater expressivity but introduce numerical challenges, and (iii) emerging approaches such as Physics-KAN and automatic basis selection open promising directions for scalability and interpretability. These insights provide a benchmark for future research and practical implementations of KAN.

Distributed denial-of-service (DDoS) attacks have become a critical threat to Internet of Things (IoT) infrastructures due to their high traffic dynamics, strong class imbalance, and strict resource constraints at the edge. This paper proposes ChebyKANRes, a lightweight intrusion detection model that combines Chebyshev polynomial expansions to parameterize learnable univariate transformations, a gate mechanism to modulate feature flow, and residual connections to stabilize optimization in deeper KAN-style stacks. Experiments were conducted on the CICIoT2023 dataset focusing on benign traffic and 12 DDoS subtypes, using a reproducible pipeline with stratified splitting, cross-validation (k = 5), and early stopping. The proposed model consistently improves multi-class performance (Accuracy: 0.9983) over an optimized MLP baseline (Accuracy: 0.9641), while maintaining a compact size suitable for edge deployment (≈123 k parameters; ~0.47 MB). Within CICIoT2023 and the evaluated split/training protocol, the proposed ChebyKANRes configuration shows improved imbalance-robust multiclass detection while maintaining a compact model size and comparable batch inference time.

This work aimsto present an experimental-computational approach designed to evaluate the performance of the Kolmogorov-Arnold Network Splines (KANS) architecture, capable of reconstructing complex data while preserving model interpretability. This networkis based on the Kolmogorov–Arnold representation theorem, which allows the decomposition of multivariate functions into compositions of univariate functions modeled through adaptive splines. A KAN was implemented using Python/PyTorch, and its performance was evaluated in comparison to multilayer perceptrons (MLPs) in tasks involving noise removal and reconstruction of the synthetic Swiss Roll dataset. The resultsshow that KANS outperform MLPs in terms of accuracy , computational efficiency , and the number of required parameters. In addition, KANS demonstrate greater generalization capabilities and superior explainability by enabling the identification of critical data points through the learned splines. It is concludedthat the KANS architecture offers anefficient and interpretable alternative in contexts where data is limited and decision-making transparency is essential, such as in clinical or engineering applications. Finally, future research directions are proposed, including integration with attention mechanisms and validation in real-world high-dimensional environments.