# A Hybrid Text Generation-Based Query Expansion Method for Open-Domain Question Answering
## 3 Experimental Results and Analysis
### Exploring the Optimal Number of Expansion Terms  
In this paper, we use three query expansion generators to generate various contextual information for initial query. However, there is yet to be a definitive answer regarding the optimal number of expansion terms for each context. The previous experiments have all assumed a default number of expansion terms to be 1. This section aims to explore the optimal number of expansion terms for various contexts. We conducted experiments with the number of expansion terms set to 1, 2, 3, 4, and 5, respectively.  
On NQ, as shown in Figure 2, we investigated the impact of different numbers of expansion terms on the Top-k retrieval accuracy. The four graphs in Figure 2 show a fairly consistent trend: for \(ctx(A)\), the performance is better when the number of expansion terms is 2 (orange line); for \(ctx(S)\), the performance is relatively better when the number of expansion terms is 1 (light blue line); for \(ctx(T)\), the performance is better when the number of expansion terms is 1 or 5(light blue line or blue line). Lastly, we combined the three individual retrieval results corresponding to the number of expansion terms to obtain a mixed effect. Overall, the optimal result can be achieved when the number of expansion terms is 5.  
\begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**NQ**} & \multicolumn{6}{c}{**Trivia**} \\ \cline{2-13}  & **Top-1** & **Top-5** & **Top-20** & **Top-100** & **Top-500** & **Top-1000** & **Top-1** & **Top-5** & **Top-20** & **Top-100** & **Top-500** & **Top-1000** \\ \hline \(ctx(AS)\) & **53.4** & 67.0 & 75.3 & 84.2 & 89.5 & 90.8 & **65.3** & **74.3** & **79.8** & **84.9** & **88.6** & 89.5 \\ \(ctx(AT)\) & 34.3 & 64.2 & 75.1 & 83.7 & 89.2 & 90.2 & 65.1 & 74.0 & 79.6 & 84.8 & 88.5 & 89.5 \\ \(ctx(ST)\) & 34.3 & 65.5 & 75.9 & **84.5** & 89.6 & 91.1 & **65.3** & 73.4 & 79.2 & 84.5 & 88.2 & 89.2 \\ \(ctx(AST)\) & **53.4** & **67.3** & **76.2** & **84.5** & **89.8** & **91.3** & **65.3** & 74.2 & 79.6 & **84.9** & **88.6** & **89.6** \\ \hline \hline \end{tabular}
\end{table}
Table 4: Discussion on hybrid strategies.  
Figure 2: Analysis of the number of expansion terms on NQ.  
As shown in Figure 3, we observed a fairly consistent trend on Trivia: for \(ctx(A)\), the performance is relatively good when the number of expansion terms is 2 or 5 (represented by the orange and blue line, respectively); for \(ctx(S)\), the performance is comparatively better when the number of expansion terms is 1 (indicated by the light blue line); for \(ctx(T)\), the optimal number of expansion terms is 1 or 5. Lastly, fusing the three individual retrieval results according to the corresponding expansion term quantities achieves the overall best performance when the number of expansion terms is 5. Although the influence of the expansion terms quantity on retrieval accuracy in \(ctx(S)\) query expansion is significant, this gap is greatly alleviated after combining the three contexts, further highlighting their complementarity.  
In summary, the best results can be achieved when the number of expansion terms is set to 5. However, the optimal performance is similar when the number of expansion terms is 1, 2, 3, or 4. Additionally, too many expansion terms can lead to an excessively long initial query, which may reduce the retrieval speed. Therefore, whether to choose a quantity of 1 or 5 for expansion terms depends on the specific application requirements. If the goal is to achieve higher accuracy, it is advisable to set the number of expansion terms to 5. On the other hand, if the focus is inference speed, opting for a single expansion term is a better choice.  
Figure 3: Analysis of the number of expansion terms on Trivia.