## 3 Public Data and Modeling Experiments
### Modeling Experiment Based on KAN-A  
First, experiments using KAN-A for training and modeling were conducted. Figure 1 illustrates three structural states of KAN-A and their evolutions during training. Guided by mathematical priors from KART, simple basis functions with uniform distributions are typically used during initialization. The initial structure has dense but redundant \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Category** & **Physical Variable** & **Symbol** & **Description** \\ \hline \hline \multirow{6}{*}{Input} & \multirow{3}{*}{Feed rate} & \multirow{3}{*}{fr} & Distance the tool travels per unit time along the machining direction, affecting machining efficiency and surface roughness. \\  & & & Vertical thickness of material penetrated by the tool in a single pass, determining material removal volume and directly correlating with cutting force. \\  & & & Linear velocity at the contact point between the tool edge and workpiece, characterizing friction and heat generation intensity during cutting. \\ \hline \hline \multirow{2}{*}{Target} & \multirow{2}{*}{Flink wear} & \multirow{2}{*}{fw} & Material loss on the tool flank due to friction with the workpiece, impacting machining precision and surface quality of parts. \\ \cline{1-1} \cline{4-4}  & & & \\ \end{tabular}
\end{table} 
Table 3: Key factors influencing flank wear of lathe tools. connections. The parameters remain unadopted to data distributions. It is analogous to an \"uncarved blank\". The post-training structure exhibits substantial differences from the initial structure: the waveform of the activation function (B-spline) adjusts its shape after one training cycle, becoming either more peaked or smoother depending on data characteristics and training parameters. Concurrently, these dynamic adjustments optimize the positions  
Figure 1: The network structure and evolution of KAN-A. **(a)** The input layer’s Speed(\(x_{3}\)) connects to 8 nodes in the hidden layer, while the output layer linearly aggregates signals. **(b)** The connections between the input layer’s \(x_{1}\) and \(x_{2}\) with the hidden layer are strengthened, while the \(x_{3}\) connections are weakened. The output layer aggregates signals through both linear and nonlinear pathways. **(c)** The irrelevant nodes in the hidden layer are pruned. The three input nodes nonlinearly connect to the remaining hidden layer nodes, and the output layer performs nonlinear signal aggregation. and coefficients of the B-spline control points. Some connection weights are significantly strengthened, while others approach zero. It is a data-driven feature selection process. Pruning endows KANs with a more compact topology by retaining task-sensitive B-spline functions and removing less relevant ones. The pruned structure, free of redundant nodes and edges, serves as the basis for symbolic computation of KANs. Notably, in the initial structure, the third input variable was connected to all nodes. The first two input variables had no connections. This was due to dimensional discrepancies between the variables. During initialization, the first two variables exhibited lower gradient magnitudes, leading to misjudgments of their importance. However, after training and pruning, their importance was significantly enhanced. It indicates that the KAN's initial structure does not necessarily reflect true feature significance. Instead, the training process involves learning the importance of input variables. Thus, it can be inferred that KANs have the ability to automatically select core features.