## 1 Introduction
[21] proposed the Kolmogorov-Arnold-Informed Neural Network (KINN) as an alternative to Multi-Layer Perceptrons (MLPs) for solving partial differential equations (PDEs). Similarly, [PERSON] and [PERSON] [22] introduced physics-informed KANs (PIKANs) tailored for power system applications. Additionally, KANs have demonstrated promising results in time-series forecasting. [PERSON] [23] developed a model known as the C-KAN, which integrates convolutional layers with the KAN architecture to improve multi-step forecasting accuracy. In image processing, KANs have also garnered attention. [PERSON] et al. [24] explored KAN-based networks for hyperspectral image classification. [PERSON] et al. [25] presented the KansNet for detecting pulmonary nodules in CT images. For load forecasting, [PERSON] and [PERSON] [26] developed the Kolmogorov-Arnold Recurrent Network (KARN), which integrates KANs with a recurrent neural network (RNN) to improve the modeling of nonlinear relationships in load data. This approach surpasses traditional RNNs in accuracy. For fault diagnosis, [PERSON] et al. [27] introduced the MCR-KAResNet-TLDAF method, which combines image fusion techniques with KANs to enhance the extraction and recognition of bearing fault features. Likewise, [PERSON] et al. [28] proposed a KAN-based approach, KAN\({}_{\text{Diag}}\), for fault diagnosis in power transformers using dissolved gas analysis. [PERSON] et al. [29] established a method for predicting the pressure and flow rate of flexible electrohydrodynamic pumps using KANs, replacing fixed activation functions with learnable spline-based functions. In structural analysis, KANs have proven to be a valuable tool. [PERSON] et al. [30] demonstrated KANs' capability to accurately predict the Poisson's ratio of a hexagonal lattice elastic network, showing how this ratio transitions with changes in geometric configuration. In environmental science, [PERSON] et al. [31] evaluated KANs' performance in predicting chlorophyll-a concentrations in lakes, confirming their robustness in handling nonlinearity and long-term dependencies. In quantum computing applications, [PERSON] et al. [32] demonstrated that KANs significantly outperformed MLP-based approaches, achieving higher success probabilities in quantum state preparation. In finance, [PERSON] et al. [33] investigated KAN integration within Finance-Informed Neural Networks (FINNs) to improve financial modeling and regulatory decision-making. For magnetic positioning systems, [PERSON] and [PERSON] [34] developed a KAN-based algorithm, incorporating learnable activation functions through spline functions. Multiple spline curves and strategic thresholds were used to enhance accuracy. Despite the importance of tool wear in manufacturing processes, research on KANs in this field remains limited. Only two studies had been published by the completion of this work. [PERSON] et al. [35] proposed a novel approach utilizing KANs to map sensor features to real-time maximum flank wear (VBmax), with a Transformer model predicting future wear sequences. [PERSON] et al. [36] employed KANs to predict tool life in gear production from carburizing alloy steels, demonstrating accurate predictions based on cutting speed, coating thickness, and feed rate. The unique advantages of KANs for tool wear modeling include the following: (1) a mathematical foundation that enables rigorous error bound analysis, ensuring prediction reliability for safety-critical manufacturing operations; (2) an adaptive basis function selection mechanism that reduces model complexity compared to conventional neural networks, facilitating deployment on resource-constrained edge devices; and (3) interpretable mathematical expressions generated by KANs that provide actionable insights for process optimization. This study proposes three KAN-based models to address tool wear modeling in CNC turning processes. First, KAN-A, KAN-B, and KAN-C models with progressively increasing complexity are developed, accompanied by detailed training protocols and parameter specifications.