This image displays a violin plot comparing the distribution of "Cross perplexity" across three different "Generator model" types. ### Chart Type The chart is a violin plot, which shows the probability density of the data at different values, smoothed by a kernel density estimator. Inside each violin, a box plot is embedded, indicating the median, interquartile range (IQR), and whiskers. ### Axis Labels and Titles * **Y-axis Title:** Cross perplexity * **Y-axis Scale:** Logarithmic (base 10) * **Y-axis Tick Markers:** * 10^0 (equivalent to 1) * 10^1 (equivalent to 10) * Intermediate dashed grid lines are present, indicating a continuous logarithmic scale between 1 and 10. * **X-axis Title:** Generator model * **X-axis Categories (Labels):** * REAP * M-SMoE * HC-SMoE ### Data Series and Trends There is no explicit legend, but each generator model category on the X-axis corresponds to a distinct violin plot with a unique color. 1. **REAP Generator Model** * **Color:** Dark blue (hex approximately #46698C). * **Visual Trend:** This violin plot is the narrowest, indicating a relatively concentrated distribution of "Cross perplexity" values. The density peaks around the median. * **Data Points (Approximate):** * **Median (white horizontal line):** Approximately 2.5. * **Interquartile Range (dark gray box):** From approximately 2.0 to 3.0. * **Whiskers (vertical dark gray line):** Extend from approximately 1.5 to 4.5. * **Overall Range (full violin extent):** From slightly above 1.0 to just below 6.0. 2. **M-SMoE Generator Model** * **Color:** Light blue (hex approximately #66B2D8). * **Visual Trend:** This violin plot is wider than REAP, particularly in the middle and upper-middle sections, suggesting a broader distribution of "Cross perplexity" values compared to REAP. * **Data Points (Approximate):** * **Median (white horizontal line):** Approximately 3.5. * **Interquartile Range (dark gray box):** From approximately 2.5 to 5.0. * **Whiskers (vertical dark gray line):** Extend from approximately 1.5 to 10.0. * **Overall Range (full violin extent):** From slightly below 1.0 to just above 10.0. 3. **HC-SMoE Generator Model** * **Color:** Olive green/khaki (hex approximately #B2A059). * **Visual Trend:** This violin plot is the widest of the three, especially in the upper half, indicating the broadest distribution and a higher density of "Cross perplexity" values at higher levels. It appears somewhat skewed towards higher values. * **Data Points (Approximate):** * **Median (white horizontal line):** Approximately 4.5. * **Interquartile Range (dark gray box):** From approximately 3.0 to 6.0. * **Whiskers (vertical dark gray line):** Extend from approximately 1.5 to 10.0. * **Overall Range (full violin extent):** From slightly below 1.0 to just above 10.0. ### Overall Observations and Trends * **Median Perplexity:** The median "Cross perplexity" generally increases across the models, from REAP (approx. 2.5) to M-SMoE (approx. 3.5) to HC-SMoE (approx. 4.5). * **Distribution Spread:** The spread of "Cross perplexity" values, as indicated by the width of the violin plots and the interquartile range, increases from REAP to M-SMoE to HC-SMoE. HC-SMoE exhibits the widest distribution and highest median perplexity. * **Range:** While all models show some perplexity values below 2.0, the M-SMoE and HC-SMoE models have distributions that extend to higher perplexity values (up to and slightly above 10.0) with greater density in the upper ranges compared to REAP.

