# NuCap: A Numerically Aware Captioning Framework for Improved Numerical Reasoning
## 4 Experiments
### Ablation Study  
**Model Components.** To assess the individual contribution of each proposed component, we conducted an ablation study by selectively removing SAGE, NFCE loss, and the structured caption format (Number | Caption) from the model. A detailed description of the evaluation metrics is provided in Section 4.5.1, and results are summarized in Table 1.  
Introducing NFCE loss alone yields a counting accuracy of 26.92%, demonstrating that emphasizing numerical tokens during training improves numerical focus. Applying only SAGE results in a slightly higher accuracy of 28.29%, validating the importance of spatially distributed visual features. Notably, using the structured caption format alone achieves the highest individual performance at 29.67%, suggesting that positioning the numeric token at the beginning of the caption imposes a strong inductive bias that encourages the model to prioritize count information during generation.  
This finding aligns with the autoregressive nature of the decoder: by generating the numeric token first, the model is naturally prompted to attend to quantity-relevant features before composing the rest of the caption. Combining the Structured Format with NFCE loss yields an accuracy of 28.29%, and with SAGE, 29.08%, both outperforming NFCE loss and SAGE in isolation. These results indicate that the Structured Format enhances the effectiveness of other components by reinforcing the model's early focus on numerical reasoning.  
The highest performance of 34.18% is achieved when all three components--SAGE, NFCE loss, and Structured Format--are integrated. This highlights the synergistic effect among the modules when used in combination. While SAGE improves spatial awareness and NFCE loss sharpens token-level sensitivity to numbers, the Structured Format directly influences the decoding pathway by steering the model to prioritize count information from the outset. Together, these elements significantly improve count-aware caption generation through the combination of structured input design and visually grounded learning.  
**Numeric Token Weight.** We also conducted an ablation study to examine the effect of the numeric token weight \(w_{n}\) used in NFCE loss. As shown in Table 2, increasing \(w_{n}\) leads to higher counting accuracy but slightly lowers the captioning quality (e.g., CIDEr). We found that \(w_{n}=1.6\) offers the best trade-off between numerical precision and overall fluency, and therefore adopted it as our default setting in all experiments.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**Factors**} & \multicolumn{1}{c}{**Accuracy (\%)**} \\ \hline
**SAGE** & **NFCE Loss** & **Number | Caption** & \\ \hline \(\chi\) & ✓ & \(\chi\) & 26.92 \\ ✓ & \(\chi\) & \(\chi\) & 28.29 \\ \(\chi\) & \(\chi\) & ✓ & 29.67 \\ \(\chi\) & ✓ & ✓ & 28.29 \\ ✓ & \(\chi\) & ✓ & 29.08 \\ ✓ & ✓ & ✓ & 34.18 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Ablation study on the impact of SAGE, NFCE loss, and structured caption format Number | Caption. Each row corresponds to a different model variant, where \(\checkmark\) indicates the inclusion of a component and \(\chi\) denotes its removal.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \(w_{n}\) & **BELU-4** & **CIDEr** & **Accuracy (\%)** \\ \hline
1.2 & 42.9 & 144.3 & 29.66 \\
1.6 & 42.0 & 143.5 & 34.18 \\
2.0 & 41.9 & 142.4 & 34.43 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Impact of numeric token weight (\(w_{n}\)) on captioning quality and counting accuracy.