## 5 Experimental Framework and Results
### Comparative Analysis of RAG and CARAG Approaches
By leveraging KDE-based density contours, CARAG explanations demonstrate tighter clustering within the intended thematic regions, underscoring its potential for theme-specific retrieval. This makes CARAG particularly suitable for tasks where contextual alignment is crucial, such as verifying claims in COVID-related topics, where thematic relevance enhances accuracy. The individual theme plots further illustrate this difference, showing that CARAG explanations are more concentrated within thematic contours, demonstrating enhanced thematic relevance compared to RAG. Figure 8: PCA (**left**) and t-SNE (**right**) visualizations of embedding distributions for RAG-generated explanations (red circles) and CARAG-generated explanations (green diamonds), shown with KDE-based thematic density contours in the background (green for COVID, blue for climate, and purple for electric vehicles). These contours illustrate thematic boundaries, enabling a comparative evaluation. Figure 9: PCA (**left**) and t-SNE (**right**) visualizations of embedding distributions for RAG-generated explanations (red circles) and CARAG-generated explanations (green diamonds) for claims related to COVID, climate, and electric vehicles, shown in (**a–c**), respectively. Each panel includes KDE-based thematic density contours in the background (green for COVID, blue for climate, and purple for electric vehicles), highlighting each approach’s alignment with underlying thematic regions. The quantitative results in Table 4 corroborate the visual patterns observed in Figure 9, providing statistical evidence of CARAG's superior alignment with thematic regions. These results are based on Euclidean distances between the embeddings of RAG and CARAG explanations and the thematic centroids in PCA and t-SNE spaces. As shown in Table 4, for each theme, CARAG demonstrates consistently lower average distances to thematic centroids compared to RAG, particularly in t-SNE space, where the differences are more pronounced. Specifically, the differences (Diff(PCA) and Diff(t-SNE)) are calculated as _Diff (PCA or t-SNE) \(=\) CARAG Distance \(-\) RAG Distance_. Negative values in the difference columns indicate CARAG's superior alignment (shorter distance to the center compared to RAG), highlighting its tighter clustering within thematic regions, and are color-coded in green. Positive values, color-coded in red, represent the rare instance where RAG outperformed CARAG, such as the Diff (PCA) for climate. In contrast, likely due to its non-linear dimensionality-reduction approach compared to PCA's linear reduction (an investigation into this aspect is planned for future work), t-SNE consistently highlights CARAG's tighter alignment. This numerical validation underscores CARAG's ability to maintain thematic specificity, with smaller distance variations highlighting its tighter clustering within the intended thematic regions. The inclusion of overall averages (calculated as averages of per-theme averages) in Table 5 provides a holistic view of CARAG's thematic alignment advantage, further demonstrating its ability to produce explanations that are more closely aligned with thematic contours compared to RAG. In summary, RAG offers broad-spectrum context suitable for general claims, while CARAG excels in generating thematically aligned, contextually precise explanations. This distinction highlights CARAG's potential for theme-specific fact-verification tasks, making it particularly effective in domains requiring context alignment, as demonstrated by its stronger alignment within each theme.