## Box Plot: Depthwise Average MIN-K% for Different Models ### Overview The image presents three box plots comparing the depthwise average MIN-K% for three different language models: LLaMA 2 13B Chat, Mistral 8B Instruct, and Mixtral 8x7B Instruct. Each box plot shows the distribution of MIN-K% values at three different depths (Depth 1, Depth 2, and Depth 3) within the model. ### Components/Axes * **Title:** Depthwise Average MIN-K% (repeated above each subplot) * **Y-axis:** Values range from 0 to 8, with tick marks at intervals of 2. * **X-axis:** Represents the depth within the model, with categories "Depth 1", "Depth 2", and "Depth 3". * **Box Plot Elements:** Each box plot displays the median (center line within the box), the interquartile range (IQR, represented by the box), the whiskers (lines extending from the box), and outliers (individual points beyond the whiskers). * **Subplot Titles:** * (a) LLaMA 2 13B Chat * (b) Mistral 8B Instruct * (c) Mixtral 8x7B Instruct ### Detailed Analysis **Subplot (a): LLaMA 2 13B Chat** * **Depth 1:** The box extends from approximately 3 to 4. The median is around 3.5. There are outliers above, reaching up to approximately 6.5. * **Depth 2:** The box extends from approximately 3.5 to 4.5. The median is around 4. There are no visible outliers below, but there are outliers above, reaching up to approximately 7. * **Depth 3:** The box extends from approximately 4.5 to 5.5. The median is around 5. There are outliers above, reaching up to approximately 8. **Subplot (b): Mistral 8B Instruct** * **Depth 1:** The box extends from approximately 3 to 4. The median is around 3.5. There are outliers above, reaching up to approximately 5.5. * **Depth 2:** The box extends from approximately 3.5 to 4. The median is around 3.8. There are no visible outliers below, but there are outliers above, reaching up to approximately 7.5. * **Depth 3:** The box extends from approximately 4 to 5. The median is around 4.5. There are outliers above, reaching up to approximately 6. **Subplot (c): Mixtral 8x7B Instruct** * **Depth 1:** The box extends from approximately 3 to 4. The median is around 3.5. There are outliers both above and below. * **Depth 2:** The box extends from approximately 3.8 to 4.5. The median is around 4. There are outliers above, reaching up to approximately 7.5. * **Depth 3:** The box extends from approximately 4 to 5. The median is around 4.5. There are outliers above, reaching up to approximately 8. ### Key Observations * Across all three models, the median MIN-K% tends to increase slightly from Depth 1 to Depth 3. * The range of MIN-K% values, as indicated by the box size, appears relatively consistent across the different depths for each model. * Outliers are present in all box plots, indicating some variability in MIN-K% values at each depth. * Mixtral 8x7B Instruct has more outliers at Depth 1 than the other models. ### Interpretation The box plots provide a visual comparison of the depthwise average MIN-K% for the three language models. The MIN-K% metric likely represents some measure of information or activity within the model at different depths. The general trend of increasing median MIN-K% from Depth 1 to Depth 3 suggests that, on average, this metric tends to increase as information propagates through the model layers. The presence of outliers indicates that there are specific instances where the MIN-K% deviates significantly from the average at each depth. The differences in the distribution of MIN-K% values between the models may reflect differences in their architectures, training data, or overall performance characteristics.

