# How Resilient Are Kolmogorov-Arnold Networks in Classification Tasks? A Robustness Investigation
## 1 Introduction
This discovery paved the way for a plethora of subsequent research focusing on designing attack methods against image recognition systems [42]. Furthermore, recent research has highlighted the susceptibility of KANs to noise. For instance, [PERSON] [43] pointed out their vulnerability to noise interference, which can significantly degrade  
Figure 1: Application domains timeline of Kolmogorov–Arnold Networks (KANs). performance. Similarly, [PERSON] et al. [44] demonstrated that KANs show reduced effectiveness when dealing with functions that include noise. More recently, [PERSON] et al. [45] compared KANs with MLPs on irregular or noisy functions, categorizing these functions into six types of categories, thus emphasizing the need for robust advancements. This paper aims to bridge this gap by validating KANs for classification tasks using various KAN architectures and traffic sign datasets and evaluating their accuracy and success attack rates against adversarial attacks. The findings underscore that while KANs present promising results, they may not consistently outperform MLPs in highly complex scenarios. Nevertheless, KANs continue to evolve, with ongoing research exploring the application of KANs underscoring the need for further research to optimize their capabilities and comprehend their behavior in adversarial and practical settings. The main contributions of our work can be summarized as follows:  
* It provides a comprehensive timeline of KAN developments, highlighting key applications and tracing the evolution of function bases and activation functions. * It conducts an in-depth analysis of KAN-based models for classification tasks, including KAN, KAN-Mixer, KANConv_KAN, and KANConv_MLP, comparing their performance against MLP and Small MLP-Mixer, as well as ConvNet_MLP models across multiple datasets (BTSD, CTSD, and GTSRB). This evaluation highlights KAN architectures' strengths and weaknesses in handling adversarial attacks at various perturbation levels. * We explore the effectiveness of adversarial defenses such as adversarial training and randomized smoothing training scenarios in strengthening the resilience of KAN models to adversarial attacks. The rest of the paper is structured as follows: Section 2, Materials and Methods, begins with the Kolmogorov-Arnold representation theorem, which serves as the theoretical foundation for KANs and the design and implementation of KANs into neural networks as well as their application in specific architectures like convolutional KAN and KAN-Mixer. Section 3 covers adversarial attacks and outlines the adversarial defense strategy. Section 4, Methodology, includes information on the datasets used; comparisons between KAN, MLP models, and KAN-based architectures like KAN-Mixer and convolutional KANs; and adversarial attack methods employed, as well as the training procedure and the evaluation metrics. Section 5, Results and Discussion, compares the performance outcomes of KAN vs. MLP models, KAN-Mixer vs. MLP-Mixer models, and KAN-convolution vs. convolution layers; finally, Section 6 concludes by presenting insights on the robustness of KAN-based models. Figure 2: Evolution of function basis and activation functions in Kolmogorov–Arnold Networks (KANs).