## Heatmap: Mean Passage Rate ### Overview The heatmap illustrates the mean passage rate of different models as the mean number of tokens generated increases. The models are represented by different colors and symbols, and the rate is measured on the y-axis. ### Components/Axes - **X-axis**: Mean number of tokens generated, ranging from 0 to 10,000. - **Y-axis**: Mean passage rate, ranging from 0.0 to 1.0. - **Legend**: - **Orange circles**: \( n_p = 1 \) - **Yellow triangles**: \( n_p = 2 \) - **Green squares**: \( n_p = 5 \) - **Blue diamonds**: \( n_p = 10 \) - **Purple stars**: \( n_p = 25 \) - **Data points**: Each point represents the mean passage rate for a specific combination of \( n_p \) and \( n_{fr} \). ### Detailed Analysis or ### Content Details - The orange circles ( \( n_p = 1 \)) show the lowest mean passage rate, ranging from approximately 0.1 to 0.2. - The yellow triangles ( \( n_p = 2 \)) have a slightly higher rate, between 0.2 and 0.3. - The green squares ( \( n_p = 5 \)) exhibit a moderate rate, between 0.3 and 0.4. - The blue diamonds ( \( n_p = 10 \)) have the highest mean passage rate, between 0.4 and 0.5. - The purple stars ( \( n_p = 25 \)) show the highest rate, between 0.5 and 0.6. ### Key Observations - The mean passage rate increases with the mean number of tokens generated for all models. - The rate increases more steeply for models with higher \( n_p \) values. - There is a noticeable difference in the rate between models with different \( n_p \) values, with higher \( n_p \) values generally showing higher rates. ### Interpretation The data suggests that as the mean number of tokens generated increases, the mean passage rate also increases. This trend is consistent across all models. The rate increases more steeply for models with higher \( n_p \) values, indicating that models with more parameters may generate more coherent and relevant passages. The significant difference in rate between models with different \( n_p \) values highlights the importance of model architecture in determining the quality of generated passages.