\n ## Box Plots: Depthwise Average MIN-K% for LLMs ### Overview The image presents three box plots, each representing the distribution of "Depthwise Average MIN-K%" for different Large Language Models (LLMs) across three depths (Depth 1, Depth 2, Depth 3). The LLMs being compared are: (a) LLaMA 2 13B Chat, (b) Mistral 8B Instruct, and (c) Mixtral 8x7B Instruct. Each box plot visualizes the median, quartiles, and outliers of the metric for each depth. ### Components/Axes * **Title:** "Depthwise Average MIN-K%" (appears above each plot) * **X-axis:** "Depth" with markers "Depth 1", "Depth 2", and "Depth 3". * **Y-axis:** Scale ranging from 0 to 8, with increments of 1. * **Box Plot Components:** Each box represents the interquartile range (IQR), with a line indicating the median. Whiskers extend to show the range of the data, and points beyond the whiskers represent outliers. * **Labels:** Below each plot, the corresponding LLM is labeled: (a) LLaMA 2 13B Chat, (b) Mistral 8B Instruct, (c) Mixtral 8x7B Instruct. ### Detailed Analysis or Content Details **Plot (a): LLaMA 2 13B Chat** * **Depth 1:** The box plot is centered around approximately 3.6. The IQR ranges from roughly 3.2 to 4.2. There are no visible outliers. * **Depth 2:** The box plot is centered around approximately 4.4. The IQR ranges from roughly 4.0 to 4.8. There are no visible outliers. * **Depth 3:** The box plot is centered around approximately 5.2. The IQR ranges from roughly 4.8 to 5.8. There is one outlier at approximately 7.2. **Plot (b): Mistral 8B Instruct** * **Depth 1:** The box plot is centered around approximately 3.5. The IQR ranges from roughly 3.1 to 4.0. There are no visible outliers. * **Depth 2:** The box plot is centered around approximately 4.3. The IQR ranges from roughly 3.9 to 4.7. There are no visible outliers. * **Depth 3:** The box plot is centered around approximately 5.1. The IQR ranges from roughly 4.7 to 5.6. There is one outlier at approximately 6.6. **Plot (c): Mixtral 8x7B Instruct** * **Depth 1:** The box plot is centered around approximately 3.7. The IQR ranges from roughly 3.3 to 4.3. There are no visible outliers. * **Depth 2:** The box plot is centered around approximately 4.5. The IQR ranges from roughly 4.1 to 4.9. There are no visible outliers. * **Depth 3:** The box plot is centered around approximately 5.3. The IQR ranges from roughly 4.9 to 5.9. There is one outlier at approximately 7.0. In all three plots, the median value increases as the depth increases. The spread of the data (as indicated by the IQR) also appears to increase with depth. ### Key Observations * The median "Depthwise Average MIN-K%" consistently increases with depth for all three LLMs. * The range of values (as indicated by the whiskers) also tends to increase with depth. * Outliers are present only at Depth 3 for all three models, suggesting that deeper processing may lead to more variable results. * Mixtral 8x7B Instruct generally exhibits slightly higher median values compared to LLaMA 2 13B Chat and Mistral 8B Instruct across all depths. ### Interpretation The data suggests that as the processing depth increases, the "Depthwise Average MIN-K%" metric also increases for all three LLMs. This metric likely represents some measure of performance or quality, and the increasing trend indicates that deeper processing leads to improvements in this aspect. The presence of outliers at Depth 3 suggests that while deeper processing generally improves performance, it can also introduce more variability or instability. The slight difference in median values between the models suggests that Mixtral 8x7B Instruct may be slightly more effective at leveraging deeper processing compared to the other two models. However, further analysis would be needed to determine the statistical significance of this difference. The box plots provide a concise visual summary of the distribution of this metric for each model and depth, allowing for easy comparison and identification of trends. The consistent trend across all models suggests a general principle about the relationship between processing depth and performance.

