## 3 Process
### GPT-4 off Knowledge Distillation  
In this study, we propose GPT-4 off, a lightweight prediction model that employs knowledge distillation (KD) from GPT-4o to estimate traversability probability in off-road environments. In this process, GPT-4o serves as a teacher model, generating diverse traversability-related data transferred to a lightweight student model. A key aspect is creating a reliable ground truth (GT) based on accurate traversability information from GPT-4o. This innovative approach aims to enhance the efficiency of GPT-4o applications. This KD method reduces the cost and time required for manual annotation while decreasing RAM usage and power consumption, thus enhancing the practicality, real-time performance, and stability of autonomous driving systems. Given the complexities of predicting traversability probabilities, our framework employs both multi-class classification and regression tasks. Various factors influence traversability probability in off-road environments, such as irregular terrain, diverse obstacles, dynamic weather conditions, and the state of the ground (e.g., mud, sand, and gravel). Additionally, natural obstacles (such as water puddles and steep slopes), vegetation density, sunlight, and visibility play crucial roles in these predictions. The proposed framework can be expressed as Algorithm 1. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Violin \#** & **OVL** & **KS Stat** & _p-Value_ \\ \hline
1 and 2 & 0.8576 & 0.0500 & 1.0000 \\
1 and 3 & 0.8543 & 0.0500 & 1.0000 \\
2 and 3 & 0.8287 & 0.0500 & 1.0000 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Assessment of the prompt robustness test shown in Figure 1.  
```
1:Input: Dataset \(D_{input}=\{x_{1},x_{2},\ldots,x_{n}\}\)
2:Result: Trained lightweight model \(\theta_{light}\)
3:Initialize GPT-4o model
4:Initialize empty dataset \(D_{generated}\leftarrow\{\}\)
5:for each input \(x_{i}\) in \(D_{input}\)do
6: Prompt GPT-4o with \(x_{i}\)
7: Receive output \(y_{i}\gets GPT-4o(x_{i})\)
8: Store tuple \((x_{i},y_{i})\) in \(D_{generated}\)
9:endfor
10: Define lightweight model \(\theta_{light}\)
11: Define loss function \(\mathcal{L}\) and optimizer \(O\)
12:while\(\theta_{light}\) not converged do
13:for each \((x_{i},y_{i})\) in \(D_{generated}\)do
14:\(y_{pred}\leftarrow\theta_{light}(x_{i})\)
15: Compute loss \(\mathcal{L}(y_{pred},y_{i})\)
16: Update \(\theta_{light}\) with \(O\)
17:endfor
18:endwhile
19:return Trained lightweight model \(\theta_{light}\)
```  
**Algorithm 1** GPT-4 off  
**Multi-class classification** categorizes traversability probability based on various factors in off-road environments, such as terrain conditions, obstacle location, and obstacle size. For instance, when predicting traversable probability for ground types such as \"mud\", \"sand\", and \"gravel\", each label is crucial for assessing a vehicle's ability to navigate obstacles. This method reflects the complexity of the driving environment, which cannot be captured by single-label prediction. By synthesizing multiple factors into distinct categories, multi-class classification allows precise definitions of driving conditions. This approach provides clear distinctions between categories, making it suitable for consistent interpretation of traversable probabilities. The experimental details for multi-class classification utilized ImageNet1K pre-trained weights. The models were trained for 20 epochs with a learning rate of \(1~{}\times~{}10^{-5}\) and a batch size of 64. The input image \(x_{i}\in R^{H\times W\times C}\) was trained using the Adam optimizer and cross-entropy loss. \[L_{\text{CE}}(y,y^{\text{GT}})=-\sum_{k=1}^{K}y_{k}\log(y_{k}^{\text{GT}}) \tag{1}\]  
Data augmentation techniques such as padding, random cropping, and color jitter were applied. The dataset was divided into 80% training data (5948 images) and 20% test data (1488 images). For evaluation, we used accuracy, precision, recall, and F1-score, along with some newly proposed metrics, Macro-Prec10, Macro-Recall10, and Macro-F110.