# Technical Data Extraction: Cross Perplexity Violin Plot ## 1. General Description This image is a violin plot comparing the distribution of **Cross perplexity** across three different **Generator models**. The y-axis is presented on a logarithmic scale. Each violin includes an internal box plot showing the median, interquartile range (IQR), and whiskers. --- ## 2. Axis Information * **Y-Axis Label:** Cross perplexity * **Y-Axis Scale:** Logarithmic (Base 10) * **Major Markers:** $10^0$ (1), $10^1$ (10) * **Minor Gridlines:** Represented by dashed horizontal lines between $10^0$ and $10^1$. * **X-Axis Label:** Generator model * **X-Axis Categories:** 1. **REAP** (Dark Blue) 2. **M-SMoE** (Light Blue) 3. **HC-SMoE** (Olive/Gold) --- ## 3. Data Distribution Analysis ### Category 1: REAP (Dark Blue) * **Distribution Shape:** The most compact distribution of the three. The bulk of the density is concentrated between 2 and 4. * **Median:** Approximately 2.5. * **Range:** Extends from approximately 1.1 to 7.0. * **Interquartile Range (IQR):** Roughly between 2.0 and 3.5. ### Category 2: M-SMoE (Light Blue) * **Distribution Shape:** Wider and taller than REAP, indicating higher variance. The density is relatively uniform across the middle section. * **Median:** Approximately 3.2. * **Range:** Extends from approximately 0.6 to 11.0. * **Interquartile Range (IQR):** Roughly between 2.2 and 4.5. ### Category 3: HC-SMoE (Olive/Gold) * **Distribution Shape:** Shows the highest overall perplexity values. The density is concentrated higher up the y-axis compared to the other two models. * **Median:** Approximately 3.8. * **Range:** Extends from approximately 0.7 to 15.0 (the highest peak in the chart). * **Interquartile Range (IQR):** Roughly between 2.8 and 5.5. --- ## 4. Key Trends and Observations * **Performance Comparison:** The **REAP** model demonstrates the lowest median cross perplexity and the tightest distribution, suggesting more consistent and lower (better) perplexity scores. * **Complexity Trend:** There is a visible upward trend in perplexity from REAP to M-SMoE to HC-SMoE. * **Outliers/Extremes:** HC-SMoE has the highest maximum perplexity values, reaching well above $10^1$. M-SMoE and HC-SMoE both show longer "tails" toward the lower end (below $10^0$) compared to REAP.

## Box Plot: Cross-Perplexity ### Overview The image displays a box plot comparing the cross-perplexity of three different generator models: REAP, M-SMoE, and HC-SMoE. The plot is designed to show the distribution of cross-perplexity values for each model, with the median, quartiles, and potential outliers represented. ### Components/Axes - **Y-axis**: Cross-perplexity, measured on a logarithmic scale from 10^0 to 10^1. - **X-axis**: Generator model, labeled as REAP, M-SMoE, and HC-SMoE. - **Legend**: The legend is located at the bottom of the plot, indicating the color coding for each model. - **Box Plot**: Each box plot represents the distribution of cross-perplexity values for a specific model. The boxes show the interquartile range (IQR), the median (line inside the box), and the whiskers extend to the minimum and maximum values within 1.5 times the IQR. ### Detailed Analysis or ### Content Details - **REAP Model**: The box plot for REAP shows a relatively narrow distribution with a median around 10^0.5. The IQR is smaller, and the whiskers are shorter, indicating less variability and a more consistent performance. - **M-SMoE Model**: The box plot for M-SMoE has a slightly wider distribution compared to REAP, with a median around 10^0.7. The IQR is larger, and the whiskers are longer, suggesting more variability and potentially better performance. - **HC-SMoE Model**: The box plot for HC-SMoE is the widest, with a median around 10^0.9. The IQR is the largest, and the whiskers are the longest, indicating the highest variability and potentially the best performance among the three models. ### Key Observations - **REAP Model**: Shows the least variability and the most consistent performance. - **M-SMoE Model**: Shows moderate variability and potentially better performance than REAP. - **HC-SMoE Model**: Shows the highest variability and potentially the best performance. ### Interpretation The data suggests that the HC-SMoE model has the highest cross-perplexity, indicating it may be less efficient or less effective in generating data compared to REAP and M-SMoE. The REAP model has the lowest cross-perplexity, suggesting it is the most efficient. The M-SMoE model falls in between, showing a balance between efficiency and variability. The wide distribution of the HC-SMoE model indicates that it may be more prone to generating data with a wide range of complexity, which could be a trade-off for its performance.

