# How Resilient Are Kolmogorov-Arnold Networks in Classification Tasks? A Robustness Investigation
## 1 Introduction  
The Kolmogorov-Arnold Networks (KANs), as introduced by [PERSON] et al. [1], have attracted considerable attention as innovative neural network architectures, presenting a promising substitutional to Multilayer Perceptrons (MLPs). These networks are grounded in the theorem of Kolmogorov-Arnold representation (KART), which asserts that any multivariate continuous function can be expressed as a sum of continuous univariate functions [2, 3]. KANs, much like MLPs, exhibit fully connected architectures. However, unlike MLPs, which utilize fixed activation functions on nodes, KANs employ adaptive and dynamically adjustable activation functions on edges. Consequently, KANs do not have linear weight matrices, as each weight parameter is substituted by a learnable 1D function represented as a spline. Despite this, KANs generally lead to much smaller computation graphs compared to MLPs [1]. KANs have demonstrated their adaptability across various domains, as illustrated in Figure 1. This figure showcases the development timeline of KANs, highlighting significantadvancements in natural language processing, time series analysis, and other areas. For instance, KAN-GPT [4] implements Generative Pre-trained Transformers (GPTs), while KAN-GPT2 [5] involves training small GPT-2 style models using KANs instead of MLPs. Additionally, kansformers [6] explore the integration of KANs in transformer architectures by replacing the linear layers of MLP with KAN and Word-Level Explainable for language modeling [7]. Moreover, KANs have been applied in tasks such as ordinary differential equations [8], physical modeling [9], mechanics problems [10], partial differential equations [11], Quantum Variational KANs (VQ-KANs) [12], time series analysis [13; 14; 15; 16; 17; 18], computer vision [19; 20; 21; 22; 23; 24], and graph learning [25; 26]. Various modifications have been made to enhance the capabilities of KANs through the replacement or combination of B-splines with other function bases to achieve more accurate solutions, as shown in Figure 2, starting with the Efficient-KAN [27] and Fast-KAN [28], which utilized Radial Basis Functions (RBFs) to enhance the speed of training. At the same time, the Chebyshev-KAN [29] introduced Chebyshev polynomials for nonlinear function approximation. The Wav-KAN [30] implemented wavelet transformations in the KAN architecture. The FasterKAN [31] combined FastKAN with Reflectional Switch Activation Functions (RSWAFs) to further benchmark the performance of KANs. The Gottlieb-KAN [32] explored the potential of polynomial basis functions, and the FourierKAN-GCF [33] leveraged Fourier transformations for efficient feature extraction in graph collaborative filtering. ReLU-KAN [34] simplified KANs by using only matrix addition, dot multiplication, and ReLU activation functions. In June 2024, fKAN [35] introduced trainable Jacobi basis functions, while BSRBF-KAN [36] combined B-splines and RBFs. Rational activation functions were explored with rKAN [37], and SineKAN [38] incorporated sinusoidal activation functions. Later advancements included UKAN [39], which eliminated the need for a bounded grid by introducing a coefficient generator model, and FC-KAN [40], which combined outputs from B-splines and Difference of Gaussians (DoGs) to improve accuracy. Despite their wide applicability, the robustness of KANs against adversarial attacks remains insufficiently explored to the best of our knowledge. This is crucial for real-world AI scenarios, and it ensures the security, safety, and robustness of learning algorithms, which become increasingly critical, particularly in safeguarding against accidents and malicious agents. Studies [41; 42] have revealed Deep Neural Network vulnerabilities that require further investigation and mitigation. [PERSON] et al. [41] discovered that introducing imperceptible perturbations to input samples could significantly impact the performance of a target classifier.