## 3 Process
### GPT-4 off Knowledge Distillation
Similar to the threshold-setting approach used in AP50 by [PERSON] et al. [49], allowing a margin of error provides a more flexible evaluation of the model's performance in recognizing patterns rather than exact values. Specifically, we define a true positive (TP\({}_{c}^{10}\)) for class \(c\) when the predicted value falls within 10% of the ground truth:  
\[\text{TP}_{c}^{10}=\sum_{i}\mathbb{I}\Big{(}y_{i}^{\text{GT}}=c\wedge y_{i}^{ \text{GT}}-y_{i}\leq 0.1\Big{)} \tag{2}\]  
where \(\mathbb{I}(\cdot)\) is an indicator function that returns 1 if the condition inside holds and 0 otherwise. Similarly, we define false positives and false negatives for class \(c\) as follows:  
\[\text{FP}_{c}^{10}=\sum_{i}\mathbb{I}\Big{(}\hat{y}_{i}=c\wedge\hat{y}_{i}-y_{i }^{\text{GT}}>1\Big{)} \tag{3}\]  
\[\text{FN}_{c}^{10}=\sum_{i}\mathbb{I}\Big{(}y_{i}^{\text{GT}}=c\wedge\hat{y}_{i }-y_{i}^{\text{GT}}>1\Big{)} \tag{4}\]  
Based on these values, we compute the per-class precision, recall, and F1-score:  
\[\text{Precision}_{c}^{10}=\frac{TP_{c}^{10}}{TP_{c}^{10}+FP_{c}^{10}} \tag{5}\]  
\[\text{Recall}_{c}^{10}=\frac{TP_{c}^{10}}{TP_{c}^{10}+FN_{c}^{10}} \tag{6}\]  
\[\text{F1}_{c}^{10}=\frac{2\times\text{Precision}_{c}^{10}\times\text{Recall}_ {c}^{10}}{\text{Precision}_{c}^{10}+\text{Recall}_{c}^{10}} \tag{7}\]  
Finally, we compute the macro-averaged metrics as follows:  
\[\text{Macro-Prec}^{10}=\frac{1}{N}\sum_{c=1}^{N}\text{Precision}_{c}^{10} \tag{8}\]  
Figure 1.0  
Figure 1.1  
where \(N\) represents the total number of classes. **Regression** predicts traversability probability as continuous values, capturing fine-grained differences based on environmental changes. Off-road environments exhibit continuous variability in traversability probability owing to factors such as terrain characteristics and obstacles. These environments often lack clear boundaries and are composed of irregular elements. For example, dense grass and overhanging branches can obscure the ground, leading to inaccurate predictions. Additionally, the depth assessment of water puddles may result in variability in the estimated traversability probability. The experimental details for regression were the same as those of multi-class classification, except for loss. In the regression task, the mean squared error (MSE) loss, which calculates the average of the squared differences between the predicted and actual values, penalizes larger errors more severely. This makes MSE well suited for optimizing models in continuous-value prediction tasks. Figure 1.2  
**The results** in Table 2 show the performance of different models in multi-class classification. The prefix'm' in mPrecision [10], mRecall [10], and mF1 [10] stands for \"Macro\". For ResNet-based models, we noticed that using a larger backbone generally led to better performance in terms of Acc [10] and other metrics. However, even though ResNet-101 had the highest Acc [10] among the ResNet models, its overall accuracy was actually the lowest. This suggests that, due to the small dataset size, ResNet-101 had trouble fully learning the patterns, which resulted in a drop in accuracy. A similar pattern was observed with ViT models. ViT-S/16 performed better than ViT-B/16 in multiple metrics, including accuracy and mF10. This suggests that, with limited data, the smaller ViT-S/16 model was able to generalize better, while the larger ViT-B/16 model may have been more prone to overfitting. This reinforces the idea that Transformer-based models effectively capture the global context of images, but their performance still depends on the quantity of data available. For a more detailed analysis of model tuning results, please refer to Appendix C.  
Table 3 shows the regression results. In general, as the backbone performance improved, the model's MSE loss decreased. However, unlike multi-class classification, convolution-based and Transformer-based algorithms showed similar results, suggesting that knowledge distilled through regression has limitations compared to multi-class classification.