# Technical Description of the Violin Plot ## Chart Overview The image is a violin plot comparing the distribution of "Cross perplexity" across three different "Generator model" categories. The plot combines a box plot with a kernel density estimation to show the distribution shape of the data. ## Axes and Labels * **Y-axis:** The vertical axis is labeled "Cross perplexity". It has a logarithmic scale with major tick marks at **10⁰** and **10¹**. Horizontal gridlines are present at these major ticks and at intermediate logarithmic intervals (e.g., 2, 3, 4, 5, 6, 7, 8, 9, 20, 30, etc., though not explicitly labeled). * **X-axis:** The horizontal axis is labeled "Generator model". It displays three categorical labels: **REAP**, **M-SMoE**, and **HC-SMoE**. ## Data Analysis by Category The plot shows three violin shapes, each corresponding to a generator model. Inside each violin is a box plot with a white dot representing the median, a thick bar representing the interquartile range (IQR), and thin lines (whiskers) extending to the rest of the distribution, excluding outliers. ### 1. REAP (Dark Blue Violin) * **Distribution Shape:** The distribution is relatively narrow and centered at a lower cross perplexity value compared to the other two models. * **Median:** The median cross perplexity is approximately **2**. * **Interquartile Range (IQR):** The IQR spans from roughly **1.5** to **3**. * **Range:** The whiskers extend from a minimum of about **1** to a maximum of about **6**. ### 2. M-SMoE (Light Blue Violin) * **Distribution Shape:** The distribution is wider than REAP and centered at a higher value. It shows a broader range of cross perplexity values. * **Median:** The median cross perplexity is approximately **3**. * **Interquartile Range (IQR):** The IQR spans from roughly **2** to **5**. * **Range:** The whiskers extend from a minimum of about **0.6** to a maximum of about **10**. ### 3. HC-SMoE (Gold/Yellow Violin) * **Distribution Shape:** The distribution is similar in width to M-SMoE but is centered at a slightly higher value. * **Median:** The median cross perplexity is approximately **3.5**. * **Interquartile Range (IQR):** The IQR spans from roughly **2.5** to **6**. * **Range:** The whiskers extend from a minimum of about **0.7** to a maximum of about **15**. ## Key Trends * **Median Cross Perplexity:** The median cross perplexity increases in the order: REAP < M-SMoE < HC-SMoE. * **Distribution Spread:** REAP has the narrowest distribution of cross perplexity values, indicating more consistent performance. M-SMoE and HC-SMoE have wider distributions, showing greater variability in their cross perplexity. * **Overall Range:** HC-SMoE has the highest maximum cross perplexity value, while M-SMoE has the lowest minimum value. REAP's range is the most contained.

# Technical Document Extraction: Cross Perplexity Analysis of Generator Models ## Figure Description This image presents a comparative analysis of **cross perplexity** across three generator models using violin plots. The data is visualized on a logarithmic scale (base 10) to emphasize distributional differences. --- ### **Key Components** 1. **Axes** - **Y-axis**: Labeled "Cross perplexity" with logarithmic scaling (10⁰ to 10¹). Dashed horizontal lines mark 10⁰ and 10¹. - **X-axis**: Categorizes generator models: - REAP (dark blue) - M-SMoE (teal) - HC-SMoE (olive) 2. **Violin Plot Structure** - **Shapes**: Each violin represents the probability density of cross perplexity values for a model. - **Width**: Indicates density of data points at specific perplexity levels. - **Tails**: Extend to show minimum/maximum values (e.g., HC-SMoE has the longest upper tail). - **Black Lines**: Represent the **interquartile range (IQR)**. - **White Lines**: Denote the **median** value within the IQR. --- ### **Key Trends and Data Points** 1. **Model Performance** - **HC-SMoE**: - Highest median perplexity (~10⁰.⁵). - Widest IQR (indicating greater variability in results). - Longest upper tail (outliers up to ~10¹). - **M-SMoE**: - Median ~10⁰.⁴. - Moderate IQR and tail spread. - **REAP**: - Lowest median (~10⁰.³). - Narrowest IQR (most consistent performance). - Shortest tails (least extreme values). 2. **Logarithmic Scale Implications** - Differences in medians and spreads are amplified due to the log scale. - HC-SMoE’s performance is notably worse than REAP by an order of magnitude in upper tail values. --- ### **Critical Observations** - **REAP** demonstrates the most stable and lowest perplexity, suggesting superior generalization. - **HC-SMoE** exhibits the highest variability and worst-case performance, despite potential advantages in other metrics. - **M-SMoE** balances performance and variability but underperforms REAP in median perplexity. --- ### **Technical Notes** - No explicit legend is present; model identities are inferred from x-axis labels and color coding. - All violins share identical axis scaling, enabling direct comparison. - The absence of numerical annotations on the violins limits precise quantification of IQR/median values. --- This visualization highlights trade-offs between model complexity (e.g., HC-SMoE’s higher capacity) and performance stability (REAP’s consistency). Further analysis could explore why HC-SMoE exhibits such variability despite its architectural sophistication.