## 5 Experimental Framework and Results
### Comparative Analysis of RAG and CARAG Approaches  
To evaluate CARAG's effectiveness in contrast to RAG, we focused on three critical aspects, contextual alignment, thematic relevance, and coverage, as key indicators of both local and global coherence. For this purpose, we conducted a comparative analysis across the three themes (COVID, climate, and electric vehicles) in _FactVer_. For each theme, we generated post-hoc explanations for 10 claims using annotated evidence and both the RAG and CARAG approaches with adjustments to \(\alpha\) in Equation (2), as demonstrated in the case study. This resulted in a total of 30 explanations per approach, organized in a CSV file for structured analysis, totaling 90 explanations across all themes. Our approach assesses the thematic alignment, coherence, and robustness of CARAG-generated explanations, using metrics such as density contours generated through kernel density estimation (KDE) for each theme and alignment comparison to that of RAG. These metrics are visualized through scatter plots and density contours to reveal the thematic depth and distribution of explanations produced by both RAG and CARAG. To facilitate an intuitive comparison of thematic clustering, we projected the embeddings of generated explanations into a 2D space using both PCA and t-SNE. The KDE-based density contours provide smooth, continuous representations of the thematic regions for each topic. Figure 8 presents an overview of all 30 explanations, with each point representing a RAG (red circles) or CARAG (green diamonds) generated explanation, plotted over density contours that illustrate thematic boundaries. These contours are color-coded by theme: green for COVID, blue for climate, and purple for electric vehicles. This visualization provides a holistic view of how explanations from RAG and CARAG distribute across thematic contexts, with PCA (left) and t-SNE (right) visualizations. PCA reduces high-dimensional data to 2D while retaining the maximum variance, allowing us to observe broad distribution patterns, clusters, and outliers. This projection shows that RAG captures a generalized, global view, evident in its broader spread, but may lack theme-specific focus. t-SNE, conversely, better highlights local relationships and reveals tighter clusters around thematic boundaries, enhancing the interpretability of context-specific alignment. This view reveals that CARAG's explanations are more centrally aligned within each thematic area, suggesting a stronger focus on theme-specific context, while RAG explanations appear more peripheral, reflecting a broader, less targeted alignment. To provide more granular insights into each theme, we present separate plots for each theme in Figure 9, showing the 10 explanation examples generated for each category, with contours for all themes included in each plot. This approach allows us to more clearly observe CARAG's ability to generate explanations that align with their corresponding thematic contours in the KDE representation. For example, in the COVID theme plot (Panel (a) in Figure 9), CARAG explanations cluster tightly within the green contour, indicating strong thematic alignment. Similarly, in the climate (Panel (b)) and electric vehicles (Panel (c)) plots, CARAG explanations are concentrated within the blue and purple contours, respectively, underscoring CARAG's capacity for contextually relevant retrieval. While some RAG points do align within their respective theme contours, the majority are positioned along the periphery, suggesting a more generalized retrieval approach rather than theme-specific targeting. This difference highlights CARAG's superior ability to produce explanations with closer thematic alignment, enhancing context-specific relevance. RAG's distribution reveals a tendency to capture generalized information across themes, which aligns with its retrieval-augmented nature but may dilute thematic specificity. Conversely, CARAG's thematic retrieval is more focused, producing explanations that closely align with each theme's contours.