\n ## Box Plot Chart: Depthwise Average MIN-K% Across Three Language Models ### Overview The image displays three horizontally arranged box plots, each comparing the distribution of a metric called "Depthwise Average MIN-K%" across three different depths (Depth 1, Depth 2, Depth 3) for three distinct large language models. The overall title for each subplot is "Depthwise Average MIN-K%". The models are identified by captions below each plot. ### Components/Axes * **Chart Type:** Box-and-whisker plots (box plots). * **Y-Axis:** Common to all three plots. Label: "Depthwise Average MIN-K%". Scale: Linear, ranging from 0 to 8, with major tick marks at 0, 2, 4, 6, and 8. * **X-Axis:** For each subplot, categorical axis with three labels: "Depth 1", "Depth 2", "Depth 3". * **Legend/Color Coding:** Consistent across all plots. * Blue box: Depth 1 * Orange box: Depth 2 * Green box: Depth 3 * **Subplot Captions (Bottom):** * (a) LLaMA 2 13B Chat * (b) Mistral 8B Instruct * (c) Mixtral 8x7B Instruct ### Detailed Analysis **Plot (a) LLaMA 2 13B Chat:** * **Depth 1 (Blue):** Median ≈ 3.5. Interquartile Range (IQR) ≈ 3.0 to 4.0. Whiskers extend from ≈ 2.0 to ≈ 5.0. One outlier diamond at ≈ 6.5. * **Depth 2 (Orange):** Median ≈ 4.0. IQR ≈ 3.5 to 4.5. Whiskers extend from ≈ 2.5 to ≈ 6.0. One outlier diamond at ≈ 6.5. * **Depth 3 (Green):** Median ≈ 5.0. IQR ≈ 4.5 to 5.5. Whiskers extend from ≈ 3.0 to ≈ 6.5. One outlier diamond at ≈ 7.5. * **Trend:** The median MIN-K% value increases progressively from Depth 1 to Depth 3. The spread (IQR) also appears to increase slightly with depth. **Plot (b) Mistral 8B Instruct:** * **Depth 1 (Blue):** Median ≈ 3.5. IQR ≈ 3.0 to 4.0. Whiskers extend from ≈ 2.0 to ≈ 5.0. One outlier diamond at ≈ 5.5. * **Depth 2 (Orange):** Median ≈ 3.8. IQR ≈ 3.2 to 4.2. Whiskers extend from ≈ 2.2 to ≈ 5.2. One outlier diamond at ≈ 5.8. * **Depth 3 (Green):** Median ≈ 4.5. IQR ≈ 4.0 to 5.0. Whiskers extend from ≈ 2.5 to ≈ 6.0. One outlier diamond at ≈ 6.5. * **Trend:** Similar increasing trend in median from Depth 1 to Depth 3, though the increase between Depth 1 and Depth 2 is less pronounced than in plot (a). The overall values are slightly lower than those for LLaMA 2. **Plot (c) Mixtral 8x7B Instruct:** * **Depth 1 (Blue):** Median ≈ 3.5. IQR ≈ 3.0 to 4.0. Whiskers extend from ≈ 1.5 to ≈ 5.0. Multiple outlier diamonds below the lower whisker, clustered between ≈ 1.0 and ≈ 2.0. * **Depth 2 (Orange):** Median ≈ 4.0. IQR ≈ 3.5 to 4.5. Whiskers extend from ≈ 2.5 to ≈ 5.5. A significant cluster of outlier diamonds above the upper whisker, ranging from ≈ 6.0 to ≈ 7.5. * **Depth 3 (Green):** Median ≈ 4.5. IQR ≈ 4.0 to 5.0. Whiskers extend from ≈ 3.0 to ≈ 6.0. One outlier diamond at ≈ 2.5 (below) and one at ≈ 6.0 (above). * **Trend:** Median increases with depth. This model shows the highest variance, particularly at Depth 2, which has a large number of high-value outliers. Depth 1 also shows notable low-value outliers. ### Key Observations 1. **Consistent Depth Trend:** All three models exhibit a clear trend where the median "Depthwise Average MIN-K%" increases from Depth 1 to Depth 3. 2. **Model Comparison:** LLaMA 2 13B Chat (a) shows the highest median values at each corresponding depth, followed by Mixtral 8x7B Instruct (c), and then Mistral 8B Instruct (b). 3. **Variance and Outliers:** Mixtral 8x7B Instruct (c) displays the most significant variance and the most pronounced outlier behavior, especially the cluster of high outliers at Depth 2. LLaMA 2 and Mistral show fewer, more isolated outliers. 4. **Spread:** The interquartile range (box height) is relatively consistent across depths within each model, suggesting the central 50% of the data has a stable spread, even as the median shifts. ### Interpretation The "Depthwise Average MIN-K%" metric appears to measure some property of model activations or performance that improves (increases) with network depth. The consistent upward trend across all three models suggests this is a fundamental characteristic related to how information is processed or refined in deeper layers of these transformer-based language models. The differences between models are noteworthy. LLaMA 2's higher overall values might indicate a different internal scaling or a stronger effect at each depth. The high variance and outliers in Mixtral, a Mixture-of-Experts model, could reflect the specialized routing of tokens to different expert sub-networks, leading to more diverse activation patterns at certain depths (like Depth 2), which manifests as a wider spread and more extreme values in the metric. This analysis suggests that depth is a critical factor for the MIN-K% metric. The presence of outliers, particularly in the MoE model, indicates that while the general trend is upward, individual data points (likely corresponding to specific tokens or sequences) can behave very differently, highlighting the complexity and non-uniformity of internal model computations.

## Box Plot: Depthwise Average MIN-K% Across Model Depths ### Overview The image contains three side-by-side box plots comparing the depthwise average MIN-K% performance of three language models across three processing depths (Depth 1, Depth 2, Depth 3). Each subplot represents a different model architecture: (a) LLaMA 2 13B Chat, (b) Mistral 8B Instruct, and (c) Mixtral 8x7B Instruct. The y-axis measures MIN-K% (0-8 scale), while the x-axis categorizes data by processing depth. ### Components/Axes - **X-axis**: Depth (1, 2, 3) - Categorical scale - **Y-axis**: Depthwise Average MIN-K% (0-8) - Continuous scale - **Legend**: Located at bottom-right corner, mapping colors to models: - Blue: LLaMA 2 13B Chat - Orange: Mistral 8B Instruct - Green: Mixtral 8x7B Instruct - **Subplot Titles**: - (a) LLaMA 2 13B Chat - (b) Mistral 8B Instruct - (c) Mixtral 8x7B Instruct ### Detailed Analysis 1. **LLaMA 2 13B Chat (a)**: - Depth 1: Median ~3.5, range 2-5, 1 outlier at 6.5 - Depth 2: Median ~4.2, range 3-5, 1 outlier at 6.2 - Depth 3: Median ~5.0, range 3-6, 2 outliers at 6.8 and 7.2 2. **Mistral 8B Instruct (b)**: - Depth 1: Median ~3.8, range 2.5-5.2, 1 outlier at 5.8 - Depth 2: Median ~4.0, range 3-5.5, 1 outlier at 6.0 - Depth 3: Median ~4.5, range 3.5-6.2, 2 outliers at 6.5 and 7.0 3. **Mixtral 8x7B Instruct (c)**: - Depth 1: Median ~3.2, range 2-4.5, 2 outliers at 1.8 and 5.0 - Depth 2: Median ~4.0, range 3-5.0, 1 outlier at 6.0 - Depth 3: Median ~4.8, range 3.5-6.5, 3 outliers at 5.5, 6.2, and 7.5 ### Key Observations - **Depth Correlation**: All models show increasing median MIN-K% values with greater depth (Depth 1 < Depth 2 < Depth 3) - **Model Performance**: Mixtral 8x7B Instruct consistently shows highest median values across depths - **Outlier Patterns**: - LLaMA 2 has highest outlier values (up to 7.2) - Mixtral 8x7B has most frequent outliers (3 instances) - Mistral 8B shows moderate outlier distribution - **Variance**: Depth 3 shows greatest interquartile range for all models ### Interpretation The data suggests that deeper processing layers (Depth 3) generally yield better MIN-K% performance across all models, with Mixtral 8x7B Instruct demonstrating the strongest performance. The increasing median values with depth indicate potential architectural advantages in deeper processing layers. Outlier patterns suggest possible anomalies in specific configurations - notably LLaMA 2's high outliers might indicate exceptional cases in its processing pipeline. The consistent color coding (blue/orange/green) across subplots allows direct model comparison, with Mixtral's green boxes showing both highest medians and most variability. The 0.5-1.0 MIN-K% increase from Depth 1 to 3 across models suggests systematic improvements in deeper processing stages.